Abstract
Superlative modifiers (SMs) are known to demonstrate an ambiguity between an epistemic reading (EPI) conveying speaker ignorance and a concessive reading (CON) conveying speaker concession. Such EPI-CON ambiguity has often been taken, implicitly or explicitly, to be a lexical coincidence. While there may be some justification for such a position when a single language is considered, we argue for an intrinsic connection between the two readings based on cross-linguistic considerations. This paper focuses on English at least and Mandarin zhi-shao as representative of superlative modifiers across a wide range of languages to propose a unified account of the two readings. The proposal builds on Biezma (2013) in relying on the role of focus and scalarity in developing a unified semantics for the two readings, but differs in capitalizing on the fact that cross-linguistically superlative modifiers use the same morphological formants as quantity superlatives. It also follows Biezma (2013) in taking pragmatic factors as crucial in deriving the variation between EPI and CON readings. Elaborating on her account, it offers a more nuanced picture of the ways in which EPI is sensitive to the question of informativity while CON relates to issues of evaluativity. The paper shows how the proposed semantics and pragmatics account for several well-known properties of superlative modifiers. It ends by noting several open issues in the literature on this topic that the current proposal sheds new light on.
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Notes
Kay (1992: 311) distinguishes three uses of at least in English: a scalar use, an evaluative use and a rhetorical use. The three uses are illustrated in (i).
(i)
a.
Mary received calls from at least three soldiers.
Scalar
b.
At least, this one is cooked.
Evaluative
c.
I see her every day, at least when I’m in town.
Rhetorical
Kay’s scalar use corresponds to N&R’s EPI and his evaluative use corresponds to N&R’s CON. This paper is concerned with these two uses of at least and its cross-linguistic counterparts. I believe that the analysis to be proposed in this paper can be extended to the rhetorical use but I do not make specific claims about it here.
Abbreviations: acc for accusative case; asp for aspect marker; cl for classifier; mod for modification marker; nom for nominative case; past for past tense; sfp for sentence-final particle; sup for superlative morpheme; top for topic marker; 3sg for third person singular.
Although both zui-shao and zhi-shao can convey the concessive reading, the latter is much more frequently used with respect to the concessive reading. This may be the source of an anonymous reviewer’s comment that zui-shao lacks the CON reading. The reviewer also notes that zh-ishao cannot be used as a quantity superlative. I address this in Sect. 3.3 when we look at further issues related to the morphology-meaning mapping.
I thank an anonymous reviewer for bringing (9a) to my attention. The sentence in (9b) was found on a Google search.
In English, a focus associate typically bears prosodic prominence, with the so-called A-accent (see e.g., Jackendoff, 1972; Büring, 2003; Beaver and Clark, 2008: chapter 2). Thus, (10a) and (10b) are not only truth-conditionally different, they are also prosodically distinct: it is the noun Bill in (10a) that bears the pitch accent, while it is the verb phrase invited Bill as a whole that bears the pitch accent in (10b).
An anonymous reviewer points out that the stress may fall on the particle at least itself and wonders whether the proposed analysis can capture the pattern of stress in sentences with at least. Unfortunately, the current study, like some of the previous studies of focus adverbs, does not delve into the issue of stress pattern concerning the interface of phonology-semantics, and thus I do not have much to say here. However, it is certainly an important line of research concerning whether the two readings can be further teased apart based on the stress pattern of at-least sentences. We may then have not only a syntactic cue (the syntactic position of at least; see Sect. 3.1) but also a prosodic cue (the stress pattern) to further distinguish the two readings. I thank the reviewer for raising the question of stress pattern.
To my knowledge, the fact that at least demonstrates TSE and BSE on both readings has not been documented before, and exactly how and why TSE and BSE arise with at least has thus not been fully explored in previous studies.
Although both studies assume a covert epistemic modal in the semantics of English at least, N&R crucially differs from Geurts and Nouwen (2007). The former takes ignorance to be due to a conventional implicature, while the latter takes it to be part of the truth-conditions. We will return to this point in Sect. 2.3.1.
For cases where the prejacent is not a proposition, I suggest the following entry, which can be obtained by the Geach Rule (Jacobson 1999).
(i)
\( \llbracket {at \, least} \rrbracket^{w,c} = \lambda \alpha_{ < a, < s,t > > }\dot \lambda \beta_{ < a > } \exists \gamma [\gamma\in \mathrm{SUP}(C, \, \alpha (\beta )) \wedge \gamma_{w} ] \)
See Coppock and Brochhagen (2013: (21)) for a similar proposal for mediating between propositional and non-propositional only and at least.
