The meaning of more / [First edition.] 9780198804659, 0198804652, 9780198804666, 0198804660

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The Meaning of More

OX F OR D STU DIES IN SEMANTICS A ND PR AGMATICS General Editors Chris Barker, New York University, and Chris Kennedy, University of Chicago recently published in the series 3 Weak Island Semantics Márta Abrusán 4 Reliability in Pragmatics E. McCready 5 Constraints on Numerical Expressions Chris Cummins 6 Use-Conditional Meaning Studies in Multidimensional Semantics Daniel Gutzmann 7 Gradability in Natural Language Logical and Grammatical Foundations Heather Burnett 8 Subjectivity and Perspective in Truth-Theoretic Semantics Peter Lasersohn 9 The Semantics of Evidentials Sarah E. Murray 10 Graded Modality Qualitative and Quantitative Perspectives Daniel Lassiter 11 The Semantics and Pragmatics of Honorification Register and Social Meaning Elin McCready 12 The Meaning of More Alexis Wellwood

The Meaning of More A L E X I S W E L LWO O D

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3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Alexis Wellwood 2019 The moral rights of the author have been asserted First Edition published in 2019 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2019933015 ISBN 978–0–19–880465–9 (hbk.) 978–0–19–880466–6 (pbk.) Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

General preface Oxford Studies in Semantics and Pragmatics provides a platform for original research on meaning in natural language within contemporary semantics and pragmatics. Authors are encouraged to present their work in the context of past and present lines of inquiry and in a manner accessible to semanticists and pragmatists in linguistics, philosophy, and cognitive science, as well as to professional linguists in related subfields such as syntax and lexicology. They are also asked to ground argument in numerous examples from English and, where possible, from a variety of other languages. This is a companion series to Oxford Surveys in Semantics and Pragmatics, which provides critical overviews of the major approaches to research topics of current interest, a discussion of their relative value, and an assessment of what degree of consensus exists about any one of them. The Studies series equally seeks to put empirical puzzle and theoretical debate into comprehensible perspective, but its authors generally develop and defend the approach and line of argument which they find most convincing and productive. The series offers researchers in linguistics and related areas—including syntax, cognitive science, computer science, and philosophy—a means of disseminating their findings to potential readers throughout the world. This book delves into the micro-semantics of comparatives, that is, the meaning of words and parts of words having to do with measurement. But small doesn’t mean unimportant—quite the contrary, the main claim of the book is that a tremendous portion of compositional semantics at the phrasal level hangs on the contribution of one crucial element, abstractly (but suggestively) identified as much. In particular, in recognition of the semantic commonality of nouns, adjectives, and verbs, Wellwood suggests that even gradable adjectives such as tall denote simple predicates of entities. The one and only element that introduces degrees into the composition is much. Needless to say, this hypothesis is as bold and unconventional as it is elegant. The first task is to simply show how this idea could work in detail. For instance, if gradable adjectives are mere properties that do not denote functions into degrees, what are they properties of? Wellwood argues they are properties of states. The second, much harder, task is to explain what adopting this perspective achieves. The answer here is intricate and beautiful: the ways in which measurement enters into the composition of various constructions both enables and constrains similarities, differences, and conversions (coercions) across the constructions. The book, then, charts an ecosystem of meaning. The argument ranges from morphology to ontology, a profound meditation on the ways in which how we conceive of and categorize the world informs the way we talk about the world, and vice versa.

