West Coast Conference on Formal Linguistics (WCCFL) (38th : 2020)

When superlative modifiers and quality superlatives are twins Yi-Hsun Chen 2020

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When superlative modifiers and quality superlatives are twins  Yi-Hsun Chen Nanjing University  West Coast Conference on Formal Linguistics (WCCFL38)  March 6, 2020 1 Outline  The morpho-semantic puzzle  The ideas  A formal proposal  Explaining the morpho-semantic puzzle  Concluding remarks     2      The morpho-semantic puzzle   3 A long-standing puzzle  Why do focus adverbs such as at least/ at most and at the tallest/ at the heaviest in English involve gradable adjectives and the superlative morpheme in their morphology?     (1)  a. Adam drank the most/ the least water.         b. Adam at most/ at least won a [silver]F medal.  (2)  a. (Of the three people) Bill is the tallest.         b. Bill is [170]F centimeters at the tallest. (3)  a. (Of the three people) Bill is the heaviest.        b. Bill is [60]F kilos at the heaviest. 4 Morphology I – Mandarin Chinese  The same expression consisting of the superlative morpheme zui and a quality adjective such as zhong ‘heavy’, is used as quality superlatives and superlative modifiers.   (4)  Quality Superlatives (QSs)        Liubei    zui-zhong.        Liubei    SUP-heavy        „Liubei is the heaviest.‟  (5)  Superlative Modifiers (SMs)           Liubei    zui-zhong     [liushi]F gongjin.         Liubei    SUP-heavy   sixty       kilo         „Liubei is sixty kilos at the heaviest.‟  5 Morphology II – Mandarin Chinese  A list of Chinese SMs and their superlative twins (not exhaustive)    zui-chang „the longest‟ or „at the longest‟   SUP-long    zui-duan „the shortest‟ or „at the shortest‟  SUP-short   zui-chao „the earliest‟ or „at the earliest‟   SUP-early   zui-wan „the latest‟ or „at the latest‟  SUP-late   zui-gao „the highest‟ or „at the highest‟   SUP-high   zui-di „the lowest‟ or „at the lowest‟  SUP-low 6 Morphology III –  Beyond Mandarin Chinese and English  Across languages, SMs involve degree morphology and quality adjectives in general.  A sample list (not exhaustive):   Chinese:  zui-gao;  zui-ai    English:  at the tallest;  at the shortest  Indonesian: paling-tinggi; paling-pendek  Japanese:  takaku-temo;  hikuku-temo  Korean:  khe-to;  cak-ato  Russian: ne vy-she;  ne ni-zhe  Vietnamese: cao-nhat;  thap-nhat 7 Semantics I –  Association with Measure Phrases  SMs with quality adjectives must associate with a scalar element (typically a measure phrase) on the scale of the involved quality adjective. (6)   a.  Liubei    zui-zhong     [liushi]F  gongjin.              Liubei    SUP-heavy   sixty        kilo              „Liubei is sixty kilos at the heaviest.‟ „         b. Liubei    zui-gao      [yi-bai-ba-shi]F               gongfen.                 Liubei    SUP-tall    one-hundred-and-eighty centimeters             „Liubei is 180 centimeters at the tallest.‟ (7)  a. Q: How heavy is Adam?                       A: Adam is [sixty]F kilos at the heaviest.   Superlative Modifier        b. Q: Of Adam, Bill & Chris, who is the heaviest?             A: Adam is the heaviest.            Superlative 8 Semantics II – A Fixed Scale  SMs formed with quality adjectives are restricted to the scale associated with the involved gradable adjective;   In contrast, those with quantity adjectives (e.g., at least/ at most) are compatible with varieties of scales.    SMs formed with quality adjectives (8)  a. This door is [forty]F centimeters at the widest.        