I am very grateful to an anonymous reviewer for pointing out some problems with the semantics of at least in an earlier version of the paper.
The meaning of SUP introduced here as a domain restrictor of at least is essentially the same as the meaning of superlatives discussed in Heim (1999), except that instead of enforcing universal quantification over the set of elements β compared with α, we use lambda-abstraction to create a set serving as the domain for at least.
The traditional analysis of English even invokes the scale of likelihood. However, this traditional view has been recently challenged by Greenberg (2016, 2018). Specifically, Greenberg (2016, 2018) argues that even invokes a contextually-given scale and then gives a gradability-based analysis of even. In this spirit, this paper shares a similar line of research in applying formal tools from previous studies on gradability to the phenomena of scalarity shown by SMs.
I use the logical form at least (C) to indicate the fact that at least contains the domain argument C.
As pointed out by two anonymous reviewers, the proposed analysis shares some features with the proposal in Coppock and Brochhagen (2013). However, the empirical issues covered are distinct. Coppock and Brochhagen focus on the EPI reading and use Inquisitive Semantics to account for it. My focus here is on the possibility of EPI and CON readings cross-linguistically. It is not clear to me that their account extends straightforwardly to CON readings. They also do not discuss the end-of-scale effects that I discuss in Sect. 2.2. The perspective I take on them would have to be incorporated into C&B's account, for both EPI and CON, in order to account for them. A more pointed comparison between the current proposal and theirs, unfortunately, lies outside the scope of this paper.
There are other, possibly more appropriate, ways of characterizing the contribution of an assertion as a discourse move that leads to an update of the context set when the discourse move is accepted by the discourse interlocutors (e.g., Farkas and Bruce 2010, among others).
The interaction between focus particles and quantifiers of individuals is more complicated than it is reported here. For example, English only does not seem to be compatible with the quantifier most or many, either: #John only saw most/ many students. Chen (2008) observes that the use of the Mandarin particle dou is felicitous only when the assertion meets or exceeds the speaker’s expectation about the core predication. Crucially, she suggests that the content about speaker’s expectation is a presupposition encoded by dou; moreover, it is considered as the opposite case of what is presupposed by English only: only three students came [the speaker’s expectation: more than three students would come]. Thus, the use of English only triggers an expectation about “more”, while the use of Mandarin dou triggers an expectation about “fewer”. The key point is that the presupposition of a given focus particle may also play a role in the interaction with quantifiers, besides the asserted content.
Note that appealing to a two-membered scale may suggest that either the BSE or TSE will be violated no matter which member sets the value of the prejacent: <no medal, some medal>.
An anonymous reviewer suggests that the CON reading may convey a kind of partial satisfaction. According to the reviewer, in the mentioned dating scenario, as far as the speaker is sure that the person under discussion is tall, he/ she can comfort himself/ herself and say ‘At least she is tall’, even without having more information. First, to my understanding, the feeling of partial satisfaction is essentially the “settle-for-less” flavor in the terminology of Nakanishi & Rullmann (2009), which has been identified as the hallmark of the CON reading. Second, if the CON reading of at least signals the speaker’s partial satisfaction (by the reviewer’s terminology), it in turn means that the speaker is not fully satisfied in the given situation. More importantly, by hearing the utterance “At least she is tall”, the hearer is entitled to ask in more details about which part the speaker is not satisfied; crucially, that very piece of information is known by the speaker (i.e., this is the part where the relevant higher alternatives are known to be false by the speaker in a given discourse).
An anonymous reviewer asks how speaker A knows that it is a case of concessive at least in speaker B’s assertion. There is one important linguistic cue here. The position of at least provides a syntactic cue: EPI is never available in a clause-initial position (see N&R and Sect. 3.1).
In this paper, I assume (a) at least is adjoined to vP in the case of the preverbal at least; (b) the subject is generated at Spec, vP and thus vP is propositional (Kratzer 1996). For simplicity, I further assume that the subject reconstructs back to its base position at Spec, vP, for interpretative purposes at LF. Nothing crucial hinges on the assumption of the reconstruction, however.
Note that the semantic underpinning of fragment answers is what delivers the restriction on CON readings. Therefore, the proposal here does not depend on a particular approach to fragment answers. See Weir (2014) and references cited there for further discussion of fragment answers.
An anonymous reviewer wonders whether the CON reading of at least is relevant to speech acts. While this is an interesting line of thought, I am more inclined to treat at least as a focus adverb, under either reading. Furthermore, the restriction on only discussed below provides additional support for it.
