Skip to main content
Log in

The Conservativity of Many: Split Scope and Most

  • Published:
Topoi Aims and scope Submit manuscript


Besides their cardinal and proportional readings, many and few have been argued to allow for a ‘reverse’ proportional reading that defies the conservativity universal (Westerståhl in Ling Philos 8:387−413, 1985). Recently, an analysis has been developed that derives the correct truth conditions for this reading while preserving conservativity (Romero, in Proceedings of the 20th Amsterdam Colloquium, ILLC, Amsterdam, 2015; Romero, On the reverse proportional reading of many, 2016a, submitted). The present paper investigates two predictions of this analysis, based on two key ingredients. First, many is decomposed into a determiner stem many and the degree operator POS. This predicts that other elements may scopally intervene between the two parts. Second, non-reverse and reverse readings arise from the versatile association possibilities of POS, as independently witnessed in the grammar. In languages in which the same versatile association profile is granted to the superlative degree operator -est, reverse readings are expected to arise for most as well. Both predictions are borne out.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. For discussion, see Partee (1989) for arguments that many and few are extensional and Fernando and Kamp (1996) for an analysis that assigns them an intensional component.

  2. As the reader will see, labeling the reading at issue as ‘reverse’ makes sense under Westerståhl’s (1985) and Herburger’s (1997) characterization of it, but it is somewhat misleading in more recent approaches to it, such as Cohen (2001) and Romero (2015, 2016a). We will use this label in a purely referential way.

  3. We leave open what mathematical notions (e.g., mean, standard deviation) are included in \(\theta.\) See Solt (2009) for a proposal for cardinal many and Schöller and Franke (2015) for experimental evidence on some mathematical aspects of threshold computation.

  4. (23b) is a simplification. If n-many alternatives to P end up yielding the same proportion, this proportion should be taken into account n-many times, not just once. See Romero (2016a).

  5. For simplicity, we treat degree operators extensionally. The intensional version of -est is (i):

    1. (i)

      \(\left[\kern-0.15em\left[ { - est} \right]\kern-0.15em\right] = \lambda \varvec{Q}_{{ <<s,dt>,t> }} \cdot\lambda P_{{ < s,dt> }}:~ P \in \varvec{Q} \cdot\lambda w \cdot \forall Q \in \varvec{Q}\left[ {Q~ \ne P \to Q(w) \subset P(w)} \right]\)

  6. The function L used in the compositional analysis of POS corresponds to the function \(\theta\) that we used as a place holder for the final truth conditions of many in (23).

  7. The parametrized determiner few will be further decomposed into little+many in Sect. 6 (Heim 2006). For the purposes of the present section, the simpler decomposition suffices.

  8. All the readings of many examined in the current and in the following section arise from relative LFs where POS moves out to the host NP to gain sentential scope. For the possibility of leaving POS inside the host NP, see Penka (2016).

  9. Other complex forms that allow for similar scope variation are, for example, adjectival stems accompanied with a measure phrase, e.g., at least/most 10 pages long, where the measure phrase sometimes scopes over and sometimes under the intensional verb. See, among others, de Swart (2000), Abels and Martí (2010) and Penka (2017).

  10. Hackl (2009) uses an adjectival version of cardinal many instead of (49).

  11. The contrast in (i) and (ii) adds an interesting nuance to this conclusion. While (i) allows for the reverse reading roughly paraphrased in (iii), (ii) does not. Lauer and Nadathur (2016) attribute this difference to the syntactic status of the clause containing -est’s associate. Both the if-clause in (i) and the relative clause in (ii) end up functioning semantically as part of the restrictor of most. But, crucially, the if-clause is syntactically not part of the host NP whereas the relative clause is syntactically part of it. Hence, English -est does not allow for a syntactically host-internal associate, though it seems to allow for a syntactically host-external associate whose semantic contribution ends up being host-internal.

    1. (i)

      Most kids asked for calculators if they had to do long divisions.

    2. (ii)

      Most kids who had to do long divisions asked for calculators.

    3. (iii)

      ‘The majority of kids who asked for calculators where ones that had to do long divisions.’

  12. The Bulgarian and Polish version of Westerståhl’s (1985) sentence (9) with POS has a reverse proportional reading.


  • Abels K, Martí L (2010) A unified approach to split scope. Nat Lang Semant 18:435–470

    Article  Google Scholar 

  • Barwise J, Cooper R (1981) Generalized quantifiers and natural language. Linguist Philos 5:159–219

    Article  Google Scholar 

  • Büring D (1996) A weak theory of strong readings. In: Galloway T, Justin S (eds) Proceedings of salt, vol 6. Cornell University, Ithaca, pp 17–34

    Google Scholar 

  • Cohen A (2001) Relative readings of many, often and generics. Nat Lang Semant 69:41–67

    Article  Google Scholar 

  • de Swart H (2000) Scope ambiguities with negative quantifiers. In: von Heusinger K, Egli U (eds) Reference and anaphoric relations. Kluwer, Dordrecht, pp 109–132