Width        b. The natural life of a hen is [seven]F years, at the oldest. Age        c. Adam must be away by [eleven]F, at the latest.    Lateness        d. This rope is [one]F meter, at the longest.         Length 9 Mandarin Chinese   (9)  a.  Liubei zui-zhong    [liushi]F gongjin.                     Heaviness (Weight)             Liubei SUP-heavy  sixty      kilo            „Liubei is sixty kilos at the heaviest.‟        b. Liubei zui-gao    [yi-bai-ba-shi]F               gongfen.   Tallness (Height)            Liubei SUP-tall  one-hundred-and-eighty centimeters            „Liubei is 180 centimeters at the tallest.‟        c.  Liubei zui-wan   [ba]F-dian       likai.                   Lateness (Temporal)             Liubei SUP-late  eight-o‟clock leave              „Liubei will leave at eight o‟clock at the latest.‟        d.  Zhe-bu-dianyin zui-chang  [san]F-ge-xiaoshi.    Duration (Temporal)             This- CL-movie SUP-long  three- CL-HOUR             „This movie lasts for three hours at the longest.‟    10 Variety of Scales – At least/ At most (10)  Numerical Scales (e.g., …4 3 2…)          John at least/ at most wrote [three]F books. (11)  Plurality Scales (e.g., abc  ab a, b)          John at least/ at most invited [Adam and Bill]F. (12)  Lexical Scales (e.g., gold silver bronze)          John at least/ at most won a [silver]F medal. (13)  Pragmatic Scales (e.g., cherries apples bananas)          John at least/ at most bought [apples]F.  11 Semantics III – The Bounding Property  The prejacent (the associate) is made as the upper bound among the set of focus alternatives.   (14)    Liubei  zui-zhong    [liushi]F gongjin.                    Liubei  SUP-heavy  sixty      kilo            „Liubei is sixty kilos at the heaviest.‟  60 kilos is the upper bound on Liubei‟s weight (at the heaviest)  (15)   Liubei  zui-gao    [yi-bai-ba-shi]F               gongfen.            Liubei  SUP-tall  one-hundred-and-eighty centimeters           „Liubei is 180 centimeters at the tallest.‟  180 cm is the upper bound on Liubei‟s height (at the tallest) 12 The Bounding Property – At least/ At most (16)  Numerical Scales (e.g., …4 3 2…)          John at least/ at most wrote [three]F books. (17)  Plurality Scales (e.g., abc  ab a, b)          John at least/ at most invited [Adam and Bill]F. (18)  Lexical Scales (e.g., gold silver bronze)          John at least/ at most won a [silver]F medal. (19)  Pragmatic Scales (e.g., cherries apples bananas)          John at least/ at most bought [apples]F.  13 Interim Summary  Some semantic properties of SMs with quality adjectives:   Association with measure phrases   A fixed scale (the dimension of the relevant quality adjective)  The bounding property      (the associate is the upper bound among the alternatives)  The morpho-semantic puzzle:  How exactly is the semantics of SMs such as zui-zhong ‘at the heaviest’ connected to its  morphology?  Why do these focus particles (SMs) involve degree morphemes and quality adjectives in their morphology cross-linguistically?  14      Main Ideas     15 Main ideas  The degree morphology and quality adjectives involved in SMs (e.g., zui-zhong/ at the heaviest)   NOT a morpho-semantic coincidence in natural language;  Deeply connected with the semantics.   More than one strategy mapping out the morpho-semantics of superlative modifiers (e.g., Japanese/ Korean and Russian; a.o.).  In this talk, I focus on the superlative strategy in Chinese (see also Indonesian and Vietnamese; cf. English).    16 Three morpho-semantic pieces  The morpho-semantics of zui-zhong has three pieces.   