Focus, Evaluativity, and Antonymy: A Study in the Semantics of Only and its Interaction with Gradable Antonyms (Studies in Linguistics and Philosophy, 104) 3030378055, 9783030378059

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Studies in Linguistics and Philosophy 104

Sam Alxatib

Focus, Evaluativity, and Antonymy A Study in the Semantics of Only and its Interaction with Gradable Antonyms

Studies in Linguistics and Philosophy Volume 104

Series Editors Cleo Condoravdi, Cordura Hall, Stanford University, Stanford, CA, USA Louise McNally, Translation and Language Sciences, Pompeu Fabra University, Barcelona, Spain Zoltan Szabo, Department of Philosophy, Yale University, New Haven, CT, USA Editorial Board Members Johan van Benthem, Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands Gregory N. Carlson, Department of Linguistics, University of Rochester, Rochester, NY, USA David Dowty, Department of Linguistics, The Ohio State University, Columbus, OH, USA Gerald Gazdar, School of Cognitive & Computing Sciences, University of Sussex, Brighton, UK Irene Heim, Department of Linguistics & Philosophy, Massachusetts Institute of Technology, Cambridge, MA, USA Ewan Klein, Division of Informatics, ICCS, Edinburgh, UK Bill Ladusaw, Department of Linguistics, Cowell College, University of California, Santa Cruz, CA, USA Terence Parsons, Department of Philosophy, University of California, Irvine, CA, USA

Studies in Linguistics and Philosophy publishes monographs and edited volumes that focus on issues related to structure and meaning in natural language, as addressed in the semantics, philosophy of language, pragmatics and related disciplines, in particular the following areas: • philosophical theories of meaning and truth, reference, description, entailment, presupposition, implicatures, context-dependence, and speech acts • linguistic theories of semantic interpretation in relation to syntactic structure and prosody, of discourse structure, lexical semantics and semantic change • psycholinguistic theories of semantic interpretation and issues of the processing and acquisition of natural language, and the relation of semantic interpretation to other cognitive faculties • mathematical and logical properties of natural language and general aspects of computational linguistics • philosophical questions raised by linguistics as a science. This book series is associated with the journal Linguistics and Philosophy: http:// www.springer.com/journal/10988

More information about this series at http://www.springer.com/series/6556

Sam Alxatib

Focus, Evaluativity, and Antonymy A Study in the Semantics of Only and its Interaction with Gradable Antonyms

Sam Alxatib The Graduate Center CUNY, New York, NY, USA

ISSN 0924-4662 ISSN 2215-034X (electronic) Studies in Linguistics and Philosophy ISBN 978-3-030-37805-9 ISBN 978-3-030-37806-6 (eBook) https://doi.org/10.1007/978-3-030-37806-6 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Ju.

Acknowledgements

Many friends and colleagues helped me prepare this book, many without knowing it. Thank you all: two anonymous reviewers for the Studies in Linguistics and Philosophy (SLAP) series, the SLAP series editors, Chris Barker, Ellen Broselow, Lucas Champollion, Gennaro Chierchia, Luka Crniˇc, Kai von Fintel, Danny Fox, Yael Greenberg, Martin Hackl, Irene Heim, Elena Herburger, Natasha Ivlieva, Joshua Knobe, Richard Larson, Rafael Nonato, Rick Nouwen, Robert Pasternak, Orin Percus, Daniele Panizza, Sasha Podobryaev, Jacopo Romoli, Philippe Schlenker, Roger Schwarzschild, Yael Sharvit, Benjamin Spector, Robert Stalnaker, Anna Szabolcsi, Yasutada Sudo, E. Cameron Wilson, and audiences at the NYU Semantics Group, Amsterdam Colloquium 21, and SUNY Stony Brook.

vii

Contents

1

2

3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Three Illustrations of Empirical Claim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 First Illustration: Betting Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Second Illustration: In Fact, and Downward Entailing Contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Third Illustration: Only as a Weakener . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Theoretical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Book Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 5 5 7 9 9 11 15

Only and Its Inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Chapter Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Semantics of Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 The Exclusive Inference of Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Interim Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Only and Its Scalar Presupposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Only and the Ban Against Its Vacuous Use . . . . . . . . . . . . . . . . . . . . 2.2.5 The Scalar Presupposition as the Ban Against Vacuous Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 23 24 28 37 38 44

The Positive Morpheme and Its Interaction with Only . . . . . . . . . . . . . . . . . . 3.1 Chapter Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Background: Many and Few as Gradable Adjectives . . . . . . . . . . . . . . . . . . 3.3 POS and the Evaluativity of Many and Few . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 N as a Modal in the Semantics of POS . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Interim Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 The Interaction of POS and Only: Answering the Missing Readings Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Theory 1 of the Only-POS Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Prediction: Negation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 53 54 57 62 65

48 51

66 68 71 ix

x

4

Contents

3.6.2 Prediction: Modals and Their Monotonicity. . . . . . . . . . . . . . . . . . . 3.6.3 Section Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Theory 2 of the Only-POS Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 The Antonym-Pair Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 78 79 84 85

The Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Chapter Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Scoping Account: Decomposing Modified Numerals . . . . . . . . . . . . 4.3 The Closure Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Van Benthem’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Bypassing van Benthem’s Problem by Constraining Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Bypassing van Benthem’s Problem by Blind Exclusion . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 The Existence Inference and the Status of Only’s Prejacent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 A Remark on the Distribution of Existentially-Closed Parses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Comparison with Other Accounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 POS as Comparative: Density?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Bonomi and Casalegno (1993) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Beck (2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Extension to Rarely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89 89 90 98 100 102 110 115 117 118 119 119 120 125 129 132

5

Only if, Its Interaction with POS, and Its Scalar Presupposition. . . . . . . . 5.1 Chapter Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Only if as Only and a Conditional Prejacent . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Only if and POS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Only if and Only’s Scalar Presupposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

137 137 139 146 148 150

6

Conclusions and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Book Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Comparatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Antonymy and the -er Morpheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Subsethood in Measure-Phrase Comparatives. . . . . . . . . . . . . . . . . 6.2.3 Innocent Exclusion and Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 LessP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 At Least and At Most?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Alternativehood of Disjuncts and Association with Only. . . . . 6.4 Another Case: Recently . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

153 153 156 157 158 162 166 167 168 168 175

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Chapter 1

Introduction

Abstract It is shown that the focus particle only behaves unexpectedly with a class of expressions, which are labeled here as “negative antonyms”. The interaction is demonstrated in detail, and its theoretical relevance is discussed. The theoretical proposal is described informally, with short synopses of later chapters.