Acknowledgments This book wouldn’t have been possible without the generous support and tireless guidance of Valentine Hacquard, Alexander Williams, Paul Pietroski, and Jeffrey Lidz. In developing the central thesis, my ideas benefited enormously from numerous discussions with Roumi Pancheva, Ewan Dunbar, Brooke Larson, Alan Bale, Roger Schwarzschild, Masaya Yoshida, Justin Halberda, Darko Odic, Tim Hunter, Michael Glanzberg, Lucas Champollion, Chris Kennedy, Colin Phillips, Matt Husband, Norbert Hornstein, Fabrizio Cariani, Paolo Santorio, Una Stojnić, Jeremy Goodman, John Hawthorne, Marcin Morzycki, Anastasia Giannakidou, Michael Israel, and Michael Morreau. Angela Xiaoxue He, Brian Dillon, Tom Grano, Chris Vogel, Rachel Dudley, J. Brendan Ritchie, Quinn Harr, Mike McCourt, Yu Izumi, and Brock Rough helped me think through the broader relevance of my thesis. Charles Reiss, Dana Isac, Mark Hale, and Brendan Gillon got me started on this journey; I hope they can find something in here that makes them proud.

List of abbreviations abs Adj Ag ANS AP Co cmp DA DAs DegP DP ev FA GA Ho I-level IE impf max NP NumP pfv pl PM pos S-level sg Th TN VP

absolute morpheme adjective ‘Agent’ thematic role approximate number system adjective phrase ‘Content’ thematic role comparative morpheme degree abstraction rule degree achievement phrases degree phrase determiner phrase eventizing morpheme functional application rule gradable adjective ‘Holder’ thematic role individual-level indexed expressions rule imperfective morpheme maximum operator noun phrase number phrase perfective morpheme plural morpheme predicate modification rule positive morpheme stage-level singular morpheme ‘Theme’ thematic role terminal nodes rule verb phrase

1 Introduction

This book is about how measurement is expressed and understood in natural language. I tell this story through the detailed investigation of sentences with more, and occasionally those with as, too, enough, and others. I call these the comparative constructions, canonical examples of which involve adjectives like tall and intelligent as in (1). Adjectives like these are said to be ‘gradable’, since their application is not all-ornothing: for an individual to have the property expressed by a gradable adjective is for that individual to have it to an extent, or to a degree. (1) a. Al is taller/more intelligent than Bill is. b. Al is as tall/intelligent as Bill is. On one major theory of the semantics of comparatives, tall and intelligent express relations between individuals and degrees. Degrees are formal objects that represent the measure of an entity along some dimension, e.g., height or intelligence. Comparative morphology like -er/more, as, etc., is correspondingly taken to express relations between degrees. In using more, we say that one degree is greater than another, (1a), and in using as we say that one is at least as great as another (1b). We can talk about degrees modally with too tall and intelligent enough, inquire about them with how tall, and we demonstrate them using that intelligent, etc. In degree-theoretic terms, a ‘measure function’ maps entities to elements of scales, total orders on a set of degrees. The gradable adjective tall associates individuals with degrees representing increasing length, and intelligent with degrees representing increasing intelligence. The degree analysis has been developed most widely through consideration of comparatives targeting adjectives like those in (1), but of course comparatives may target nouns, (2), and verbs, (3). These non-canonical comparatives exhibit similar semantic properties as their adjectival cousins, but with some differences in their morphosyntactic realization. (2) a. Al ate more soup than Bill did. b. Al ate as much soup as Bill did. (3) a. Al ran more than Bill did. b. Al ran as much as Bill did. Generally, differences in the grammatical packaging of adjectival, nominal, and verbal comparatives are thought to reflect fundamental semantic differences between the lexical items targeted. That is, nouns like coffee and traffic cone, and verbs like run The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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introduction

and die are generally interpreted as properties (e.g., true of portions of coffee, running activity, etc.), and any degrees involved in understanding sentences like (2) and (3) are introduced by an expression like much;1 contrast (2)–(3) and (4)–(5).2 (4) a. ∗ Al ate as soup as Bill did. b. ∗ Al ate too soup to feel comfortable. (5) a. ∗ Al ran as as Bill did. b. ∗ Al ran too to feel refreshed now. Data like this, in combination with (6), support the widely-held assumption that gradable adjectives belong to one semantic class—a class that includes much—with the proprietary degree predicate type, while nouns and verbs belong to a distinct, and more boring class—those with the (monadic) property type. A central goal of this book is to take another look at this assumption and to argue that the comparative data do not support such a fundamental semantic division between the lexical categories. Instead, all of the relevant relevant adjectives, nouns, and verbs express properties, and only one expression—much or, abstractly, much—introduces degrees. (6) a. ∗ Al is as much tall/intelligent as Bill is. b. ∗ Al is too much tall/intelligent to date Bill.

1.1 The central thesis There isn’t really a deep semantic difference between adjectives, nouns, and verbs, nor between the phrases they head. Extended consideration of how expressions of these categories interact with comparative morphology suggests, rather, a high degree of compositional uniformity, even while what is talked about (portions of coffee, tallness) feels very different. The theory I develop considers a very broad range of occurrences of the comparative form, treating none as antecedently ‘basic’: those with adjectives, mass/count nouns, atelic/telic verb phrases, and others. The core idea that only one morpheme introduces degrees was initially sketched in Wellwood (2012), influenced by Wellwood et al. (2012), and developed in Wellwood (2014) and Wellwood (2015). My theory builds on, but departs from, extant semantic theorizing about comparatives in two important ways. First, of the two core assumptions of a degree semantic framework, I retain one and propose an alternative to the other. I retain the assumption that comparative constructions express relations between degrees; in Chapter 2, I hope to give the reader sufficient reason to think that there is something basically right 1 The occurrence of more in (2a) and (3a) reflects the realization of two distinct morphosyntactic pieces (Bresnan 1973), which we might write as much and -er. I discuss this analysis in detail in Chapter 3. 2 Here and in what follows I prefix sentences with ‘∗ ’ to indicate that the sentence is ungrammatical (i.e., it has no interpretation). I will often prefix sentences with ‘?’, which indicates that my understanding that the sentence is grammatical but semantically marked in some way.

1.1 the central thesis

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about this analysis of sentences with more. I argue against the assumption that gradable adjectives lexicalize the functions that introduce degrees into the compositional semantics, however, in Chapter 4. Instead, I reimagine the semantics of gradable adjectives such that they express properties of (neodavidsonian) states. This analysis is preceded and supported in part by Landman (2000), Fults (2006), Husband (2012), and Baglini (2015). Second, since Schwarzschild (2002, 2006), Nakanishi (2004, 2007), and Wellwood et al. (2012), it is generally accepted that nominal and verbal comparatives are subject to a certain constraint on their interpretation. Essentially, this constraint captures the fact that while different measures are possible in any given comparative, the range of available measures depends on the structure of the measured domain: e.g., portions and parts of those portions for coffee, stretches of running activity and their parts with run, etc. I describe and formalize this constraint in Chapter 3, and in Chapter 4 I suggest that it is operative with forms like taller as well. It is here that my theory goes beyond that originally sketched by Schwarzschild (2002). In Chapter 5, I capture the restrictions evidenced with forms like more coffees by positing an additional constraint. Developing this idea involves rejecting the assumption that the form many in English expresses a semantic primitive distinct from much. My theory thus depends on but revises Bresnan’s (1973) decompositional analysis of forms like more. I analyze it as the morphophonological realization of two morphemes, much and -er. These two divide the important semantic work of the comparative construction between them: much introduces measures, and -er a comparative relation. The semantic role of much is to check the nature and structure of the entities targeted for comparison, and to select an appropriate measure. Differences in dimensionality thus reflect differences in ontology: for example, substances are different from (pluralities of) objects, processes are different from (pluralities of) events, etc. In each case, the nature of the entities targeted, and the structural relations that natively hold between them, are what is important to fixing dimensionality, not whether a lexical item itself introduces a measure function. Here the theory echoes Bale and Barner (2009), for whom the interpretation of (non-decomposed) more is sensitive to domain properties like atomicity. Since explaining dimensionality in any given case depends to a large extent on the ontology, I spend a good deal of time considering how the functional vocabulary can shift or modify what is talked about. This requires positing, in some cases, silent morphemes that shift from, say, talk of substances to talk of objects. I argue that a univocal analysis of more is worth the cost of the additional abstraction. First, all of these shifts can be independently motivated; for example, the silent ‘singularizing’ morpheme in Chapter 5, and the silent verbal plural in Chapters 5–6. Second, the theory helps to address a number of otherwise puzzling questions, like: why does the correlate of more across languages have a common morphophonological shape regardless of the lexical category it targets, just as it does in English? And why do we observe the same ontology-dependent variability and constraints across languages?

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introduction

Finally, the theory unifies the explanation of what are intuitively similar ‘coercive’ effects across lexical targets. On standard accounts, any such intuitive parallelism is not expected, since those accounts characterize the nature of the effects differently: combining non-gradable adjectives with more leads to a type clash, whereas it leads to something more like presuppositional failure in the case of ‘non-gradable’ nouns and verbs. Yet the felt oddity of more hexagonal, more traffic cone, and die more is highly similar—one just doesn’t immediately know what the measure is supposed to be. In my theory, these failures are all assimilated to failures of presupposition. Assuming that all else is equal, an account that matches similarities in intuition with a similar analytic source is to be preferred. I hope that the reader will take away a couple of major points from this work. First, there is a deep sense in which the semantics of expressions like more depends on abstract, formal properties of the things that we talk about—whether substances, objects, processes, events, states, pluralities, or other things. If so, we can understand and use comparative constructions as diagnostic for the nature and structure of those things (cf. Bale & Barner 2009). Second, it raises to salience that, as semanticists, we’re standing on the precipice of understanding what it even means to say what the nature of ‘those things’ is. From the current vantage, it’s not obvious how or whether those things are provided to us by physics or metaphysics, and so we must look elsewhere, perhaps internally, to find them. The semantics of more is measurement-theoretic in a strong sense, as we will see. Across domains, the mapping from entities to elements of scales embedded in its semantics strongly preserves the structural relations that obtain between those entities, independently of our comparative talk. All I need to tell my story of this semantics is that we can identify strict ordering relations (or lack thereof) between the measured entities. And it may be that, in the end, this is all that I need to say. Yet, at the same time, both the mass/count and telicity literatures describe richer structural properties, ones defined equally well by ordering relations and by operations like join ⊔ or sum ⊕. One question I will raise, but leave open, is that of exactly how much structure is preserved in the mapping to degrees. The work shifts our thinking about strange combinations of lexical items and comparative morphology—e.g., more traffic cone, more dead, buy your first CD more, etc.—towards a unified picture in which each domain can be divided into measurable and non-measurable sub-domains. The difference between these domains is correspondingly simple: the measurable domains have non-trivial structure, and the non-measurable domains do not. This perspective suggests new avenues along which potential ‘coercion’ effects may be explored, to consider not so much the syntactic category or even the conceptual content of a given lexical target, but instead the structural relations that obtain, or fail to, on its domain of predication. Importantly, while this work occasionally considers data from languages other than English, it does not address the cross-linguistic picture in any depth. I discuss some prospects for language variation in light of my theory in Chapter 9. Meanwhile, recent work suggests dramatic variation in the expression of comparison relations across languages; for detailed discussion and references, I refer the reader to recent works

1.2 overview

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including Beck et al. (2004, 2010), Kennedy (2009), Bhatt & Takahashi (2007), Lin (2009), Xiang (2003, 2006), Pancheva (2009), Grano (2012), Grano & Davis (2017), and Bochnak (2013).

1.2 Overview 1.2.1 Chapter 2 This chapter introduces the formal system that I assume (cf. Heim & Kratzer 1998, Davidson 1967). I briefly motivate the addition of degrees and scales (Cresswell 1976; cf. Klein 1980, 1982). In what I will call the ‘lexical theory’ of comparatives, gradable adjectives like those in (7) express mappings from entities to degrees (i.e., measure functions; Kennedy 1999), and gradable adverbs like those in (8) as mappings from events to degrees. (7) Ann and Bill are both tall and intelligent. a. Ann is taller / more intelligent than Bill is. b. Ann is as tall / intelligent as Bill is. (8) Both Ann and Bill ran quickly. a. Ann ran faster / more quickly than Bill did. b. Ann ran as fast / quickly as Bill did. The lexical theory distinguishes gradable tall and quickly from non-gradable hexagonal, (9), and daily, (10) in their types. ‘Non-gradable’ adjectives and adverbs, those that are marked or unnatural in some way in the comparative form,3 are assigned a simple property type, while the gradable ones denote more richly-typed degree predicates. (9) Both A and B are hexagonal. a. ?A is more hexagonal than B. b. ?A is as hexagonal as B. (10) Both Ann and Bill ran daily. a. ?Ann ran more daily than Bill did. b. ?Ann ran as daily as Bill did. The end of this chapter raises the question of how measurement is expressed on the lexical theory, and sets up my alternative view at this level. On both theories, the object or target of measurement is whatever entity (whether individual or event) input to a measure function. But they differ on what is input to the relevant function, given a question like How hot is the Coffee? On the lexical theory, the coffee is measured for its temperature. On the alternative, compositional theory I propose, the answer involves measuring heat directly.

3 I depart from many in the literature in not supposing that these combinations are ungrammatical, and thus deserving of a ‘∗ ’ prefix. I think that understanding the combination of more with non-gradable expressions requires some work, suggesting that they fail to provide a default gradable sense.

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introduction

1.2.2 Chapter 3 I now begin to develop my semantics for comparatives, starting with their realizations targeting nouns and verbs. This study reveals two major empirical generalizations. First, the dimension for comparison within a given comparative can vary: (11a) can be used to indicate a comparison by volume and weight, and (11b) can be used to indicate a comparison by duration or distance. Second, the choice of dimension is constrained: (11a) can’t be used to indicate a comparison by temperature, among many other conceivable dimensions, and (11b) can’t be used to indicate a comparison by speed. (11) a. Both Ann and Bill bought coffee. Ann bought as much coffee as Bill. b. Ann and Bill both went running. Ann ran as much as Bill did.

vol, weight, ∗ temp dur, dist, ∗ speed

I follow Schwarzschild (2002, 2006), Nakanishi (2004, 2007), and Wellwood et al. (2012), Wellwood (2015) in positing that such facts are explained by ‘S-monotonicity’ in (12). (12) constrains the context-sensitive selection of measure function μ, ensuring that permissible μs preserve mereological properties of the measured domain—e.g., partial orderings, ≺Part , in the case of coffee and run. Second, it presupposes that the measured domain has such structure (i.e., the second clause of (12) can’t be vacuously satisfied). (12) S-monotonicity (simplified presentation) A measure function μ : DP → Dδ is S-monotonic if, for all v, v′ ∈ DP , if v ≺Part v′ then μ(v)≺δ μ(v′ ). P I thus distinguish ‘measurable’ from ‘non-measurable’ predicates as follows: a predicate is measurable if its domain has non-trivial structure, and non-measurable otherwise. Thus we classify the mass noun coffee as ‘measurable’ (11a), while the count noun traffic cone is ‘non-measurable’, (13a). The same goes for atelic run (11b), and telic buy her first cupcake, (13b). Use of ‘measurability’ here—as opposed to ‘gradability’—helps accomplish two things: (i) it highlights the measurement-theoretic implications of my analysis, and (ii) it sidesteps a common usage whereby ‘gradable’ is taken to directly imply a degree-based semantics. (13) Ann and Bill each bought a traffic cone, and their first cupcake. a. ?Ann bought more traffic cone than Bill did. b. ?Ann bought her first cupcake more than Bill did. The role of degree introduction in such nominal and verbal comparatives is, I suggest, played by the morpheme much, which occurs as a morphosyntactic piece of more, as much, etc (cf. Bresnan 1973).

1.2 overview

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1.2.3 Chapter 4 I now revisit the canonical comparatives discussed in Chapter 2 in light of the theory developed in Chapter 3. I argue for a reimagining of adjectival comparatives based on the interpretation of gradable adjectives as properties of states Landman (2000) and Fults (2006) (cf. Husband 2010, 2012, Baglini 2015, Francez & Koontz-Garboden 2017), and degree introduction is performed by much. There is some surface evidence for this morphosyntactic analysis in English and other languages (esp. Bresnan 1973, Corver 1997). Thus the goal of this chapter is to show that comparatives targeting adjectives are not as different from those targeting nouns and verbs as usually thought (Wellwood 2012, 2014, 2015). An important piece of evidence comes from pairs of adjectival comparatives and comparatives with their nominalized counterparts, (14)–(15), which seem equivalent. On the latter account, something measurable must be introduced in (14b), and much must introduce a measure of intelligence. If it does, then the same theory will have what is required to interpret (14a): both (14a) and (14b) involve measurement of states. I give other reasons for thinking that adjectives are not grammatically so different from nouns. I’ll suggest weakening S-monotonicity, however, so that we needn’t assume such states are structured mereologically. (14) a. Ann is more intelligent than Bill is. b. Ann has more intelligence than Bill does. (15) a. Ann is as intelligent as Bill is. b. Ann has as much intelligence as Bill does. The goal of this chapter, then, is to extend the category of measurable predicates to include gradable adjectives, and to analyze them, too, as introducing non-trivial structure on their domains of predication. In this case, I posit that gradable adjectives introduce ordered sets of states, while non-gradable adjectives introduce unordered sets of states. On this view, the relevant difference between, e.g., more intelligent and more hexagonal is in their domains of predication, rather than in their type. Among other things, I suggest that this characterization of the data is truer to the intuition that more hexagonal is odd in the same way that more traffic cone is.

1.2.4 Chapter 5 So far, my study can be seen as primarily an exercise in lexical semantics. Yet my theory expects that embedding the targeted lexical items in greater functional structure can shift the dimensions available for comparison. In this chapter, I focus on capturing the fact that, when more occurs with plural nouns, the comparison must be by number (Bale & Barner 2009; cf. Hackl 2001), contrast (16a) and (16b). The same holds of

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relevantly plural telic verb phrases (Nakanishi 2007, Wellwood et al. 2012), contrast (17a) and (17b). (16) a. Al drank more coffee than Bill did. b. Al drank more coffees than Bill did.

vol, ∗ number ∗ vol, number

(17) a. Al ran in the park more than Bill did. b. Al ran to the park more than Bill did.

dur, ∗ number ∗ dur, number

It would be unsatisfying to capture the number restriction by positing that forms like more are ambiguous: on one decomposition (i.e., much-er), the selection of measure functions varies up to the limit of S-monotonicity, but on another (i.e., many-er) it hard-codes a cardinality function (cf. Cresswell 1976, von Stechow 1984, Heim 1985, Hackl 2001, Bhatt & Pancheva 2004, Solt 2015, among many others). I argue that more is unambiguous, based on the fact that cross-linguistically, its occurrences correspond to plural instances of a univocal form, and that much-er itself shows the relevant restriction, given relevantly plural domains (e.g., more furniture; cf. Bale & Barner 2009). To ensure that much is restricted to number in these contexts, I propose an additional condition on the contextual selection of measures: only measure functions that are permutation invariant with respect to the measured domain are admissible, i.e., (18). In other words, an Invariant μ assigns the same degree to every entity v in the measured domain, Dη , as well as to v’s image under any strongly structure-preserving permutation of Dη . Appeal to Invariance excludes many intuitively plausible measures, but which fail to appropriately represent the structure of plural domains. (18) Invariance A measure function μ : Dη → Dδ is Invariant if, for all automorphisms h on ⟨Dη , ≽⟩, and for all v in Dη , μ(v) = μ(h(v)). This analysis extends to the verbal domain, too, if we allow for the existence of a covert verbal plural morpheme (à la Ferreira 2005; see Wellwood et al. 2012). Given a domain consisting of pluralities of events, A-invariance will guarantee number-based comparison here as well.

1.2.5 Chapter 6 I explore data in the adjectival domain that display similar grammatical effects on dimensionality. For example, while 19(a) suggests the usual ‘degrees of A’ interpretation, (19b) intuitively involves comparing numbers of occasions of being A (Wellwood 2016). Such postadjectival occurrences of more are good with stage-level drunk, but odd with an individual-level adjective like tall; cp. (20a) and (20b). Post-adjectival more seems to require comparing numbers of distinct occasions of a property holding, which clashes with what we know about individual-level properties.

1.2 overview

drunkns, ∗ num ∗ drunkns, num

(19) a. Ann was more drunk than Bill was. b. Ann was drunk more than Bill was. (20) a. Ann was taller than Bill was. b. ?Ann was tall more than Bill was.

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tallness, ∗ num tallness, ?num

∗

I distinguish the (b) examples in (19) and (20) as involving higher attachment of the comparative morphology than is realized by the (a) examples. This greater height is mediated by covert functional vocabulary like that posited in Chapter 5 to derive alternations like run in the park (atelic, variable dimensions) and run to the park (telic, only number). Presently, this involves mapping a property of states to a property of (atomic) events. (For precursors to this sort of analysis, see Rothstein 1999, Kratzer 2000, von Stechow 2002, and Schwarzschild 2012.) The derived property may be pluralized, just like a telic predicate. In making my case for this ‘double-eventuality’ analysis of predications with S-level adjectives, I appeal to truth-conditional differences between a sentence like (19b) and minimal variants on its template, combined with temporal for-phrases (cf. Rothstein 1999, 2008). My analysis of the facts echoes elements of previous analyses, but what is interesting about my particular approach is the explicit continuity it affords between the double lives of adjectives that are gradable and S-level, with that of verbs that show variable telicity. S-level adjectives, at the appropriate level of analysis, are semantically just like plural VPs.

1.2.6 Chapter 7 Some adjectives in English take the -er form of the comparative as opposed to the more form, e.g., synthetic taller versus analytic more intelligent. Yet under certain circumstances those adjectives that normally take the synthetic form, (21a), can surface in the analytic, (21b). Sentences like (21b) have been called ‘metalinguistic’ (Bartsch & Vennemann 1972, McCawley 1988), but I will wish to remain neutral on whether they are properly understood in the manner implied; thus, I will call them instances of ‘categorizing’ comparatives, since they intuitively involve comparison of how well two entities fit into a category or categories. (21) a. Ann is taller than Bill is wide. b. Ann is more tall than Bill is wide. I characterize the analytic/synthetic distinction in these cases as tracking a semantic difference. For example, where (21a) expresses a comparison between degrees of length, (21b) expresses a comparison relation between degrees of accuracy—i.e., the degree to which it is accurate to say that Ann is tall, compared to how accurate it is to