The quality adjective zhong ‘heavy’ can order sets of individuals (e.g., individuals who are 61 kilos, individuals who are 60 kilos, individuals who are 59 kilos, etc.) with respect to how much they weigh, along the dimension of heaviness;.  The superlative component:  • A strict comparison relation between the prejacent and its alternatives. • A domain restrictor, structurally embedded under an existential operator E-OP.   The (covert) existential operator E-OP: An existential statement over a anti-specific domain.   The ordering between focus alternatives is a strict comparison,  instantiating a structure of phrasal comparatives.  17      A Formal Proposal     18 The internal structure of zui-zhong ‘at the heaviest’  (20)       zui-zhong (C)    E-OP   SupP            Sup      AdjP           zui   zhong 19 Compositionality –  The quality adjective  (21) ⟦zhong⟧ = λd.λP.μheavy(d)(P)  <d, <<e, t>, t>>  The traditional entry (of  <d, <e, t>>):      ⟦zhong⟧ = λd.λx.μheavy(d)(x)   A generalized entry (of <d, <η, t>>, where η could be e or <e, t>):      ⟦zhong⟧ = λd.λα.μheavy(d)(α)   (22)  The semantics of measure phrases          ⟦luishi gonjin⟧ = λx.μkilos(x) = 60   <e, t> (See the literature on measure classifiers and pseudo-partitives;  Li 2013; Rothstein 2017; cf. Scontras 2014, 2017)  20 Compositionality –  The superlative component     SupP   Sup      AdjP  zui      zhong  (23) ⟦zui⟧ = λG<d, <et, t>>λC<et, t>λP<e, t>.         Q[QCQ ≠ P  max(λd.G(d)(P)) > max(λd.G(d)(Q))]   (24) ⟦SupP⟧ = λC<et, t> λP<e, t>.         Q[QCQ ≠ P  max(λd. μheavy(d)(P))  > max(λd. μheavy(d)(Q))]  For all the alternative properties Q non-identical to the prejacent,  they are ranked lower than the prejcent. 21 The internal structure of zui-zhong  The whole superlative component, serving as a domain restrictor, is structurally embedded under an (covert) existential operator: E-OP.  The internal structure of zui-zhong ‘at the heaviest’:  (25)  [E-OP  [SupP  zui [AdjP zhong]]]  The semantics of E-OP  (26) ⟦E-OP⟧w, c           = λSUP<<et, t>, <et, t>>λC<et, t> λP<et>.λx<e>.  r[rC  r(x)  SUP (C, P)]  There is one alternative (a property) r in the domain (i.e., CSUP) such that the property r holds true of the individual x.  22 Compositionality –  The morpho-semantics of zui-zhong        zui-zhong (C’)   E-OP  SupP    Sup  AdjP    zui  zhong   (27) ⟦ zui-zhong(C’)⟧ =           λP<et>.λx<e>.r[rC’  r(x)      Q[QC’Q ≠ P  max(λd. μheavy(d)(P))        > max(λd. μheavy(d)(Q))]]  There is one property r in the domain (i.e., CSUP) such that the property r holds true of the individual x.   23      Explaining the morpho-semantic puzzle     24 Association with Measure Phrases (28)  Liubei zui-zhong [liushi]F gongjin.        „Liubei is sixty kilos at the heaviest.‟   The semantics of focus from Rooth (1985, 1992, 1996) (29)  a. LF: [Liubei  [zui-zhong(C) [[[liushi]F gongjin]~C]]]          b. α ~C is defined iff    ⟦α⟧ o  C α‟[α‟≠α  ⟦α‟⟧o  C]  C ⟦α⟧f          c. ⟦(28)⟧ = 1 iff    ∃r[r∈C ∧ r(Liubei) ∧ ∀Q<e,t> [Q ≠ λx.μkilo(x)≥60 ∧ Q ∈ C     → max(λd.μheavy(d)( λx.μkilo(x)≥60)) > max(λd.μheavy(d)(Q))]          d. CSUP = {60 kilos, 59 kilos, 58 kilos, …etc.} 25 A Fixed Scale  SMs formed with quality adjectives are restricted to the scale associated with the involved gradable adjective;  (30) ⟦ zui-zhong(C’)⟧ =           λP<et>.λx<e>.r[rC’  r(x)      Q[QC’Q ≠ P  max(λd. μheavy(d)(P))        > max(λd. μheavy(d)(Q))]]  The restriction follows from the current analysis straightforwardly: the semantics of the involved quality adjective plays a role.  