The linguistic problem that makes this book is specific. It is about the semantic interaction between the focus particle only and a class of expressions that I will call negative antonyms. The interaction, as I will show in informal terms in this chapter, is unexpected given what is standardly assumed about the meaning of only. But what I aim to show in addition, partly in this chapter but also in the remainder of the book, is that this apparently specific problem has implications that pertain to more than just the paradigm that demonstrates it. The puzzling interaction, and the account that I will develop in the coming chapters, has consequences on (i) the formal view of only’s meaning, in particular the conditions that (we feel) govern the particle’s use, (ii) the meaning of bare gradable terms, the so-called “positive” gradable expressions, and the way in which these terms semantically interact with only, (iii) the connection between monotonicity of inference and scalarity, and (iv) the relation between the structure and the interpretation of upper-bounded degree operators, in light of the famous theoretical puzzle currently known as van Benthem’s problem (van Benthem 1986). Each of (i–iv) will play a crucial role in the final proposal that I will present in response to the puzzle. In what follows, I will introduce the central problem of the monograph, and later outline the structure of the presentation. I have kept the description of the problem, and the description of its theoretical context, as informal as I could manage without affecting its essentials. Repeating these with more up-to-date technical terms ought not to change the significance of the data to the theory, nor to the broader theoretical interests that I mentioned above. I will return to those below.

© Springer Nature Switzerland AG 2020 S. Alxatib, Focus, Evaluativity, and Antonymy, Studies in Linguistics and Philosophy 104, https://doi.org/10.1007/978-3-030-37806-6_1

1

2

1 Introduction

1.1 Overview Most accounts of the semantics of only converge on the claim, which we may leave imprecise for the moment, that the particle communicates its “prejacent”, and communicates the negation of the relevant alternatives to that prejacent. The prejacent to only is the result of removing the particle, and its prosodic effects, from the sentence of interest; the alternatives to the prejacent are those expressions that are nearly identical to it, differing only in the part that carries focus. Consider (1).1 (1)

a. Jess only did some of the homework b. Prejacent: Jess did some of the homework c. Stronger alternative(s) to prejacent: Jess did all of the homework

Intuitively, (1a) clearly implies (1b), that Jess did some of the work, and also implies the negation of (1c), that he did all of it. In contemporary research, beginning in Horn (1969), this is thought to result from a multi-tiered semantic core of only: the presupposition that the prejacent is true, and the assertion that the stronger alternatives to it are false. Roughly: [Only φ] presupposes φ, and asserts ¬ψ for every stronger alternative ψ to φ. (To be revised)

(2)

This characterization also captures the correct meaning of (3a), assuming higher numerals to be stronger than lower ones: (3)

a. Only two cars were parked in the lot b. Prejacent: Two cars were parked in the lot

1A

generalization along these lines was reportedly identified as long ago as the thirteenth century, by Peter of Spain in his Tractatus Exponibilim, and even longer ago than that by Peter Abelard (1079–1142). Horn (1996) writes that [f]or Peter of Spain [. . . ], (1a) entails the conjunction of (1b) and (1c) and thus entails each of them singly. (1)

a. Only God can make a tree. b. God can make a tree. c. No one distinct from God can make a tree.

The ‘only’ particle, solus or tantum, is an EXPONIBLE to be expounded or unpacked into ‘an affirmative copulative proposition whose first part is the same proposition without only’ — the ‘PRAEIACENS’ or PREJACENT — ‘and whose second part is a negative proposition denying the predicate of all others apart from the subject’ (Tractatus Exponibilium 21 ff, in Mullally 1945:106–7) Horn also mentions that Abelard (1079–1142) analyzes (2a) as (2b) in his Dialectica (Horn 1996, fn. 2): (2)

a. Socrates tantum est Socrates. b. Socrates est Socrates et nulla alia res est Socrates.

1.1 Overview

3

c. Stronger alternative(s) to prejacent: Three/four/· · · cars were parked in the lot (4)

[Only two cars were parked] (=(3a)) presupposes (3b), and asserts ¬(3c).

The starting point in this project is the problem posed by examples like (5–7) below: (5)

There are only (very) few surviving copies of this record.

(6)

Jess only rarely reads the newspaper.

(7)

It only takes at most an hour to finish the DVD copying.

What is the predicted meaning of, say, (5) given the findings above? The meaning should include the presupposition of the prejacent, that there are very few surviving copies of the record, and include the assertion that the stronger alternatives to that prejacent are false. But what are the stronger alternatives in this case? It is standard in the semantics literature to assume that “fewness” increases in logical strength when quantity decreases. This means that, when the focused element very few is replaced with a term that expresses even lower quantity, e.g. (speaking informally) extremely few or no, the result will be a stronger alternative. (I ask readers who are troubled with my assumption that no and never entail few and rarely to indulge me for just a moment.) Assuming this, and applying the generalization drawn from (1) to the example in (5), we would have something like (5 ): (5 )

a. There are only (very) few surviving copies of this record b. Prejacent: There are very few surviving copies of this record c. Stronger alternative(s) to prejacent: {There are no surviving copies of this record, There are extremely few surviving copies of this record}

Now, if the alternatives in (5 c) are stronger than (5 b), we expect the contribution of only in (5 a)—i.e. in sentence (5)—to negate (5 c). The resulting meaning should then be, roughly, that there are very few surviving copies of the record, and that it is false that there are none, and false that there are extremely few. In other words, the sentence should say that the record has a small number of surviving copies, and only should add that the number is not smaller than that. Let me now address the potential concern brought up above, about the assumption that no is logically stronger than few and likewise for never and rarely. On first glance few and rarely on their own seem to clearly suggest existence. How, then, can they be logically compatible with non-existence, let alone logically follow from it? The answer is that the existence inference is not part of the literal meaning, but is of a similar status to the famous exclusive meaning of or, or the negation of all in the case of some: the existence inference of few (and its analog in rarely) is a scalar implicature. Observe, for example, that while or takes its exclusive meaning in unembedded cases like (8a), it loses that inference in the scope of a negative quantifier like no one (8b), and when embedded in a yes/no question (8c). (8)

a. Charlie visited New York or Boston. ( Charlie visited NY or B but not both)

4

1 Introduction

b. No one visited New York or Boston. ( No one visited NY or B but not both) ( No one visited either NY or B) c. Did Charlie visit New York or Boston? Yes, he visited both / #No, he visited both. Similarly, the existence inference of few and of rarely, while intuitively present in positive uses like (9a, 10a), appears to disappear under negation and in yes/no questions (9b, 10b)–(9c, 10c). (9)

(10)

a. Charlie ate few donuts. ( Charlie few but some donuts) b. No one ate few donuts. ( No one ate few but some donuts) ( No one ate a small number / everyone ate many) c. Did Charlie eat few donuts? Yes, he ate none / #No, he ate none. a. Alex rarely exercises. ( Alex rarely but sometimes exercises) b. No one I know rarely exercises. ( No one I know rarely but sometimes exercises) ( Everyone I know exercises often) c. Does Alex rarely exercise? Yes, in fact he never does / #No, he never does.

