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Additivity, scalarity and Mandarin Universal wh’s

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Abstract

This paper offers a compositional analysis of Mandarin universal wh’s in construction with an additive/scalar adverb ye ‘also/even’. In the analysis, universal force is derived from exhaustification of the subdomain alternatives activated by wh-items under stress, and the tendency of wh-ye to appear in negative sentences is explained by the interaction between ye and domain widening. Specifically, the ye in wh-ye is argued to be a scalar ye imposing a total order presupposition on its associated set of alternatives. In wh-ye it associates with the domain argument of the wh, and the requirement can be met by either an ordered wh or a two-point scale \(\langle D',D \rangle \) made available through domain widening, specifically by widening of QUDs. The negative preference follows from the fact that a QUD is most naturally widened when it is settled negatively, as in the case of negatively biased questions with minimizers/maximizers.

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Notes

  1. # marks the infelicity of ye under the relevant readings. Of course, an additive or scalar interpretation of ye would be fine in (2).

  2. The classification closely follows Biq (1989) and Yang (2020) The term “modal use” is also from Yang (2020). See also Ma (1982) and Hole (2004) for discussion of ye.

  3. Consider the following entry for lian from Xiang (2020, ex. (80)), which states that lian indicates the presence of focus within its argument, without making any semantic contribution.

    figure k

  4. A reviewer reports their judgment that ye without lian (e.g., (10a)) can only have an additive reading, and suggests that lian, rather than ye, contributes scalarity. We do not share this judgment. To our consultants, lian is not necessary for ye to express a scalar meaning. Indeed, examples of ye conveying scalarity without lian are easy to find (e.g., Ernst and Wang 1995, p. 235; Hole 2004, p. 25; Liao 2011, p. 257; Yang 2020, p. 101), and acknowledged in the typological literature (e.g., Forker 2016, p. 73). We further add the following observation from Sybesma (1996), who remarks that “like dou, ye, when used as a focalizer, is unstressed; it can be stressed, in which case it means ‘also’ .” As is clear from Sybesma’s example in (i), focalizer-ye is just ye used as even, and ye without lian can convey scalarity. Exactly the same observation is made in Hole (2004, p. 25): in the case of lian without ye, “emphatic stress on the foci will yield the even-readings, otherwise, we get also-readings.” We find the generalization empirically correct; that is, when lian is absent, ye is ambiguous between also and even and stress disambiguates. This might explain why the reviewer finds it hard or even impossible to construe ye as even without lian, if we assume lian, as a special focus marker, can be used to disambiguate and unequivocalness is preferred.

    figure l

  5. A reviewer offers another interesting example where scalar-dou and ye differ:

    figure m

    The reviewer claims that (i) with ye is unacceptable because this is a scalar context, and ye, unlike dou, is not scalar without lian (see the same reviewer’s comment in fn. 4). We however find an explanation based on additivity more plausible, noting that (i) was initially used in Rullmann (1997) as evidence that even does not encode additivity, as the alternatives here are mutually exclusive. We propose that this feature of the alternatives, combined with the conclusion drawn from (11) that only scalar-ye has an additive component, explains the contrast in (i). We offer two pieces of evidence for such an explanation. First, adding lian to ye in (iB) does not improve the sentence, showing that scalarity (assuming with the reviewer that lian-ye is always scalar) is not the issue. Second, adding negation saves the sentence: Ta (lian) FUF jiaoshou ye bu shi ‘he is not even an associate professor.’ This is fully expected under the present view, as negation, without rendering the context non-scalar, makes the alternatives compatible.

  6. See Xiang (2020) for the proposal that Mandarin minimizers like the one in (10b) undergo focus-reconstruction and get interpreted below negation.

  7. An operator F is nonveridical iff, for any p, F(p) does not entail p. Please refer to Giannakidou (1998) and related literature for a framework that uses nonveridicality to explain polarity and free choice items.

