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Numerals Denote Degree Quantifiers: Evidence from Child Language

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Measurements, Numerals and Scales

Part of the book series: Palgrave Studies in Pragmatics, Language and Cognition ((PSPLC))

Abstract

A large body of work in both the theoretical and experimental literature suggests that upper bound implications in simple sentences with bare numerals are entailments arising from the semantics of the numeral, rather than implicatures of the sort associated with other scalar terms. However, not all semantic analyses of numerals make the same predictions about upper bound implications in all contexts. In particular, in sentences in which numerals are embedded under existential root modals, only a semantic analysis of numerals as maximizing degree quantifiers derives upper bound implications as entailments; other analyses must derive upper bound implications as implicatures. In this paper, we provide an argument for the degree quantifier analysis by demonstrating that young children interpret such sentences as imposing upper bounds at an age at which they do not reliably calculate scalar implicatures.

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Notes

  1. 1.

    Baseball enthusiasts will recognize that the math is a bit more complex than (3) lets on, since batting average also depends on the number of official at-bats. So (3) should really be heard as prefaced by an implicit “Assuming he has n official at-bats...” for some appropriate n.

  2. 2.

    To keep our logical representations as perspicuous as possible, we omit the relation contributed by the verb, since this plays no crucial role in distinguishing between the different analyses of numerals we are considering. A complete version of (4a) (and mutatis mutandis, the other examples considered in this paper) would look like (i).

    figure d

    .

  3. 3.

    The assumption that exclusion of alternatives is based on asymmetric entailment is a gross but hopefully benign oversimplification, for the purposes of illustrating this type of analysis. There is a rich and nuanced literature on the question of what this relation actually is (see e.g., Gazdar 1977; Hirschberg 1985; Sauerland 2004; Fox 2007; Bar-Lev and Fox 2017), but this does not bear on the issues discussed in this paper.

  4. 4.

    (11b) says that three is the maximum n such that in every world in the modal domain (worlds in which Mookie wins the batting title), there’s a group of hits of size n that Mookie gets. There are groups of size three in worlds in which he gets more than three hits, but there are no groups of size three in worlds which he gets fewer than three hits. (11b) thus places a lower bound of three on the number of hits that we find in each world that satisfies the modal claim.

  5. 5.

    We take it that the semantic difference postulated by the local analysis presumes a fully pragmatic theory of implicature calculation, since there would be no reason for the language learner to posit an upper bounded semantics for numerals if upper bounds could be independently derived from exhaustification of the lower bounded semantics.

  6. 6.

    Our experimental stimuli, as well as the results of a separate experiment demonstrating that children and adults assign the same range of interpretations to sentences in which numerals are embedded under universal root modals, are available at https://semanticsarchive.net/Archive/2E3Y2FjO.

  7. 7.

    Syrett et al. (2020) report similar results in a study of how monolingual English and Spanish-English bilingual children interpret sentences of the form ‘You may take two/all of the N’ in scenarios in which a conversational participant took less than the amount indicated by the numeral. While the child participants from different language backgrounds diverged on other scalar target items, they patterned the same with these control sentences, diverging from adult controls.

  8. 8.

    Panizza et al. (2009), in contrast, found a penalty for upper bounded meanings in a reading time study, and a preference for lower bounded meanings in downward entailing contexts. The latter result is consistent with a general preference for stronger meanings, given the possibility of deriving lower bounded meanings from the upper bounded degree quantifier meaning (Kennedy 2015), but the former finding appears to conflict with results like those described in Huang et al. (2013) and Marty et al. (2013), as Panizza et al. themselves note.

  9. 9.

    An open question is how this account of the developmental path—as well as Barner and Bachrach’s, to which it is largely isomorphic—relates to Carey’s (2004) suggestion that children initially organize numerals according to a more basic system for representing sets of objects.

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Acknowledgements

We are very happy to be able to contribute this paper to a volume in honor of Stephanie Solt, whose work has engaged and inspired us over the years in ways that know no upper bounds, and we send her big congratulations on the acquisition of her very own number. We are grateful to several anonymous reviewers for constructive feedback on this work, to the research assistants in the Laboratory for Developmental Language Studies at Rutgers University, and to audiences at the Boston University Conference on Language Development, the Rutgers Center for Cognitive Science, The Ohio State University, and the Hebrew University of Jerusalem.

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  1. University of Chicago, Chicago, IL, USA

    Christopher Kennedy

  2. Rutgers, The State University of New Jersey – New Brunswick, New Brunswick, NJ, USA

    Kristen Syrett

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  1. Cognitive Science/Linguistics Department, University of Potsdam, Potsdam, Brandenburg, Germany

    Nicole Gotzner

  2. ZAS, Leibniz-Centre General Linguistics, Berlin, Germany

    Uli Sauerland

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Kennedy, C., Syrett, K. (2022). Numerals Denote Degree Quantifiers: Evidence from Child Language. In: Gotzner, N., Sauerland, U. (eds) Measurements, Numerals and Scales. Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-73323-0_8

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