There are five possible lexical items in Russian that can be translated as at least: kak minimum, po men’šej mere, po krajnej mere, hot’a by and hot’. The first three demonstrate the ambiguity (though they all seem to be subject to the distributional restriction, similar to English at least). The expression xotja reported in Grosz (2011) seems morphologically related to the latter two, but it is not clear whether they are the same.
Japanese semete, unlike concessive at least in English, cannot occur in a plain declarative sentence, as in (i).
(i)
*Semete
John-wa
3-ko
ringo-o
kat-ta.
Semete
John-top
3-cl
apple-acc
buy-past
‘John at least bought three apples.’
As shown in (iv), Japanese semete is strongly preferred in a desiderative sentence, i.e., sentences expressing the speaker’s wishes or needs—it almost always appears with -tai ‘want’ in declarative sentences.
(ii)
Semete
3-ko
ringo-o
kai-tai.
Semete
3-cl
apple-acc
buy-want
‘I want to at least buy three apples.
I am very grateful to an anonymous reviewer for drawing my attention to the distinction between zui-shao and zhi-shao, with respect to the use of quantity superlatives in Mandarin Chinese.
I thank an anonymous reviewer for bringing up the issue of the EPI-CON ambiguity in the absence of degree morphology and quantity adjective. It is worth noting in this connection that Greenberg (2016, 2018) argues for a gradability-based semantics for English even, even though even does not involve any degree morphology or gradable adjective.
Ihara & Mizutani (2020) recently proposes a decompositional analysis of Japanese sukunakutomo ‘at least’ in connection with its morphological makeup in concessive conditionals. Interested readers are referred to their paper for more details.
The same observation applies to disjunction, where in subsequent discourse, the content of each disjunct must be (epistemically) available to the speaker.
(i)
Context: Speaker B knows that John read Hamlet yesterday.
A: What did John read yesterday?
B: #John read Hamlet or Macbeth.
(ii)
Context: Speaker B knows that John read Macbeth yesterday.
A: What did John read yesterday?
B: #John read Hamlet or Macbeth.
For cases where the prejacent is not a proposition, I suggest the following entry, which can be obtained by the Geach Rule (Jacobson, 1999). See Coppock and Brochhagen (2013: (21)) for a similar proposal for only.
(i)
\( \llbracket {at \, most} \rrbracket^{w,c} = \lambda \alpha_{ < a, < s,t > > }\cdot \lambda \beta_{ < a > } \neg \exists \gamma[\gamma \notin SUP(C,\alpha (\beta )) \wedge \gamma_{w} ] \)
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Acknowledgements
This research grows from my dissertation, which was supported by the Mellon Fellowship from The Andrew W. Mellon Foundation and Rutgers University. Earlier versions of this work have been presented at the 48th North East Linguistics Society (University of Iceland), GLOW in Asia XI (University of Singapore) and the 40th Deutschen Gesellschaft für Sprachwissenschaft (University of Stuttgart). I would like to thank the audience at these venues for their comments and questions. I am greatly indebted to my colleagues and consultants, and I wish to thank them: Deepak Alok for Hindi/ Magahi, Matt Barros for Brazilian Portuguese, Diana Constansz Sahertian for Indonesian, Luca Iacoponi for Italian, Shiori Ikawa and Kunio Kinjo for Japanese, Woojin Chung for Korean, Vera Gor for Russian, Yaǧmur Saǧ and Ümit Atlamaz for Turkish, Minh-Hieu Phan for Vietnamese. I have also greatly benefited from discussion with Peter Alrenga, Yu Cao, Simon Charlow, Viviane Déprez, Jane Grimshaw, Haoze Li, Chen-Sheng Luther Liu, Mingming Liu, Jon Ander Mendia, Marcin Morzycki, Roger Schwarzschild, Kristen Syrett, Yimei Xiang, Beibei Xu. Finally, I would also like to thank six anonymous reviewers and the Editors of Linguistics and Philosophy for their insightful remarks and valuable questions. My special thanks go to Veneeta Dayal, whose detailed suggestions have substantially and tremendously improved the presentation and analysis in the paper. All errors of judgment, theory, and transcription, are the sole responsibility of the author.
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Chen, YH. Ignorance and concession with superlative modifiers: a cross-linguistic perspective. Linguist and Philos (2024). https://doi.org/10.1007/s10988-023-09400-6
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DOI: https://doi.org/10.1007/s10988-023-09400-6