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The dynamics of negative concord


Concord describes a natural language phenomenon in which a single logical meaning is expressed syntactically on multiple lexical items. The canonical example is negative concord, in which multiple negative expressions are used, but a single negation is interpreted. Formally similar phenomena have been observed for the redundant marking of distributivity and definiteness. Inspired by recent dynamic analyses of these latter two phenomena, we extend a similar dynamic analysis to negative concord. We propose that negative concord items introduce a discourse referent (like an existential), but then test that no discourse referent has been introduced in any assignment. These apparently contradictory requirements are licensed with split scope around negation: introduction occurs below negation; the test appears above it. The analysis successfully predicts that negative concord items must be licensed by a sufficiently local negative operator. We further show that modulation of what is at-issue can account for cases in which NC items themselves carry negative force.

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  1. 1.

    Zeijlstra (2004) reports that NC items are licensed by without in Bavarian, Berber, Catalan, Czech, French, Greek, Hebrew, Hungarian, Italian, Polish, Portuguese, Quebecois, Romanian, Spanish, and Yiddish. But there are exceptions: in Russian and Serbo-Croatian, for example, acceptability of NC items under without varies based on dialect and register. I will have relatively little to say about these cross-linguistic differences, though see discussion in Sect. 4.2.

  2. 2.

    The expression \(\hbox {s}^{u\mapsto d}\) returns the state t that is exactly like s except that \(t_g(u)=d\).

  3. 3.

    Note that this definition is distributive; for non-distributive definitions of dynamic negation, see relevant discussion in van Eijck and Cepparello (1994), Aloni (1997), and Charlow (2019c).

  4. 4.

    The sentence Zero children saw a cat also generates the inference that no cats were seen. The numeral zero is nevertheless not generally a licensor of NC items. On the other hand, zero displays a number of other unusual properties (e.g., it also doesn’t license NPIs), leading Bylinina and Nouwen (2018) to hypothesize that zero means ‘at least zero,’ and that the ‘exactly zero’ interpretation arises from obligatory exhaustification of alternatives. On such an analysis, the literal meaning of zero does not in fact create a downward entailing environment.

  5. 5.

    On the other hand, relative clauses generally are scope islands. This means that no theory predicts NC items to be grammatical in a relative clause modifying the restrictor of a universal quantifier, since locality is not satisfied (‘Every boy who loves nobody\(_{\text {NC}}\)...’). In this respect, the sentence in (68) provides a more tightly controlled test case than the examples that appear in Gajewski (2011) and Chierchia (2013), which involve relative clauses.

  6. 6.

    One notable exception is Chierchia (2013). When presuppositions are removed from the picture, the exhaustification account laid out in Chierchia (2013) predicts that NC items will be licensed in anti-additive environments. However, NC items in the restrictor of every are ruled out for a different reason under the exhaustification account, due to the presupposition that the restrictor of every is non-empty.

  7. 7.

    Lasnik (1972) reports an almost identical sentence (without ‘but’) as ungrammatical. Although I agree that (i-a) is not so great, I find the grammaticality of both (77) and (i) to be exactly parallel to sentences with few, which is generally taken to allow discourse anaphora (Kamp and Reyle 1993; Nouwen 2003). The same pattern holds for sentences in which not is syntactically separated from many, as in (ii).

  8. 8.

    Such strategies are often marked by a modal verb, but even this may not be foolproof. A reviewer points out that the discourse in (i) sounds perfectly natural. Even though there is no modal verb, I am inclined to say that this is a special case of accessing a discourse referent in a different world or time. This can be seen if one replaces the pronoun with a definite description; the pronoun does not denote ‘the car he owns,’ but rather, ‘the car he owned’ or ‘the car he would own, had he not sold it.’

  9. 9.

    Thank you to Simon Charlow for discussion on these points.

  10. 10.

    The analyses of Henderson (2014) and Brasoveanu (2013) use rather different formal mechanisms that do not involve scope-taking.

  11. 11.

    On any such account, the exact nature of syntactic competition must be made precise. In particular, although preverbal NC items are too high to be licensed by overt sentential negation, an equivalent meaning can of course be communicated with an alternative word order, as in (111). When calculating whether the covert operation is allowed, one must thus consider alternatives that are derived by manipulating lexical material (e.g. the presence of negation), but not by manipulating the syntax. For similar discussion about the alternatives used in implicature calculations, see Katzir (2007), Fox and Katzir (2011).

  12. 12.

    On Szabolcsi’s (2018) analysis, the difference between Russian and Italian arises not from the meaning of sentential negation or of NC items, but in the possible landing sites of leftward movement. In languages like Russian, NC items may move into the specifier of sentential negation, so may be interpreted in its scope. In languages like Italian, NC items must move to a position above the negative projection, so cannot be interpreted in the scope of negation.

  13. 13.

    Similar discussions on the necessity (or not) of polyadic quantification revolve around the semantics of the word same (Keenan 1992; Barker 2007). Interestingly, the analysis sketch in Kuhn (2017) of same as a (non-polyadic) dynamic quantifier is highly similar to the analysis of negative concord presented here.

  14. 14.

    An exactly similar situation holds for distributive concord. See the discussion in Kuhn (2019) on innocent redundancy and distributive operators versus plurality filters.


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Thank you to Amir Anvari, Nadine Bade, Adrian Brasoveanu, Dylan Bumford, Simon Charlow, Milica Denic, Anamaria Fălăuş, Carlo Geraci, Janek Guerrini, Salvador Mascarenhas, Lena Pasalskaya, Orin Percus, Philippe Schlenker, Benjamin Spector, and Hedde Zeijlstra. The research leading to these results received funding from ERC H2020 Grant Agreement No. 788077–Orisem (PI: P. Schlenker). Research was conducted at the Département d’Etudes Cognitives (ENS), which is supported by Grants ANR-10-IDEX-0001-02 PSL and ANR-17-EURE-0017 FrontCog.

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Kuhn, J. The dynamics of negative concord. Linguist and Philos (2021).

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  • Negative concord
  • Dynamic semantics
  • Split scope
  • n-words
  • Negation