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Finding the force: How children discern possibility and necessity modals

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Abstract

This paper investigates when and how children figure out the force of modals: that possibility modals (e.g., can/might) express possibility, and necessity modals (e.g., must/have to) express necessity. Modals raise a classic subset problem: given that necessity entails possibility, what prevents learners from hypothesizing possibility meanings for necessity modals? Three solutions to such subset problems can be found in the literature: the first is for learners to rely on downward-entailing (DE) environments (Gualmini and Schwarz in J. Semant. 26(2):185–215, 2009); the second is a bias for strong (here, necessity) meanings; the third is for learners to rely on pragmatic cues stemming from the conversational context (Dieuleveut et al. in Proceedings of the 2019 Amsterdam colloqnium, pp. 111–122, 2019a; Rasin and Aravind in Nat. Lang. Semant. 29:339–375, 2020). This paper assesses the viability of each of these solutions by examining the modals used in speech to and by 2-year-old children, through a combination of corpus studies and experiments testing the guessability of modal force based on their context of use. Our results suggest that, given the way modals are used in speech to children, the first solution is not viable and the second is unnecessary. Instead, we argue that the conversational context in which modals occur is highly informative as to their force and sufficient, in principle, to sidestep the subset problem. Our child results further suggest an early mastery of possibility—but not necessity—modals and show no evidence for a necessity bias.

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Notes

  1. In this paper, we put aside two other possibilities. First, children could learn force on the basis of explicit negative feedback: they would be corrected by adults when they produce necessity modals to describe mere possibilities. We leave a systematic investigation of whether children receive such feedback, but, anecdotally, we haven’t encountered any. In their study on every, Rasin and Aravind (2020) report only one case of explicit negative feedback out of 72 every uttered by children. Second, children could exploit the principle of contrast (Clark 1987) (e.g., knowing a possibility modal could lead children to hypothesize a necessity meaning for the next modal they encounter). However, as we discuss in Sect. 2.1, learners cannot expect two modals to necessarily express different forces, since several modals express the same force. If children heard necessity claims explicitly contrasted with possibility claims (e.g., “you can, but you don’t have to”), they could infer that the former expresses possibility, and the latter necessity, based on logical compatibility. While we did not systematically examine the transcripts for such cases, we did extract all cases where two modal claims were related by the logical connectives or, but, and and. We found only 85 such cases (out of 18,853 utterances). Among these, only three were possibly useful to figure out the force of possibility modals (e.g., “it might be in your box or it might be lost”), but we found no informative cases for necessity modals. This may be an underestimation, since we did not look for the occurrence of modals across different utterances. However, this very low frequency makes it unlikely that children can learn from such contrasts.

  2. Many variants of this idea can be found in the literature. The Subset Principle (Baker 1979; Berwick 1985; Dell 1981; Manzini and Wexler 1987; Pinker 1979, a.o.) was originally proposed for the acquisition of syntactic phenomena. Later on, the Semantic Subset Principle (SSP) was introduced by Crain and Thornton (1998) to account for semantic set/subset problems at the sentential level (see also Crain et al. 1994; Crain 2012).

  3. We were unaware of Rasin and Aravind’s methodology when we started this project with Dieuleveut et al. (2019a) and thus approached the problem for modals differently. We leave an application of Rasin and Aravind’s methodology to modals for future research, though we suspect that it might not always be easy to tell whether a possibility is already part of the common ground when a necessity statement is made, as all kinds of possibilities may be open at any given point in a conversation, even if they may not be salient.

  4. The difference between weak and strong necessity is illustrated in the following example: ‘Employees must wash their hands. Everyone else should’ (von Fintel and Iatridou 2008). Weak necessity modals are still treated as necessity modals, but quantify over a smaller domain than their strong counterparts.

  5. Logical entailment relations hold within flavor only: for example, epistemic necessity (e.g., ‘given what we know, he must be upstairs’) does not entail deontic possibility (e.g., ‘given the rules, he can be upstairs’). Horn scales are thus defined within a flavor. Because of flavor variability, this means that the same lexeme can appear in different scales. We leave aside debates about ability modals, often argued to have no necessity counterpart (Horn 1972; Hackl 1998) (e.g., ‘Jo can speak German; in fact, he has to’ leads to oddity, or forces a switch in flavor interpretation). It is also argued that ability modals do have duals, compulsion modals, but they are just extremely infrequent (e.g., ‘I have to sneeze’) (Mandelkern et al. 2015).