Readers may disagree and find some of the allegedly missing readings available, but to my knowledge the default readings are the ones indicated. This is sufficient support for the main point that few and rarely do not entail existence in their literal semantics. I take this as given from this point onward. Turning back now to the prediction under association with only: we saw above that if no or something like is logically stronger than few, then the negations of these stronger expressions should be the content of only in examples like (5/5 a)— likewise in the case of rarely in the parallel examples. However, there are many ways of showing that this not the resulting meaning, and that only in (5), as indeed in all of (5–7), negates alternatives of higher degrees of quantity rather than logical strength. (5), for instance, demonstrably says that there is a small number of surviving copies of the record, and that there is no greater number of surviving copies than that. Note that these same truth conditions are the ones that we associate with the variant of (5) where only is removed—(5 ). The same is true of (6) and (7) as well: (5 )

There are (very) few surviving copies of this record (≈ There are only (very) few surviving copies of this record)

(6 )

Jess rarely reads the newspaper (≈ Jess only rarely reads the newspaper)

1.2 Three Illustrations of Empirical Claim

(7 )

5

It takes at most an hour to finish the DVD copying (≈ It only takes at most an hour to finish the DVD copying)

In Chap. 2 I will emphasize the significance of this near-equivalence, and use it to test the plausibility of some possible accounts of this phenomenon. My goal now is to try and convince the reader that (5–7) do not have the reading that they are predicted to have. The illustrations in the next section are intended to do this. After those, I turn to a discussion of the implications of the findings, and to an overview of the book.

1.2 Three Illustrations of Empirical Claim The first two of the three illustrations below are built on tests that in current research are used to distinguish literal semantic inferences from non-literal ones, resembling those used in the discussion above about the meanings of few and rarely. They are (1) betting scenarios and (2) in fact continuations and embeddings in downward-entailing contexts. Readers will recognize these as tests that diagnose scalar implicatures. Their use here is intended to show that what is predicted to be a semantic inference of only, its exclusive assertion, appears to behave like an implicature rather than a semantic inference. The demonstrations will contain baselines where only behaves as predicted with other scalar items, thus supporting the conclusion that something is different about the associations with few/rarely seen in (5–7). The third illustration uses only as a weakening device, and compares its acceptability as such in examples like (5–7) to examples with other scalar items. In more concrete terms, the test will show that the particle only is acceptable with a prejacent containing some as a way of disagreeing with a prior “all” claim— this is expected—but we will also see that the particle is not suited to perform the same function with a prejacent containing few, to mark disagreement with a prior “no” claim. The conclusion will be that only∼(very) few does not say not none (i.e. some), and only∼rarely does not mean not never (i.e. sometimes).

1.2.1 First Illustration: Betting Scenarios The target items in this first illustration are contexts where (i) a bet is made that S, for some sentence S, (ii) an outcome that verifies a particular truth condition, and (iii) an intuitive judgement about whether the bet on S is won or lost, given that outcome. Let us begin with a baseline. Imagine that a bet is made that (11): (11)

Alex spoke to some of the students

6

1 Introduction

Here, without any special prosodic marking, we intuitively would award the bet in scenarios where Alex spoke to all of the students, and would not award it if s/he spoke to none. The contrast tracks the contrast between the informational content that is expressed literally by the sentence, and the informational content that is inferred from other, non-literal sources.; (11) requires by its semantics that Alex speak to at least some students, but although it may, by default, suggest that Alex did not speak to all the students, this inference is not part of the literal meaning. The second part of the baseline is similar, but has some as an associate of only. The imagined bet is a bet that (12): (12)

Alex only spoke to some of the students

The judgement now is different. If it turns out that Alex spoke to all of the students, the bet in this case would be lost. This difference between (11) and (12) is of course expected given our assumption about what only means. (12) says literally that Alex did not speak to all of the students, an inference that only contributes by negating the stronger alternatives to the some-prejacent. The same comments can be repeated about the pair of sentences in (13): a bet on the only-less “weak” sentence intuitively leaves its maker open to stronger possibilities; a bet on the same sentence where the weak element is associated with only does not—it commits its maker to the condition that the stronger alternative, here always, is false. (13)

a. Jess sometimes reads the newspaper. b. Jess only sometimes reads the newspaper.

Now consider the sentence pairs in (14, 15): (14)

a. Jess spoke to very few students. b. Jess only spoke to very few students.

(15)

a. Jess rarely reads the newspaper. b. Jess only rarely reads the newspaper.

The contrasts in each of the cases is very different from the contrast in e.g. (13). Say someone bets (for whatever reason) that Jess spoke to very few students—(14a)— and suppose that in fact Jess spoke to no students at all. Then, intuitively, the bet would justifiably be won. So far this fits the pattern (few is compatible with no, as I tried to show earlier). But in the other case where the bet is made on the only-variant in (14b), the judgement does not seem to change in the same way as it did in the some/sometimes cases. While it is indisputable that a bet on only some would be lost when all holds, a bet on only very few is most likely also won when none holds. The same can be said of (15a,b). I have said “most likely also won” above because I have found some speakers to still detect a difference between (14a) and (14b): (14b) does carry a subtle existence inference, though its strength and effects in these scenarios is qualitatively different from the effect of only in the some/sometimes sentences above. I will come back to

1.2 Three Illustrations of Empirical Claim

7

this inference in Chap. 4, noting for now that, if it is present, it does not take part in only’s assertion as stronger alternatives do in other cases. The point, then, is that the predicted contribution of only, as measured by the baselines above, is not felt to be there when the particle is associated with few and with rarely.

1.2.2 Second Illustration: In Fact, and Downward Entailing Contexts Other tests of scalar implicature confirm further that there is a difference between association of only with few/rarely, and association of only with some. In this section we will see that the existence inference in [only very few] can be explicitly cancelled, and that it disappears in Downward Entailing (DE) contexts. This is unexpectedly similar to analogous sentences where only is removed, and contrasts with some: some licenses a cancellable “not all” inference which disappears in DE contexts, but in the case of [only some] the inference is not cancellable and does not disappear in DE contexts. Consider the contrast between (16) and (17). (16)

Jess only spoke to someF of the students. #In fact he spoke to all of them.

(17)

Jess only spoke to [very few]F students. In fact he spoke to none.

The oddness of the continuation in (16) is expected on the analysis of only sketched earlier: the particle semantically negates the stronger all-alternative, so the continuation where that alternative is asserted is odd. When few appears as only’s associate, we predict the continuation to the stronger proposition “no” to be equally odd, since only should semantically say that the stronger alternative is false. We find, however, that the continuation is better in this case. In continuing to build the paradigm, let us turn to sentences where the relevant constructions are placed in a DE environment, e.g. the restrictor of a universal quantifier. Everyone knows that scalar implicatures (by default) disappear in DE contexts. Though (18a) has the strengthened meaning in (18b), embedding the scalar item some in the restrictor of a universal quantifier, as in (19a), fails to license the parallel inference in (19b). (18)

a. Jess did some of the homework b. Strengthened Meaning = Jess did some but not all of the homework

(19)

a. Everyone who does some of the homework will pass the course. b. Strengthened meaning = Everyone who does some but not all of the homework will pass.

At present there is no need to explain these facts. For our purposes it is enough to observe that the implicature ordinarily associated with e.g. (18a) is not felt to

8

1 Introduction

arise when the scalar item (some) is itself placed in the restrictor of a universal quantifier, as in (19a). This implies, correctly, that the second predicate argument of the quantifier, [will pass the course], holds of those individuals who did all of their homework. In other words, the satisfaction conditions of some are felt to be more inclusive when some is embedded in the restrictor of a universal quantifier than when it appears unembedded. We will shortly examine these facts with few, but first, let us note that adding only inside the restrictor of (19), as in (20), makes a significant semantic difference. In this case only forces the some-but-not-all reading, and blocks the ‘all’ truthconditions from satisfying the restrictor clause. This is expected, because the strengthening of ‘some’ to ‘some but not all’ is in this case contributed by the exclusive component of only, rather than as a scalar implicature. (20)

Everyone who does some of the homework will pass the course. Everyone who only does someF of the homework will receive a low grade.