    Chapter  Google Scholar 

  • Fernando T, Kamp H (1996) Expecting many. In: Galloway T, Spence J (eds) Proceedings of salt, vol 6. Cornell University, Ithaca, pp 53–68

    Google Scholar 

  • Hackl M (2009) On the grammar and processing of proportional quantifiers: most versus more than half. Nat Lang Semant 17:63–98

    Article  Google Scholar 

  • Heim I (1999) Notes on Superlatives. MIT lecture notes

  • Heim I (2001) Degree operators and scope. In: Féry C, Sternefeld W (eds) Audiatur vox sapientia:a festschrift for arnim von stechow. Akademie Verlag, Berlin, pp 214–239

    Google Scholar 

  • Heim I (2006) Little. In: Gibson M, Howell J (eds) Proceedings of salt, vol 16. Cornell University, Ithaca, pp 35–58

    Google Scholar 

  • Herburger E (1997) Focus and weak noun phrases. Nat Lang Semant 5:53–78

    Article  Google Scholar 

  • Keenan EdL, Stavi J (1986) A semantic characterization of natural language determiners. Ling Philos 9:253–326

    Article  Google Scholar 

  • Kennedy C (1999) Projecting the adjective: the syntax and semantics of gradability and comparison. Garland, New York

    Google Scholar 

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

    Google Scholar 

  • Lauer S, Prerna N (2016) Quantified indicative conditionals and the relative reading of most. Talk at Sinn und Bedeutung, vol 21. Stanford University, Stanford

    Google Scholar 

  • Mostowski A (1957) On a generalization of quantifiers. Fundam Math 44(2):12–36

    Article  Google Scholar 

  • Pancheva R, Tomaszewicz B (2012) Cross-linguistic differences in superlative movement out of nominal phrases. In: Arnett N, Bennett R (eds) Proceedings of the 30th west coast conference in formal linguistics. Cascadilla, Sommerville, pp 292–302

    Google Scholar 

  • Partee BH (1989) Many quantifiers. In: Powers J, de Jong K (eds) Proceedings of the fifth eastern states conference on linguistics. The Ohio State University, Columbus, pp 383–402

    Google Scholar 

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

    Google Scholar 

  • Penka D (2016) One many, many readings. Talk at Sinn und Bedeutung, vol 21. University of Edinburgh, Edinburgh

    Google Scholar 

  • Penka D (2017) Splitting ’at most’. In: Remberger KHEM, Cruschina S (eds) Negation: syntax, semantics and variation. Vienna University Press, Vienna, pp 185–212

    Google Scholar 

  • Romero M (2015) The conservativity of many. In Proceedings of the 20th Amsterdam Colloquium, ILLC, Amsterdam, pp 20–29

  • Romero M (2016a) On the reverse proportional reading of many (submitted)

  • Romero M (2016b) POS, -est and reverse readings of many and most. In: Hammerly C, Prickettto B (eds) Proceedings of the 46th annual meeting of the North East Linguistic Society, vol 3. GLSA, Amherst, pp 141–154

    Google Scholar 

  • Rooth M (1992) A theory of focus interpretation. Nat Lang Semant 1:75–116

    Article  Google Scholar 

  • Schöller A, Michael F (2015) Semantic vales as latent parameters: surprising few and many. Talk at SALT. University of Tübingen, Tübingen

    Google Scholar 

  • Schwarz B (2010) A note on for-phrases and derived scales. Handout for talk at Sinn und Bedeutung, vol 15. University of Edinburg, Edinburg

    Google Scholar 

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

  • Szabolcsi A (1986) Comparative superlatives. In: Fukui N, Rapoport T, Sagey E (eds) Papers in theoretical linguistics. MITWPL, Cambridge, pp 245–265

    Google Scholar 

  • Tomaszewicz B (2013) Focus association in superlatives and the semantics of -est. In: Franke M, Aloni M, Roelofsen F (eds) Proceedings of the 19th amsterdam colloquium. ILLC, Amsterdam, pp 226–233

    Google Scholar 

  • van der Does J, van Eijck J (1996) Quantifiers, logic, and language. CSLI Publications, Stanford

    Google Scholar 

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

    Google Scholar 

  • Westerståhl D (1985) Logical constants in quantifier languages. Ling Philos 8:387–413

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Maribel Romero.

Ethics declarations

Conflict of interest

The author, Maribel Romero, declares that she has no conflict of interests. The research reported in this paper was not carried under any research grant.

Ethical Approval

This paper does not contain any studies with human participants or animals performed by the author.

Additional information

I am indebted to Lucas Champollion, Irene Heim, Doris Penka, Bernhard Schwarz and two anonymous reviewers for their helpful questions and insights. Special thanks to Roumyana Pancheva and Barbara Tomaszewicz for the Bulgarian and Polish data. This paper has also benefited from the valuable input of the audiences at NELS 46, the 20th Amsterdam Colloquium and the speaker series at the Dept. of Linguistics and Philosophy at M.I.T. Remaining errors are mine.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romero, M. The Conservativity of Many: Split Scope and Most . Topoi 37, 393–404 (2018).

Download citation

  • Published:

  • Issue Date:

  • DOI: