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Granularity in Number and Polarity Effects

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Logic and Engineering of Natural Language Semantics (LENLS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14213))

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Abstract

This paper offers a granularity-based account of the fact that round and non-round numbers may exhibit polarity effects when they are appended by even-type focus particles. The key observation is that non-round numbers appended by mo ‘even’ in Japanese cannot be in the scope of negation, while round numbers exhibit no restriction in scopal relation. Adopting the scope theory of mo and a theory of granularity ([6, 10]), we propose that an asymmetric entailment relation holds between propositions with a non-round and a round number and this entailment relation invites a proposition with a coarser granularity into the set of alternatives in computing the scalar presupposition of mo. Given that the scalar presupposition of mo with numerals is only sensitive to asymmetric entailment, we argue that the availability of asymmetric entailment from the prejacent to this additional alternative proposition is responsible for the polarity effects. We also discuss the related issues such as polarity effects observed in explicit approximators (e.g. about, approximately) and numerals with the contrastive topic marker wa.

We would like to express our gratitude to Stephanie Solt and anonymous reviewers of LENLS 19 for their invaluable comments on an earlier version of the paper. This work is supported by JSPS Grant-in-Aid 21K00525.

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Notes

  1. 1.

    Mo has several usages as exemplified below. We will confine ourselves to the scalar usage with a similar meaning to ‘even’ in this paper. We do not make any specific assumption about the issue of whether these different usages come from a single source or not.

    figure a

    .

  2. 2.

    [9] notes that there is yet another reading for (2b), where truth-conditionally, John solved fewer than five problems and ‘5’ is implicated to be large. We will not consider this reading here, but our analysis can explain why this reading is legitimate both with round and non-round numbers.

  3. 3.

    Nakanishi [8, 185] notes that the large-number reading is indeed not impossible in English, as shown in (i):

    (i) Al, Bill and Conan always read everything they are assigned, but this time, they each had some books that they didn’t read. Al didn’t read book, Bill didn’t read books and Conan ended up not even reading .

  4. 4.

    Ijima [3] takes the sentence with 48 in (5b) is unacceptable. We found this description unsatisfactory because the 48-version of the sentence does have a legitimate interpretation with the large-number reading.

  5. 5.

    Even-items including mo may also introduce an additive presupposition (=(i)), but we will put this component aside in this paper.

    figure l

    .

  6. 6.

    We do not claim that the unlikeliness of mo is always based on asymmetric entailment: this simply makes a wrong prediction. In (i), for example, it has to be the case that Taro came to the party is less expected than, say, Mary came to the party, which is not in entailment relation with the former.

    figure n

    What seems to be the case is that in the case of mo appended to numerals, the unlikeliness based on other than asymmetric entailment is not available.

  7. 7.

    In footnote 2 we pointed out that (2b) has the third reading. The scopal relation involved in this reading should be [\(\lnot>\) mo > n]. This apparent inconsistency to what we claim here is resolved if we consider this reading to be actually a case of external negation. A piece of evidence for this view comes from the fact that this use requires a preceding discourse that refers to the number, as in (i).

    (i) A: How many students are enrolled in your class this semester? 50 students have enrolled in mine.

        B:

    figure t

    .

  8. 8.

    See [12] for morpho-syntactic reasoning of this obligatory wide-scope reading of focus particles.

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Author information

Authors and Affiliations

  1. Osaka University, 1-5 Machikaneyamacho, Toyonaka, Osaka, Japan

    Eri Tanaka

  2. Aichi Prefectural University, 1522-3 Ibaragabasama, Nagakute-shi, Aichi, Japan

    Kenta Mizutani

Authors
  1. Eri Tanaka
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  2. Kenta Mizutani
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Correspondence to Eri Tanaka .

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Editors and Affiliations

  1. Ochanomizu University, Tokyo, Japan

    Daisuke Bekki

  2. Keio University, Tokyo, Japan

    Koji Mineshima

  3. Aoyama Gakuin University, Tokyo, Japan

    Elin McCready

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Tanaka, E., Mizutani, K. (2023). Granularity in Number and Polarity Effects. In: Bekki, D., Mineshima, K., McCready, E. (eds) Logic and Engineering of Natural Language Semantics. LENLS 2022. Lecture Notes in Computer Science, vol 14213. Springer, Cham. https://doi.org/10.1007/978-3-031-43977-3_4

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  • DOI: https://doi.org/10.1007/978-3-031-43977-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43976-6

  • Online ISBN: 978-3-031-43977-3

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