The first restrictor of (20) includes (intuitively) both the individuals who do some but not all of the homework, and the individuals that do all of it: they all pass. In the second restrictor, only blocks students who do all of their homework, and the restrictor is limited to just those who do part of it. The speaker says of those students that—though they pass, given the first sentence—they will receive a low grade. Let us now turn to very few. The prediction is similar to the case of some: when few is embedded in the restrictor of a universal quantifier, the implicature that negates no should disappear. We predict, then, that the restrictor is satisfied even when the stronger no-alternative is true. But importantly, we predict that this strengthening (the inference from few to some) reappear in the semantics when only is added to the restrictor, because the inference will be contributed by the particle. The example is shown in (21). (21)

Everyone who submits very few assignments will get a low grade on the course. #Everyone who submits only [very few]F assignments will pass it.

The first half of (21) says that those who submit few or no assignments will get a low grade the course. Those who submit no assignments are included because the restrictor does not semantically keep them out. In the second half, the restrictor is predicted to refer to just those who submit few but at least some assignments. The sentence says of these students that they will pass the course. The contrast between the two restrictors should be (roughly) the same as the contrast in (20): there, the instructor says that submitting some homework is enough to pass it, but failing to submit it all leads to a low grade. In (21), the intended announcement is similar: submitting a small number of assignments (few) leads to a low grade, but submitting few but not-none—i.e. few but some—is enough to pass it. Why, then, is (21) odd? Intuitively, the addition of only in the second restrictor does not seem to make narrower than the first. This indicates that both restrictors refer to the same group of students. Once again, we see evidence that placing few, or [very few], in association with only does not give rise to a meaning that excludes the stronger ‘no’ alternative.

1.3 Consequences

9

Instead, it seems that ‘only [very few]F / rarelyF ’ is in fact compatible with scenarios where the ‘no’/‘never’ alternatives are true.

1.2.3 Third Illustration: Only as a Weakener Suppose a conversation is taking place between A and B, both executives in a company. A and B are discussing the recent behavior of Jess, an employee. (22)

A: It looks like we’re gonna have to let Jess go. S/he’s been slacking off recently, and over the past two weeks s/he’s shown up late to every meeting. B: Well, let’s be fair. S/he only showed up late to someF meetings.

(23)

A: It looks like we’re gonna have to let Jess go. S/he’s been slacking off recently, and over the past two weeks s/he submitted none of the required reports. B: Well, let’s be fair. #S/he only submitted [very few]F of those reports.

B’s defense of Jess is legitimate in (22), but not in (23). If B’s sentences had the predicted meanings, given the semantic sketch of only introduced earlier, both (22) and (23) should be equally good: in both cases, B weakens A’s claim by negating the stronger alternative, all for some, and no for few, and in both cases the negations should serve to make Jess’s position seem better than A makes it out to be. Yet, only the continuation in (22) is felicitous. The same (incorrect) prediction applies to rarely. (24)

A: It looks like we’re gonna have to let Jess go. S/he’s been slacking off recently, and over the past while he always came in late. B: Well, let’s be fair. S/he only sometimesF came in late.

(25)

A: It looks like we’re gonna have to let Jess go. S/he’s been slacking off recently, and over the past while he never came in on time. B: Well, let’s be fair. #S/he only rarelyF came in on time.

1.3 Consequences The findings above show that we need to revise at least some of our assumptions about the meaning of only, and the meanings of the NAs few, rarely, etc. A number of possible moves suggest themselves. Maybe only does not generally negate stronger alternatives as we have assumed, but operates on scales that are sensitive

10

1 Introduction

to quantity.2 Or maybe only does negate stronger alternatives, but “fewness” (or “rareness” etc.) does not increase in logical strength when quantity decreases, as I have assumed, despite the evidence seen earlier. Or maybe few and rarely do increase in strength with smaller quantities/frequencies, and only does target logically stronger alternatives, but the expressions few and rarely themselves do not have the stronger terms no/none and never as formal alternatives. Later, and in detail in Chap. 4, I will present Bonomi and Casalegno (1993) as an example of the first of these possibilities—only is sensitive to quantity rather than logical strength—and Beck (2012) as an example of the second—few is not upward scalar in its lexical semantics. I do not know of analyses of the third kind, but it is not difficult to show that things are not as simple as such an analysis would suggest. In (26–27), where only’s associate appears across the verb know or the verb say, the predicted readings do arise, via the negation of stronger alternatives to few: (26)

A: It looks like we’re gonna have to let Jess go. S/he’s been slacking off recently, and we know that over the past two weeks s/he submitted none of the required reports. B: Well, let’s be fair. We only know that s/he only submitted [very few]F of those reports.

(27)

A: Jess has been slacking off recently. S/he is said to have submitted none of the required reports. B: Well, let’s be fair. S/he is only said to have submitted [very few]F of those reports.

The position that I will take in this book is that none of the possibilities described above is right after all. The correct account of the facts, I propose, is derived from observations about the “evaluativity” of only–what has sometimes been called its “scalar presupposition” or “mirative presupposition”—and observations about its interaction with gradable expressions. These crucially include not only few and rarely, but their positive antonyms many and frequently as well. I argue that the (default) oddness of associations between only and these positive antonyms, as in (28–30), provides the first clue about the unexpected behavior of (5–7), repeated below for convenience. (28)

??There are only (very) many surviving copies of this record

(29)

??Jess only frequently reads the newspaper

(30)

??It only takes at least an hour to finish the DVD copying

(5)

There are only (very) few surviving copies of this record

2 Buccola (2018)

has reported judgements where only appears not to negate stronger alternatives as it is predicted to. His examples contain sufficiency constructions, e.g. Only two eggs are enough to make this kind of cake. I do not discuss Buccola’s findings here, and leave relating them to the claims of this book to future work.

1.4 Theoretical Implications

(6)

Jess only rarely reads the newspaper

(7)

It only takes at most an hour to finish the DVD copying

11

From (28–30), we can provide an answer to what I will call the missing readings question, that is, the question why (5–7) do not mean what they are predicted to mean, given standard assumptions. The answer, informally speaking, is that only’s scalar presupposition in (5–7) and in (28–30) conflicts with the evaluativity of few and many, though as we will see in Chaps. 2 and 3, the details will lend themselves to a simpler account, where the evaluativity of only and bare gradable expressions receive a contextualistic analysis. The other half of the puzzle is the available readings question, that is, why sentences like (5–7) have a reading where only appears to target alternatives that express higher quantities. The answer, I propose, is that the prejacents in (5–7) are structurally different from what their surface forms suggest. Specifically, I propose Logical Forms where the relevant scalar term, e.g. (very) few, is existentially closed before it composes with only. In these LFs, the inferential conflict between only’s scalar presupposition and the evaluativity of many/few does not come up, with the result that only presupposes an existentially-closed prejacent—this, I will suggest, is the reason behind the weak existential inference mentioned above. More importantly, the fact that the prejacent is in effect an existential quantificational claim, it follows that its stronger alternatives will likewise denote existential quantificational claims, whose logical strength increases with greater quantity: they each say that some plurality exists whose size is greater than “few”. This leads to exclusions (by only) of propositions relating to greater quantity, thus giving us the “quantity” based reading.