  6. Other analyses take variable modals to neither be underlying possibility nor necessity. Kratzer (2012) analyzes them as upper-end degree modals, roughly equivalent in meaning to ‘it is somewhat probable (/desirable) that p’.

  7. See, for example, Cinque’s (1999) hierarchy.

  8. Such considerations might explain why necessity but not possibility modals tend to be PPIs.

  9. This asymmetry has been attributed to conceptual and grammatical factors, but it might instead reflect a frequency asymmetry in the input. For how children learn that modals can be used to express various flavors, see van Dooren et al. (2017, 2022).

  10. We do not differentiate among subtypes of root flavors (ability, teleological, deontic, …).

  11. Results from another HSP study where participants had to fill in the blank (instead of making a forced choice) are reported in Dieuleveut et al. (2019b).

  12. An example of the experiment can be accessed at https://frm.pcibex.net/r/HDtxJP/.

  13. Accuracy for controls was very high (94.6%). There was no difference between groups in accuracy.

  14. We sometimes had to step back to random-intercepts-only models when the model failed to converge with the full random-effects specification.

  15. We used the same procedure (based on model comparisons) for all subsequent experiments reported in this paper, but don’t systematically report the reduced model.

  16. Answers were coded as 1 if the response was accurate, and 0 otherwise. Effect sizes (β), standard errors (SE), z-values, and p-values for the logistic models are reported in online Appendix C for Experiment 1 and all following analysis.

  17. Contexts involving interrogative sentences appeared almost exclusively in root-AFF-1 and root-AFF-2, as epistemic and negated modals are rare in interrogatives. Out of 80 contexts for root-AFF, there were 21 interrogative sentences (19 involving possibility modals; 2 involving necessity modals).

  18. This higher accuracy in possibility contexts might also reflect a general tendency to answer with possibility modals by default, maybe because of their relative frequency. To test for the effect of frequency, we compared accuracy for can and able-to (used in root-aff-2 and root-neg), which are both root possibility modals but strongly differ in frequency (3 able vs. 100 can in the Manchester corpus). The general accuracy on able was not significantly lower than on can (overall: able: 80.8% vs. can: 89.8% vs. have to: 71.7%).

  19. Few other corpus studies address the distribution of possibility and necessity modals with respect to negation, and fewer look at child-directed speech, but they also suggest that negated necessity modals are not frequent. De Haan (2011) reports that negation is very rare with must: 2.5% in the Brown corpus (written English) and 1.4% in the Switchboard corpus (spoken English). Thornton and Tesan (2013) report the frequencies of some negative auxiliary verbs in the input to children in the Providence corpus, but don’t specify their frequency relative to the positive forms. Jeretič (2018) reports that negation on necessity modals is infrequent in the input to French and Spanish children (French: 15.5%; Spanish: 6.2%).

  20. Horn focuses on a different but related problem, namely the fact that cross-linguistically, the ‘O’ corner of the Aristotelian square of opposition (corresponding to negated universals, e.g., non-necessity meanings) never seem to be lexicalized, whereas the other three corners (possibility, necessity, and impossibility) can be. Horn argues that this follows from the fact that there is no functional pressure to lexicalize non-necessity meanings: speakers already have a way to express non-necessity, using scalar implicatures.

  21. We thank an anonymous reviewer for pointing this issue out.

  22. Examples of the experiments can be accessed at https://farm.pcibex.net/r/sohaoF/ (Exp. 2) and https://farm.pcibex.net/r/ZbVcQT/ (Exp. 3).

  23. Accuracy on attention checks and tense controls was very high (attention checks: 99.4%; tense controls: 95.8%), with no difference between groups. To compute accuracy on tense controls, we only included sentences that could not lead to an ambiguity (e.g., because of containing a temporal adverb) (10 out of 20 cases).