  8. A reviewer, based on Xiang’s (2020) claim that (i) with the perfective marker le is less natural than with experiential guo, suggests that the acceptability of wh-dou in positive episodic sentences may vary among speakers. While we acknowledge that positive episodic wh-dou’s may have special pragmatic requirements, we do not find them to be unacceptable. For instance, all of our consultants accept (i) with le as an answer to the question shei lai-le? “who came?” Our empirical standpoint also aligns with previous research, such as Giannakidou and Cheng (2006, p. 137), Liao (2011, p. 97) and Chen (2018, §2). Moreover, sentences with episodic positive wh-dou are often used as experimental items to assess children’s comprehension of universal wh’s, accompanied by pictures describing episodic events (e.g., Zhou 2015, ex. (25) as shown in (ii) and Yang et al. 2022, ex. (19)). These sentences are consistently accepted as ∀-statements by both children and adults. Lastly, the reviewer suggests examining corpus data to pinpoint the exact contextual requirements of positive episodic wh-dou, which we plan to investigate in future work.

    figure u
    figure v

  9. Two clarifications are needed. First, the marker buguan in (24a), likewise wulun, is usually glossed as ‘no matter’. These markers can optionally attach to universal wh’s and to antecedents of unconditionals, referred to as nominal and clausal-wulun, respectively, in Lin (1996). Second, speakers may have varying judgments about (24) and positive wh-ye in general. The variation is discussed below.

  10. Specifically, we first searched for “duoshao $4 ye”, which looks for tokens with ≤4 characters between duoshao and ye. This query yielded 1,182 results. We then added the condition “ye–6(bu∣mei∣wu∣bie∣ xiu∣nan∣mo∣beng∣wei)”, requiring that there be no negation of any kind after ye within the next 6 characters. This returned 463 occurrences. See http://ccl.pku.edu.cn:8080/ccl_corpus for the CCL corpus.

  11. For application of the idea to various phenomena, see, e.g., Bowler (2014), Singh et al. (2016), and Bar-Lev (2021).

  12. There are three maximal subsets of \(\left \{a\wedge \neg b, b\wedge \neg a, a\wedge b \right \} \) that can be jointly negated with a∨b being true: \(\left \{a\wedge \neg b, a\wedge b \right \} \), \(\left \{b\wedge \neg a, a\wedge b \right \} \), and \(\left \{a\wedge \neg b, b\wedge \neg a \right \} \). Their intersection is ∅, and thus there is no innocently excludable alternative. See also Chierchia (2013, pp. 120-122).

  13. To address a concern raised by a reviewer regarding the claim that existential-wh’s trigger partial modal inferences, we offer (i) involving Mandarin exceptive chule to sharpen the intuition. Assuming that exceptives are sensitive to some sort of ∀-quantification, the contrast between (ia) and (ib-c) shows that existential-wh’s, unlike universal-wh’s and universal FCI renhe ‘any’, do not convey free choice of the universal variation type. See Giannakidou (2018, §5) for additional evidence that Mandarin existential wh’s are not “exhaustive”.

    figure au

  14. One way to guarantee that only subdomain alternatives are triggered, as proposed for any in Jeong and Roelofsen (2022), is to assume that the domain argument of the wh that receives focus is the set \(D_{e}\) of all entities, and contextual restriction happens when \(D_{e}\) is intersected with \(D^{c}\), the set of things relevant in c. Under this treatment, \([\!\![{\text{shei}_{D}}_{e} ]\!\!]^{c} = \lambda P\exists x\in D_{e} \cap D^{c} [\text{person}(x)\wedge P(x)]\), and focus on \(D_{e}\) will deliver all and only subdomain alternatives.

  15. We can also use indexed foci (Wold 1996) to regulate associations, as in (i). We prefer (44b) using movement however, as there is indeed overt movement of the wh to the left of ye (see, e.g., (17) and (39a)).

    figure ay

  16. That is, if p entails q, then p is also less likely than q, unless p and q are contextually equivalent (see, e.g., Crnič 2019b,c). This means that the scalar presupposition is satisfied in any context where the prejacent is not contextually equivalent with its alternatives. The latter requirement is easy to satisfy in normal contexts.

  17. There is a syntactic difference: the focus in (49) appears to ye’s right while in (50) to its left. This does not affect the point under discussion, as moving the focus in (49) to ye’s left does not save the sentence.

  18. A total order is a partial order in which any two elements are comparable. We suspect that this may be a requirement for other even-like particles, as similar puzzles have been observed for English even, as shown in (i) from Greenberg (2016, ex. (20)). Greenberg considers several accounts of (i), but finds them inadequate and uses (i) as evidence against the standard likelihood-based semantics of even. It remains to be seen whether total order can offer a new perspective. Interestingly, total order has also been used by Chierchia (2013) to regulate the choice between O(nly)-exhaustification and E(ven)-exhaustification, as shown in his Optimal Fit in (ii) (with O being our exh). Thus, total order, according to Chierchia, also plays a role in the felicitous use of covert even.

    figure bf
    figure bg

  19. In (51a) we assume that the individual conjuncts are alternatives to the conjunction. This is a standard assumption as they are simply the domain alternatives of the conjunction (Chierchia 2013, p. 138).