1.4 Theoretical Implications When expanded and tested in detail, the sketch outlined above requires discussion of a number of important issues. The issues are in principle separable, but in the role they play in explaining our data, they are naturally connected. I expand on this in what follows. The themes that will take center stage in the presentation of this book are summarized in (31). (31)

(i) Only’s scalar/mirative presupposition, (ii) The so-called positive morpheme (POS), in particular as a “mirative” term, (iii) Van Benthem’s problem and the solution to the available readings question, and (iv) Only if, with respect to the predictions of (i) and (ii).

12

1 Introduction

Because the core of the proposal in this book is built on (31i) and (31ii) above, it will be necessary to (a) offer a working characterization of only’s so-called scalar/mirative presupposition, and (b) discuss connections between that presupposition and the semantics of POS, the silent element that many believe to come with bare occurrences of gradable expressions. I will consider two possible approaches to (a), and following that, two matching approaches to (b). In the case of (a), I will begin with the idea that only semantically makes reference to a kind of ‘neutral’ modality (cf. Klinedinst 2005, Zeevat 2008, and Beaver and Clark 2008), and later entertain the possibility of removing the modality from the particle’s semantics. On the alternative non-modal view, I propose to derive only’s scalar presupposition from two sources: contextual considerations, which constrain the space of relevant alternatives and also establish equivalence between them, and an independently motivated constraint on the use of only, namely the constraint against its vacuous use.3 The important difference between this account and the first is that, here, it is the ban against vacuous use that produces what appears to be a separate scalar presupposition, or “mirative” presupposition, of only. I offer two reasons for adopting this reductive view, each an argument from theoretical simplicity. First, since the ban against vacuous use is independently needed, and since (as I will argue) it cannot be derived from only’s scalar presupposition, it follows that using it to derive the scalar presupposition is desirable to the extent that doing so can account for the facts. Second, having a separate scalar presupposition will require additional representational details that can be avoided altogether on the vacuity-based view. I will also suggest that, from the perspective provided by the vacuity account, an apparent “reversed” scalar presupposition in the case of only if receives a simple explanation. This relates to Point (31iii) above, as I will explain shortly. Task (b) provides the next part of the proposal: a semantics for POS, and a connection between it and only. This connection will be presented with some conceptual points of support, but the crucial arguments will be empirical. In implementing the details, special attention must be given to the details of how Task (a) is done: if only is lexically “mirative”, then given the way with which it interacts with POS, POS must be mirative in a related way also. Alternatively, if only is not lexically mirative, but shows this behavior because of a ban against vacuous use, then (once again) given the interaction it shows with POS, it follows that POS does something in its semantics that leads to a violation of that ban. To this end, I will propose that POS, when accompanying a degree property φ, denotes that degree d such that all stronger degrees of φ are irrelevant given contextual considerations. It follows from this that the ban against vacuous use of only is bound to be violated when only’s associate is POS; since by its semantics POS denotes the strongest relevant degree, within what context provides as criteria for what might count as relevant, nothing would be left for only’s exclusive component to do. The consequence is vacuity.

3 Krifka

(2000) had similar ideas about the meanings of already and still.

1.4 Theoretical Implications

13

The most important result of this is that it provides an answer to what I called the missing readings question above. Association between only and few, or very few or rarely, etc. does not generate the readings that are theoretically expected, because getting those readings requires that only compose consistently with a POS-marked (or a “very”-marked) gradable term, and it cannot. The same reason keeps only from taking the positive antonyms of these expressions as associates: many, very many, and frequently. With this result, we take a step in the direction toward a solution to the puzzle, but also, by taking that step, we arrive at some conclusions about the meaning of the POS morpheme: if the conflict between the morpheme and only is semantic, then either both items are at some representational level modal, or else they are both non-modal, and POS’s core meaning is simply that the given gradable property reaches (roughly) the strongest relevant extent. As the presentation unfolds, it will be seen that the “vacuity” based proposal naturally predicts no conflict to arise between POS and only when the former does not occur as the latter’s associate. This will form part of the motivation to depart from the lexical “mirative” view of only’s scalar presupposition, since maintaining that view while accounting for this finding will require some undesirable complications. This summarizes how Tasks (a) and (b) will be done, and the findings of the book that pertain to issues (31i,ii). But tasks (a) and (b) only solve half of the theoretical puzzle; the other half, summarized in what I called the available readings question, remains unanswered. On this, I will claim that the associates of only are interpreted as existentially closed predicates of individuals/events. Essentially the idea is that in the cases of interest, only operates on a prejacent whose meaning is not quite what we may paraphrase as “few · · · ”, but something that is better paraphrased as “a few · · · ”. The stronger alternatives to these prejacents do not increase in logical strength with stronger degrees of fewness, but with weaker ones. These weaker degrees correspond to greater degrees of quantity, which is why the problematic sentences have the meaning that they do. Of course, that is all very well to say, but once we look at the details it turns out that the proposal is practically incoherent, unless more is said about how negative expressions like few come to make any meaningful semantic contribution under existential closure. This is van Benthem’s problem, the theme in (31iii). To fix the problem, I will propose two non-standard ways of dividing focus alternatives: on one of them, alternative generation is limited so that only some substitutions/simplifications are allowed; on the other, the notion of excludability is defined on “incomplete” or “skeletal” representations of the given formal alternatives, specifically with respect to the distributivity of the predicates that they contain. Each possibility has precedents in the literature, as I will show, and each produces just the right readings for the constructions of interest. Because of the nature of the logic that keeps only from taking POS-marked associates, and because the logic is presented as the primary reason for the absence of the missing readings in the examples above, an important prediction emerges. In cases where association between only and POS does not require reference to POS ’s “stronger” alternatives, which by hypothesis are irrelevant, the association should work. One case of this, mentioned above, is the case where POS’s argument is a negative term (an upward scalar one) like few but which is outscoped with an