  24. The fact that participants perform better than chance on possibility contexts in the Jabberwocky experiment might reflect a general tendency to answer with possibility modals when given a forced choice task—perhaps because of their higher frequency, see fn. 24. It may also be driven by their higher accuracy in interrogative sentences, as discussed in Sect. 3.2.3 (mean accuracy for possibility in interrogatives: Exp1: 98.1%; Exp2: 96.2%; Exp3: 76.1%; in declaratives: Exp1: 75.1%; Exp2: 65.8%; Exp3: 59.5%).

  25. This is not true stricto sensu, as participants also lose the information about the subject (e.g., I/you/Caroline…).

  26. An example of the experiment can be accessed at https://farm.pcibex.net/r/lrxZaB/.

  27. We sometimes had to step back to random-intercepts-only models when the model failed to converge with the full random-effects specification. We also checked that there was no significant difference between groups (root-aff-1 vs. root-aff-2) (Answer=1)∼Group+(1|Subject)+(1|Item). Results of the model comparison were not significant (\(\chi^{2}(1)=0.22\), p = 0.64).

  28. Similar distributional patterns (possibility modals being used more frequently than necessity modals and occurring frequently with negation) are found in Spanish and French (Jeretič 2018) and Dutch (van Dooren et al. 2022).

  29. An example of the experiment can be accessed at https://farm.pcibex.net/r/mYOcOz/.

  30. Because some of the negated have to in child productions were particularly unclear (e.g., ‘I can’t have to read it.’), we also used not gotta and not need. Details are provided in online Appendix B.

  31. Out of 148 contexts, 36 of them had the modal appear in the preceding dialogue (24.3%) (uttered by the child: 11; by the mother or another adult: 20; by both: 5).

  32. As a proxy, we checked that the mean length of dialogues was the same for adults and children (mean number of words for children’s contexts: 39.6 words/dialogue; for adults’ contexts: 38.9).

  33. For the adult version, the proportion of errors on controls was very low (5.4%), with no difference between groups. For the child version, however, the initial proportion of errors on controls was quite high (21.6%): post-hoc analysis revealed that this came from five control contexts for which the accuracy was particularly low, and thus were not reliable controls. We decided to remove these five controls from our exclusion criteria, as they were particularly difficult and probably do not indicate that subjects were not doing the task correctly. After restricting to the 15 remaining controls, mean accuracy on controls was 90.0%, showing that participants were not answering randomly.

  34. As pointed out by an anonymous reviewer, our results may also be consistent with theories of acquisition that use a necessity bias that is sensitive to input frequencies, along the lines of Piantadosi et al.’s (2012b) Bayesian learner (see also Piantadosi et al. 2012a). We intend to address this in future work.

  35. We do not have enough data from each child to see whether children’s adult-like uses of necessity modals correlate with frequency in their input (i.e., whether children who hear more necessity modals use them more appropriately), but we intend to pursue this question in future work. We thank an anonymous reviewer for this great suggestion. See Dieuleveut (2021) for preliminary results and discussion.

  36. For a similar investigation of what aspects of the input predict children’s understanding of think and know, see Dudley (2017).

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Acknowledgements

We thank Alexander Williams, Jeff Lidz, Tyler Knowlton, Yu’an Yang, Anissa Zaitsu, Dan Goodhue, Rémi Varloot, the Modality Group, the Language Acquisition Lab at the University of Maryland, Florian Schwarz, and two anonymous reviewers for helpful comments and suggestions, as well as our research assistants Monica Pizzo, Joon Lee, David Whitcomb, Madisen Fong, and Avni Gulrajani.

Funding

This project is supported in part by NSF grant #BCS-1551628.

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Authors and Affiliations

  1. Université Paris Cité, CNRS, LLF, Paris, France

    Anouk Dieuleveut

  2. University of Groningen, Groningen, The Netherlands

    Annemarie van Dooren

  3. New York University, New York, USA

    Ailís Cournane

  4. University of Maryland, College Park, MD, USA

    Valentine Hacquard

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  1. Anouk Dieuleveut
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Correspondence to Anouk Dieuleveut.

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Dieuleveut, A., van Dooren, A., Cournane, A. et al. Finding the force: How children discern possibility and necessity modals. Nat Lang Semantics 30, 269–310 (2022). https://doi.org/10.1007/s11050-022-09196-4

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