Prediction 1: Those adjectives with no conventional measure phrases   CANNOT participate in the formation of SMs. Prediction 2: Exactly what adjectives participate in the formation of   SMs may be subject to cross-linguistic variation.  26 The bounding property of SMs Traditional wisdom: it is done by a non-strict comparison relation. (31) The degree approach (e.g., Nouwen 2010, Kennedy 2015)         a. ⟦at least⟧ = λm<d> λP<d, t>. max{n | P(n)}  m         b. ⟦at most⟧ = λm<d> λP<d, t>. max{n | P(n)}  m  (32) The discourse-based approach          a. ⟦at least (C)⟧ w, g = λp<s, t>.q [qC  q(w)  q i p]         b. ⟦at most (C)⟧ w, g = λp<s, t>.q [qC  q(w)  q i p]  E.g., Coppock & Brochhagen 2013, among others 27 The bounding property of SMs  The non-strict comparison raises many questions:  What is the nature of the non-strict comparison relation?  Where does the non-strict comparison come from?   Is it a semantic primitive or a derived result?    A superlative typically involves a strict comparison:   (33)  Adam climbed the highest mountain.  Relative reading (e.g., Heim 1999, Sharvit & Stateva 2002, a.o.):  Adam climbed a mountain higher than anyone else did. y[yC  y ≠ adam  max(λd.z[mountain(z)  high(z)d   adam climbed z]) > max(λd.z[mountain(z)  high(z)d   y climbed z]) 28 The bounding property of zui-zhong The current analysis:   The non-strict comparison relation is derived from focus presuppositions combining with the superlative component. (34) a. ⟦ zui-zhong (C)⟧ =    λP<et>.λx<e>.r[rC’  r(x)      Q[QC’Q ≠ P  max(λd. μheavy(d)(P))        > max(λd. μheavy(d)(Q))]]                    b. α ~C is defined iff   ⟦α⟧ o  C α‟[α‟≠α  ⟦α‟⟧o  C]  C ⟦α⟧f         c. CSUP: {the prejacent α, the lower alternatives of α}         d. There is one property r in the domain (CSUP) such that the   property r holds true of the individual x. 29 Concluding Remarks - I  More than one morpho-semantic mapping of SMs:   Quality adjectives plus even-if (e.g., Japanese and Korean)           a. omoku-temo „at the heaviest‟   b. karuku-temo „at the lightest‟               heavy-even.if                                light-even.if  Quality adjectives plus comparative morphemes (e.g., Russian)     a. ne vy-she                                   b. ne ni-zhe         not high-CMPR                             not low-CMPR         „at the highest‟                               „at the lowest‟  Not every language has SMs formed with quality adjectives:  Brazil Portuguese, Italian, Romanian, Turkish, etc.           Adam is 170 cm at the tallest   Adam is at most 170 cm.  30 Concluding Remarks - II  Constraints on the formation of SMs with quality adjectives  Not every quality adjective participates in the formation of SMs  Mandarin Chinese:  #zui-congming;  #zui-keai  English:          #at the smartest; # at the cutest Similar facts holds in other languages (Japanese, Korean, etc.)  English SMs seem restricted to the form with the bound superlative morpheme –est.   #at the most expensive   cf. at the cheapest Fact 1: The Mandarin counterpart is well-formed: zui-gui  Fact 2: Indonesian has both free and bound superlative morphemes participating in the formation of SMs: parling tinggi vs. ter-tinggi  31 Concluding Remarks - III  A fundamental split between researchers on the semantics of measure phrases  In the study of measure classifiers/ pseudo-partitives: they denote a property, of type <e, t> (Li 2013; Rothstein 2017; among others)  In the study of gradable adjectives/ comparatives: they are degree terms, of type d or its degree variants (Kennedy 1999; Rett 2008).    