14

1 Introduction

existential quantifier. But more general cases exist too, where the scalarity of POS’s argument does not matter. These include cases where the POS-marked associate is separated from only by a downward entailing modal, and cases where the associate appears in an only if construction. The predicted obviation of the only/POS conflict is met in both kinds of data, as we will see. I assume, of course, that only if consists of an instance of only with a conditional prejacent. Here, while it is tempting to think that the monotonicity of conditionals plays a role in making the only-POS association possible, I will show that this is not true. The key lies in the kinds of formal alternatives that a conditional prejacent has, given the meaning that it intuitively gives rise to on composition with only. This is the fourth and final theme in (31). Along with extensions to other constructions that allow upward and downward scalarity, like comparatives and so-called “Type-B” modified numerals like at least four and at most half, the claims summarized above make the main bulk of the content of this monograph. What appears at first to be a self-contained set of problematic datapoints is shown to require a complex solution. The solution has implications for: (a) views of how the meaning of only ought to be stated, specifically whether or not it should be said to say anything about “mirativity” or “excession” in its lexical meaning; (b) views of the semantics of bare gradable expressions, and similarity between their “evaluative” inferences and those of only; (c) accounts of antonymy, given the connection between positive and negative antonyms that I noted above; and (d) views of how informative meanings can be extracted from structures that have near-trivial truth conditions. In the rest of this chapter I will offer brief synopses of Chaps. 2, 3, 4, 5, and 6. Before I get to that, however, I want comment briefly on the levels of descriptive/analytic precision that I will employ throughout the book, and on the overall shape of the presentation. As I said above, much of what I will propose about the meaning of only and the conditions of its use will depend on contextually determined considerations. The fact that context affects the interpretation of only is obvious. However, I want to make it clear that when I resort to things like “contextual considerations”, “conversational goals”, “relevance”, and so on, I do not intend to use these as complete explanations of the data that I will discuss. For example, when I talk about a context of speech that makes two propositions p, q effectively equivalent, and claim this as a reason why [only p] is odd or unacceptable, I am certainly abstracting over a myriad details that contribute to the equivalence, and to the judgement that it leads to. But an incomplete story like this is not meant to be a full proposal in its own right. It is instead meant to provide an alternative perspective of some aspect(s) of only’s meaning. And though that aspect remains, on the proposed view, sensitive to subtle context-dependent factors like (say) relevance, the intention behind the view is to think differently of what only says in its lexical meaning, and what comes from sources that are external to that meaning. Likewise, when I say that POS denotes the strongest “relevant” degree, relative to the given degree property, I do not claim that saying this makes it clearer what distinguishes relevant degrees from irrelevant ones. Such a move restates the

1.5 Book Overview

15

inescapably vague truth conditions that other proposals associate with the positive morpheme. My hope is that, despite my need to often talk in vague terms, about context and relevance etc., I will still be able to propose with sufficient concreteness some new way of connecting certain datapoints, and to use the connections to put together a solution to a new problem. Another comment that is worth making at this point is about the structure of some of the upcoming chapters, in particular Chaps. 2, 3, and 4. On occasion, the presentation in these chapters may seem to point in more that one direction. For example, in Chaps. 2 and 3 I will talk about two broad perspectives on the “mirativity” or “evaluativity” of only and POS, respectively—the lexicalist view and the vacuity-based view. As the presentation goes on, I will make the case for the second of these two, but in both chapters this will happen after a detailed discussion of what the first view may look like. I do this because the first view is appealing intuitively, and in the literature on only I think it is the prevalent one. Thus the points of these discussions, which may seem to suggest something different from what I want to propose eventually, is to show what a proponent of the lexicalist view would have to assume in order to capture the relevant findings. A similar clarification is necessary for Chap. 4, where one scope-based answer appears initially to be inviting, to the available readings question, but is ultimately argued to have important flaws, and to have a better alternative in the view that includes existentially-closed logical forms. I turn now to an overview of the next five chapters.

1.5 Book Overview Chapter 2 begins with a short review of the semantics of the particle only. The review draws primarily on Horn’s (1969) multi-tiered analysis of the particle’s semantics, where it is taken to have both a presuppositional and an assertoric component. Building on this, the chapter goes on to review some of the problems that have been found with Horn’s characterization, with attention paid in particular to only’s assertion, its scalar readings, and consequences of the scalar readings for only’s presupposition. Here, from a close look at a problem diagnosed in Klinedinst (2005), I will show how the scalar readings of only can be related to its non-scalar (or logical) uses, following the very logic that make scales what they are. The discussion will provide an explanation to a puzzle about only’s presupposition: that it is best characterized, given Klinedinst’s problem, as a disjunction of the prejacent together with its higher alternatives. This disjunction will be argued to follow from the logic of scales. The remainder of the chapter concerns only’s scalar presupposition, the so called “mirative” aspect of its meaning (König 1991, Zeevat 2008, Beaver and Clark 2008 a.o.), and the ban against its vacuous use. I will first talk about ways of formulating the scalar presupposition in terms of mirativity, and will find tempting

16

1 Introduction

points of criticism that (I will argue) are not convincing. The scalar presupposition will be defined using Kratzer’s (1991) notion of doubly-relative modality, with contextually-determined goals playing the role of the conversational background, and typicality playing the role of ordering source. Later I turn to *Vac, the constraint that bans vacuous use of only. Given the data that motivate the constraint, I will argue for a formulation of it that blocks instances of [only p] when the only’s assertion follows from its presupposition. I will show that *Vac cannot be derived entirely from only’s scalar presupposition, and instead argue that the scalar presupposition can in fact be derived from *Vac, given the fact that only permits scalar orderings. In a little more detail, the claim will be that only’s scalar presupposition is reducible to the following two independently motivated findings: (32)

a. That only is illicit when it is used vacuously, and b. that contextual considerations render certain alternatives equivalent.

To see the idea schematically, assume an ordered scale of alternatives A, B, C, D, where D is strongest and A is weakest. Then, given (32a), we predict that [only A/B/C] be licit and that [only D] be illicit; in the former cases the use of only is not vacuous because the negation of, say, C, which would be the assertion of [only B], does not follow from the presupposition B. In the case of [only D], however, the assertion (as it will be formulated below) is vacuously true, and therefore follows from the presupposition that D. Now, suppose that some relevant consideration fails to distinguish C from D. To the extent that such a consideration can be defended in a given context, an utterance of [only C] in that context will be infelicitous, owing first to the (contextual-)equivalence that is assumed to hold between C and D, and second to the absence of other alternatives that can rescue only from vacuity. As an example, consider the sentence Jess only visited 40 of the continental US states. We can imagine many contexts where we might be entitled to say What do you mean ‘only 40’?! These contexts happen to be precisely those in which visiting 40 states and visiting more than 40 states are seen be to equivalent, not in the sense that they are truth-conditionally indistinguishable, but in the sense that they provide the same answer to a legitimate question, e.g. the question of whether Jess is well-traveled, or whether Jess has seen a big part of the continental USA, etc. To both these questions the answer remains “yes” regardless of whether Jess visited 40 states or whether s/he visited more. It is to the extent that such questions are judged valid in the given context that the what do you mean ‘only’? response is defensible. This, I propose, is the scalar presupposition of only: it is simply a special violation of the general ban against vacuity, in contexts where logically-excludable alternatives happen to be thought equivalent to the prejacent. Chapter 3 has two parts. The first reviews the semantics of bare gradable adjectives but focuses primarily on many and few. The justification of this choice is the role that the expressions many and few play as the exemplars in the phenomenon of interest—see examples (5–7) and (28–30) on pg. 10 above. The chapter points out reasons to treat many/few as adjectives (following Link 1983, Hoeksema 1983,