  20. Assume that there are exactly three persons a, b and c in the model. The prejacent in (57c) is equivalent to ¬speak(a)∧¬speak(b)∧¬speak(c), and its set of subdomain alternatives in (57d) is {¬spk(a),¬spk(b),¬spk(c),¬spk(a)∧¬spk(b),¬spk(a)∧¬spk(c),¬spk(b)∧¬spk(c),¬spk(a)∧¬spk(b)∧¬spk(c)}. The set is obviously not totally ordered.

  21. See also Fălăuş and Nicolae (2022) for using domain widening to explain the presence of an additive particle in a class of Romanian free choice items.

  22. Maximizers like in a million years are not discussed in Jeong and Roelofsen (2022), but as pointed out in van Rooij (2003, p. 259) and clear from the discussion below, they can be analyzed in the same way.

  23. Clemens Mayr (NLS editor) points out correctly that the proposed negative bias also conflicts with ye’s additive presupposition, which requires everyone in \(D'\) to be speaking, and wonders whether the additive presupposition might actually prevent the emergence of the negative bias in the first place. We suggest that the negative bias is a calculable obligatory implicature (potentially a manner implicature due to the speaker’s act of widening the QUD), and its conflict with the meaning of the wh-ye sentence, whether in terms of its assertion or presupposition, would result in deviance. Furthermore, several recent proposals (e.g., Szabolcsi 2017, Fălăuş and Nicolae 2022) argue that the standard additive presupposition of (scalar) additives is not inherent to the particles but derived from obligatory exhaustification. From this perspective, the conflict between the negative bias and the additive “presupposition” can been seen as a clash of implicatures. We appreciate the editor’s valuable comment, and hope to study the precise nature of the negative bias and the additive presupposition in future work.

  24. There are other options. For instance, the alternative set could be built below and without negation, as Rooth (1996, §5.1) and Beaver and Clark (2008, §3.2) propose for the “focus sensitive” negation in (66). A Roothian LF for (66b) under this treatment would be [neg [IF took your car]\(\sim _{C}\)], with the focus evaluated below ¬. Rooth’s solution is not adopted for wh-ye because it requires negation to scope over the focus, but as we saw in Section 3.1, there are cases of negative wh-ye where negation cannot scope over the wh. Alternatively, we could adopt the structure-based theory of alternatives in Fox and Katzir (2011), where positive alternatives without negation are deletion-alternatives. It is worth noting that under both of these accounts, positive sentences do not readily activate negative alternatives, in line with the treatment assumed in the main text.

  25. It is worth highlighting the fact that enriching the alternative semantic value of ye’s prejacent need not affect the value of \(C'\), the actual input for ye, since \(C'\) is only required to be a subset of the former.

  26. While our consultants all agree there is a contrast between (68a) and (68b), some find it not as sharp as Zhang (2021) claimed. Specifically, some speakers indicate that (68a) is not entirely unacceptable, while a few judge (68b) less natural. We hypothesize that the variation may be attributed to the varying levels of ease or difficulty among speakers in accommodating negative QUDs for positive wh-ye sentences.

  27. Further research is needed to investigate the possibility of positive sentences with negative QUDs and their specific contextual requirements. If it turns out that (67) (i.e., IF passed) involves a negative QUD, as suggested by Clemens Mayr, and ordinary question-answer pairs are not constrained by the Focus Principle as stated in (64), we can still maintain the current analysis, by directly building a version of (64) into the semantics of ye. Specifically, we can add into the lexical entry of ye an additional requirement stating that \([\!\![\mathit{ye}_{C} S ]\!\!]^{g}\) is defined only if QUD \(\subseteq [\!\![S ]\!\!]_{\mathrm{alt}}\). By doing so, we can preserve the asymmetry predicted by the Focus Principle solely for wh-ye sentences.

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Acknowledgements

I am very grateful to the editor Clemens Mayr and the anonymous reviewers for their invaluable feedback and guidance, which greatly improved the paper. I also thank Yanyan Cui, Xiaolei Fan, Daniel Hole, Fengkui Ju, Shumian Ye, Linmin Zhang, and Sha Zhu for their valuable comments and suggestions. Support from the grant (22&ZD295) of the National Social Science Fund of China is acknowledged.

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  1. Department of Foreign Languages and Literatures, Tsinghua University, Beijing, China

    Mingming Liu

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Liu, M. Additivity, scalarity and Mandarin Universal wh’s. Nat Lang Semantics 31, 179–218 (2023). https://doi.org/10.1007/s11050-023-09207-y

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