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The Conservativity of Many: Split Scope and Most

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Abstract

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.

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Notes

  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.

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  1. Department of Linguistics, University of Konstanz, 78457, Konstanz, Germany

    Maribel Romero

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  1. Maribel Romero
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Correspondence to Maribel Romero.

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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.

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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.

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Romero, M. The Conservativity of Many: Split Scope and Most . Topoi 37, 393–404 (2018). https://doi.org/10.1007/s11245-017-9477-5

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