1.5 Book Overview

17

Partee 1989, Solt 2009, 2015, a.o.), and ways of deriving their determiner-like meanings from the basic adjectival treatment. In this, the chapter hints at ideas from Buccola and Spector (2016), Alxatib (2013), and Alxatib and Ivlieva (2018). In the second part of the chapter, the case is built that the same kind of “mirativity” witnessed in the meaning of only (Chap. 2) takes part in the semantics of bare gradable adjectives. In the case of bare gradable expressions, this “mirativity” is identified with the silent POS morpheme that is thought to co-occur with them (also with very). The connection between only and POS, as I mentioned earlier, is defended on empirical grounds, and it is emphasized that its robustness in the key cases is far from trivial; a wide variety of contextual considerations play a role in only’s scalar presupposition, and likewise in POS, yet when the latter appears as the associate of the former, it seems that these considerations are required by default to be the same. The conclusions that follow from this finding depend on our theory of only’s scalar presupposition, and because there are two of these discussed in Chap. 2, it follows that two extensions to POS must be discussed in Chap. 3. Thus the presentational structure, where two different theoretical possibilities are discussed side by side, continues here. If only has some lexically-specified modality that underlies its scalar presupposition, then POS must be represented with a similar kind of modality in its semantics. This comes with significant costs, however, as I will show. On the other alternative, following the idea that only’s scalar presupposition is nothing more than *Vac, I propose that POS (or very) must have a lexical property that makes its stronger alternatives irrelevant, in a contextually-determined sense. Here I draw on contextualistic accounts of vague adjectives, like Fara’s (2000), where it is said that POS holds of a degree property D when D reaches an extent that “stands out”. I interpret this as saying that D’s maximal extent is surpassed only by degrees that are irrelevant, given some contextual considerations. For example, Jess is tall, with the logical form [Jess is POS-tall] or [POS [λd Jess is d-tall]], holds in a world of evaluation w iff all degrees of height exceeding Jess’s maximal height in w are irrelevant given some contextually-understood matter. This differs from e.g. von Stechow’s (2006) and Heim’s (2006) “neutrality”-based semantics, but it provides the needed connection between only and POS. A crucial note that will be made in this context is the predicted (and attested) difference between cases where the focus associate of only contains an occurrence of POS, and cases where POS appears outside the associate of only. (33a) and (33b) below are examples. (33)

a. *Jess only read [(very) many]F books b. Only JessF read (very) many books

(33a) is quite odd by default, while (33b) is acceptable; in the first, only and many are felt to contradict one another, while in the second they are not. The conflict in the first case is connected crucially to the association between only and POS-many, an association that is absent in (33b). The difference in acceptability receives the following explanation: in (33a), only must negate some stronger alternative to its prejacent in order to escape vacuity, but because the alternatives to the prejacent vary by the associate [(very) many], and because the “evaluativity” of that associate

18

1 Introduction

evicts stronger degrees from the set of relevant alternatives, nothing is left for only to exclude, and vacuity results; in (33b), on the other hand, the alternatives vary with respect to a different associate, Jess, and there is nothing in the semantics of that associate that leads to vacuity. Crucially, this account of (33a) extends to cases where many is replaced with few, and it is because of the same conflict between only and POS that cases like (34) below, and (5–7), are not interpreted as predicted; only does not exclude stronger alternatives, because the evaluativity of the given scalar expressions keeps stronger degrees (of fewness etc.) out of the set of relevant alternatives. (34)

Jess only read [(very) few]F books

And when (very) few appears outside of the focus associate, the sentence behaves as it is predicted to: its presupposition and assertion say, respectively, that Jess read a small number of books, and that no other relevant individual did: (35)

Only JessF only read (very) few books

In (35) the assertoric part of only does not require alternatives to the prejacent with stronger degrees of fewness, because the focus associate is the subject Jess, not [(very) few]. Though I will talk about how these data might be handled on the “modal” view of only’s scalar presupposition, and the corresponding modal view of POS, I will take the position that the account is inelegant in the representational detail that it needs, when compared with the vacuity-based view. The discussion in Chap. 3 therefore offers an answer to the missing readings question, and culminates in a generalization. The generalization is based on the observation that the inferences which keep many from appearing as an associate of only, are also the ones that keep few (and similar expressions) from taking its expected “logical” reading. The converse holds too: configurations in which these inferences do not play this role, and where therefore many is permitted to co-occur with only, are also configurations where few co-occurs with only and where the composition gives rise to the expected meaning. I will propose a generalization that suggests just this: whenever the positive expression in a pair of antonyms does not appear acceptably as an associate of only, the negative expression is either unacceptable as well, or is acceptable but does not give rise to the predicted “logical” interpretation. Chapter 4 provides an answer to the available readings question, that is, the question why [only (very) few] associations mean anything at all, and what their meaning is. The chapter begins by noting a theoretical possibility that is based on scope-taking: given independent reasons to give few scope-mobility, it is suggested that perhaps POS-few (and POS-rarely etc.) takes scope above only in the problematic examples. (36) is an example:

1.5 Book Overview

19

(36) a. Jess only baked [(very) few]F cookies b. (very) few

ld only(d)

ld E

d -MEAS cookies

l x Jess baked x

Speaking in informal terms, the idea of interpreting (36a) using LF (36b) is to predicate “fewness” of the set of degrees d for which it is true that Jess baked only d-many cookies—the operator MEAS makes from a degree d a predicate of individuals, which holds of x iff x contains at least d-many atoms in it. In order for only not to be vacuous in (36), its degree argument must fall below the greatest number of baked cookies that might count as relevant in context. If that number turns out to qualify as a “POS-few” number, no conflict is expected. So, by taking scope above only, the otherwise problematic POS-marked phrase leads not only to an interpretable logical form, but also to the correct interpretation. On first glance, something along these lines seems to be on the right track. But the details, as I show in the chapter, are problematic; allowing such scope-taking mobility overgenerates, because it opens the possibility for other degree-sensitive expressions to outscope only, and therefore to take readings where only does not put the upper bound that it ought to. From this discussion I conclude that the better solution involves leaving POSfew in the scope of only, but interpreting it as an existentially closed predicate of individuals. This is what I will call fewP for short: the structure denotes a predicate that holds of x iff x’s “size” or numerosity counts as POS-few: (37)

POS-fewP OP

lx POS

ld

d-few

ld

x d -MEAS

On this proposal, (36) takes its meaning from an LF where few appears as fewP :

20

(38)