It is highly undesirable to claim that all measure phrases are homophones, systematically ambiguous between a meaning of type <e, t> and one of type d, even within one language, say, Mandarin.  How to connect one meaning with another is an important task. But see Scontras (2014, 2017) for a degree-as-kind suggestion.    32 Concluding Remarks - IV  Formal tools developed in the studies of gradability can be applied to those of scalarity.  Greenberg (2016, 2017) proposes a gradability-based analysis of English even.   In the current study, SMs make a case as well. What‟s more, the degree morphology is obviously part of these focus operators.   The non-strict comparison relation is NOT a semantic primitive, but derived from focus presuppositions and the superlative meaning (encoding a strict comparison).   33      Thank you!     34 Acknowledgment I am very grateful to Peter Alrenga, Rajesh Bhatt, Simon Charlow, Gennaro Chierchia, Veneeta Dayal, Yoshitaka Elewine, Hadas Kotek, Haoze Li, Chen-Sheng Luther Liu, Chris Kennedy, Manfred Krifka, Jon Ander Mendia, Marcin Morzycki, Doris Penka, Roger Schwarzschild, Yasu Sudo, Kristen Syrett, Yimei Xiang, and the audiences at CLS54 for valuable comments and constructive suggestions on my previous work of the decomposition of superlative modifiers formed with quantity adjectives.  Special thanks to my dear informants, friends and colleagues:  Deepak Alok (on Hindi and Maghi data), Woojin Chung (on Korean data), Diti Bhadra (Bangla), Vera Gor (on Russian data), Luca Iacoponi (on Italian data), Kunio Kinjo (on Japanese data), Livia Camargo Tavares Souza and Matt Barros (on Brazilian Portuguese), U ̈mit Atlamaz and Yaǧmur Saǧ (on Turkish data). Teodora Mihoc (on Romanian data). I also thank Hazel Mitchley and Lydia Newkirk for valuable discussions and constructive comments on English sentences collected in this work.  35 Selected References  Büring, D. (2008). The least at least can do. In Proceedings of the 26th meeting of West Coast Conference         on Formal Linguistics (WCCFL 26), pp. 114–130. Coppock, E., & Beaver, D. (2014). Principles of the exclusive muddle. Journal of      Semantics, 31, 371 – 432.  Coppock, E., & Brochhagen, T. (2013). Raising and resolving issues with scalar modifiers. Semantics and       Pragmatics, 6(3), 1–57. Geurts, B., & Nouwen, R. (2007). At least et al.: The semantics of scalar modifiers.  Language, 83(3),        533–559. Greenberg, Y. 2016. A novel problem for the likelihood-based semantics of even. Semantics and        Pragmatics 9: 1–28. Greenberg, Y. 2017. A revised, gradability-based semantics for even. Natural Language Semantics 26(1):      51–83. Kennedy, C. (2015). A “de-fregean” semantics (and neo-gricean pragmatics) for modified and unmodified       numerals. Semantics & Pragmatics, 8(10), 1–44. Mendia, J. A. (2016). Focusing on scales. In Proceedings of the 46th meeting of North East Linguistic Society      (NELS 46) (Vol. 1, pp. ) Amherst: GLSA. Nouwen, R. (2010). Two kinds of modified numerals. Semantics and Pragmatics, 3(3), 1–41. Nouwen, R. (2015). Modified numerals: The epistemic effect. In Luis Alonso-Ovalle & Paula Menéndez-Benito      (eds.), Epistemic Indefinites: Exploring modality beyond the verbal domain, Oxford: Oxford University Press. Rooth, M. (1985). Association with focus. Ph.D. Thesis, University of Massachusetts at Amherst.  Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics, 1(1), 75–116. 36 

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