1 Introduction a. Jess only baked [(very) few]F cookies b. only E

[POS-fewP ]F cookies

l x Jess baked x

The presupposition of only in (38) says that there was a plurality of cookies that Jess baked, and whose size was “few”; its assertion says that no such plurality existed of a greater size than that. Here too, the details are problematic however, and it is here that van Benthem’s problem comes up. Because the prejacent in (38) has very weak truth conditions, the assertive component of only will be predicted to be overly strong—so strong, in fact, that it will be false if Jess baked practically any number of cookies, no matter how small. I will propose two ways of getting around this issue: one involving a constraint on generating formal alternatives, and one involving a constraint on what matters in determining whether a formal alternatives is excludable. The alternative-based view uses some findings in the literature on scalar implicatures to argue for a restriction on how different a prejacent’s alternative can be from the prejacent itself. The second view is more involved: it is built on the assumption that some information about the formal alternatives is not visible, or known, to the mechanism that determines whether or not they are excludable with respect to the prejacent. The proposal finds precedent in Gajewski’s (2002) definition of L-analyticity using “skeletal” logical forms. Chapter 4 therefore completes the proposal in its essentials: it adds to the previous chapter’s answer to the missing readings question an answer to the available readings question. With that laid out, the chapter concludes with a short review of two alternative accounts of our problematic data: Bonomi and Casalegno’s (1993), and Beck’s (2012). These two views, in effect, take two routes that I earlier said that I would not. To Bonomi and Casalegno (1993), only does not negate stronger alternatives to its prejacent; it negates descriptions of bigger events. The second account, proposed by Beck (2012), has it that few and similar expression do not in their lexical semantics increase in strength with lower quantities; their scalarity is just like that of their positive antonyms. Their negative meanings come from an external licenser, and only can sometimes serve as that licenser. I will explain my arguments against these two views when I turn my attention to them. Chapter 5 is about only if. I will show, first, that in order to get the correct semantics of only if constructions, it is necessary to assume (until a more principled account is found) that the prejacent conditional—the if in only if —has alternatives whose antecedents are each exhaustified with respect to the antecedent of the prejacent itself. For example, in Jess will only go if Charlie and Alex go, the intuited

1.5 Book Overview

21

meaning cannot be derived by negating the conditionals Jess will go if Charlie goes, and Jess will go if Alex goes, because that would lead to an inconsistent set of inferences: Jess will go if Charlie and Alex go, but will not go if Charlie goes, and will not go if Alex goes. The correct meaning, rather, is derived by negating internally-exhaustified versions of these alternatives: only should say that it is false that Jess will go if Exh(Charlie goes), and false that Jess will go if Exh(Alex goes). I will show that a proposal like this is necessary if we want to make room for uses of only if where the associate appears inside the if -clause—these are cases that were pointed out by von Fintel (1997). Once the basics of the proposal are explained and motivated, the chapter moves on to instances of only if that contain POS-marked focus associates. Here I point out that the association is predicted to effect no conflicts of the kind derived in Chap. 3, because the excludable formal alternatives in [only if [POS-φ]F , · · · ] are not alternatives where POS is replaced with stronger degrees of φ—recall from the overview of Chap. 3 that POS excludes these degrees from the set of alternatives. But in the case of conditional prejacents this is of no consequence, and the result is that POS-many and POS-few can both serve as focus associates without any surprises in outcome. It is worth adding that the discussion will not be specific to treatments of conditionals as (variably-)strict operators, but will be shown to be compatible with existential accounts of conditionals like Herburger’s (2015, 2019) and Bassi and Bar-Lev’s (2018). The final point of the chapter is that only if constructions give rise to subtle scalar presupposition effects, but I argue that such effects are predicted to be limited to just those contexts where the prejacent, [if p, q] is seen by some legitimate consideration to be equivalent to its alternative(s) [if Exh(p ), q]. This is expected on the *Vac view of only’s scalar presupposition. Chapter 6 provides a summary of the main findings of the book, and extends them to cases where only takes as associate a comparative form (downward and upward scalar, like more than and less than), and a superlative modified numeral, like at least and at most. These paradigms are crucially relevant, even though their interaction with only does not depend in any obvious way on only’s scalar presupposition. Both types of construction were reported not to license the kind of scalar implicature that unmodified numerals give rise to (Krifka 1999), and there appears to be related factors that keep the forms from appearing as associates to only. In the case of comparatives, I will use Fox and Hackl’s (2006) proposal that, at the level where excludability of alternatives is calculated (for implicatures just like for association with only), the domain of degrees is densely ordered regardless of the lexical semantics of the given gradable expression. I show how this leads to contradictory inferences when only takes a comparative as its associate independently of scalarity. This is why neither more than nor less than can appear as only’s associate. With less than, however, I will say something similar to what I said about POS-few: a parse that includes existential closure over the phrase generates a different reading—the intuited reading—without running into the contradictory inferences that make association with comparative problematic. In the case of at

22

1 Introduction

least and at most, the problem that I will claim is one of vacuity. I will show how these modified numerals resemble disjunction, both in the ignorance inferences that they give rise to when unembedded, and the free choice inferences that result under modals. From this comparison, I will point out that, like disjunction, these forms do not have any “subdomain” formal alternatives that only can operate on, and for this reason, they cannot be associated with only. The availability of an existentiallyclosed parse in the case of at most will be discussed following the other cases.

Chapter 2

Only and Its Inferences

Abstract A semantic entry for only is developed, based first on Horn (A presuppositional analysis of only and even. In: Binnick RI, Davidson A, Green GM, Morgan JL (eds) CLS 5. Department of Linguistics, University of Chicago, pp 98–107, 1969) but revised with scalar uses in mind, specifically observations from Klinedinst (Scales and Only. Master’s thesis, UCLA, 2005). The scalar presupposition of only is discussed, and argued to be reducible to the ban against its vacuous use.

2.1 Chapter Preview As promised, the topic in this chapter is the semantics of only. We will first take a look at Horn’s (1969) influential proposal, where only’s semantic contribution is divided into a presuppositional component and an assertoric component. We will then turn to some of the challenges that have been leveled against this account over the years. As we do this, we will talk a little about what only presupposes, but most of our focus will be on the assertoric part. Section 2.2 will conclude with a formulation of that component, written in terms of Innocent Excludability (Fox 2007a). Soon afterwards, however, we will turn to only’s scalar uses. There we will begin with a simple characterization of only’s assertion that operates on an underspecified scalar ordering between the relevant alternatives. However, we will use an observation from Klinedinst (2005) to motivate an improvement on the entry, and in spelling out that revision we will use terms from Beaver and Clark (2008). Our final proposal about the assertion of only—shown in (1) below for the benefit of the more experienced readers—combines the scale-based semantics of the particle, stated in terms of MIN and MAX, with the Innocent-Excludability condition from Fox (2007a). Once the semantic entry for only is formulated, the discussion will turn to only’s so-called “scalar” presupposition, the intuited inference that only’s propositional argument is, in a context-dependent sense, low—the inference has also been called ‘mirative’ (Zeevat 2008). The discussion will be about the idea of treating only’s scalar presupposition as a modal inference. We will see easy ways of criticizing the idea, taking as our example a point made by Löbner (1989), but we will also © Springer Nature Switzerland AG 2020 S. Alxatib, Focus, Evaluativity, and Antonymy, Studies in Linguistics and Philosophy 104, https://doi.org/10.1007/978-3-030-37806-6_2

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24

2 Only and Its Inferences

see that the criticism is not as effective as may seem at first. Still, the final stance taken in the chapter will be one when the scalar presupposition is derived from another constraint on the use of only; the constraint that bans its vacuous use. The two inferences are discussed in Sects. 2.2.3 and 2.2.4, respectively. (1)

Given a world w, a proposition p, a set of propositions C and an ordering < on C, (i) onlyw (C)(p) is defined only if MIN