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say that Bill is wide.⁴ My analysis contrasts with previous formal proposals in which (21b) but not (21a) compares degrees of desirability (Giannakidou & Yoon 2011) or precision (Morzycki 2011). I follow Embick (2007), who attributes the apparent optionality in comparative formation witnessed by (21) to the presence or absence of a covert morpheme, κ. I interpret κ the same way I would interpret the adjective accurate—as a property of states (cf. Chapter 4). However, where overt accuracy claims explicitly mark their intended propositional complement (e.g., the that it’s raining in It’s accurate (to say) that it’s raining), the propositional material needed in (21b) is derived via abstraction. I support this analysis by considering parallels in the distribution and interpretation of sentences like (21b) with those in (22).⁵ (22) a. It’s more accurate (to say) that Ann is tall than that Bill is wide. b. There’s more accuracy in (saying) Ann is tall. This analysis allows me to retain a univocal semantics for more, unlike previous accounts which require different items for the regular and categorizing comparatives. This chapter represents the second to last in which I survey the cases in which more than one expression has been assigned the semantics of degree introduction. In each case, I have argued that there is in fact just one—much. Chapter 8 reviews some of the remainders.

1.2.7 Chapter 8 The semantics I have offered for more provides a recipe for addressing other cases where a lexical degree-based semantics has been posited. In this chapter, I briefly show how the recipe applies to a variety of such cases: comparatives with attitude verbs, e.g., want ϕ more (Villalta 2008, Lassiter 2011a,b); degree achievements, e.g., cool more (Dowty 1979, Hay et al. 1999, Kennedy & Levin 2008); ‘path scale’ verbs, e.g., ascend more (Rappaport Hovav 2008); and ‘intensity’ count nouns, e.g., more of a fool (Bolinger 1972, Morzycki 2005). In each case, I play off of the possibility of derivations involving the hidden morphemes posited in Chapters 5–6. For example, while the most natural interpretation of a comparative with want ϕ compares degrees of desirability, this form can also be used to compare numbers of desiring occasions. The former reading is most natural in episodic contexts, e.g., (23a), and the latter in habitual or repeated contexts, e.g., (23b).

⁴ In Wellwood 2014, I analyzed sentences like (21a) as covert confidence reports; cf. Cariani et al. under review. Many people have given me reasons to think that this analysis might be wrong. John Hawthorne (p.c.) convinced me, however, by noting that Ann wonders whether Bill is more tall than he is wide fails to report Ann wondering about her own confidence, which is what the earlier analysis would expect. ⁵ (22b) seems a bit forced, though to the extent that it is interpreted as I suggest, the example will be sufficient for my purposes.

1.2 overview

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Furthermore, non-gradable know ϕ, (24a), is licensed in the comparative if occasions of knowing are at issue, (24a)–(24b). (23) a. On Tuesday at lunch, Ann wanted cupcakes more than Bill did. b. Last week, Ann wanted cupcakes more than Bill did. (24) a. When the question was asked, ?Ann knew the solution more than Bill did. b. As they went through the homework problems, Ann knew the solution more than Bill did.

desire, ∗ num desire, num ?know, ∗ num

know, num

An account of comparatives with degree achievements and path scale verbs requires one piece over and above those I have previously posited. I want to say that comparing degrees of cooling for (25a), or ascension for (26a), involves the measurement of states, while comparing the duration of cooling or ascension, (25b)–(26b), involves the measurement of processes. So far, the morpheme ev maps stative properties to properties of (atomic) events. This will not be sufficient for the present case, where we want a mapping from properties of states to properties of processes. (25) a. The pie cooled by 20 degrees, the soup by 15 degrees. The pie cooled more than the soup did. b. The pie cooled for 20 minutes, the soup for 15 minutes. The pie cooled more than the soup did. (26) a. Red ascended 20 meters, Blue 15 meters. Red ascended more than Blue did. b. Red ascended for 20 minutes, Blue for 15 minutes. Red ascended more than Blue did.

cooling duration ascending duration

1.2.8 Chapter 9 Until this chapter, I have focused almost entirely on the formal semantics of comparative constructions. I focused on the usual sorts of evidence for such theories: judgments of truth and falsity in context, intuitions about anomaly, patterns of reference and quantification, etc. I drew on independent morphosyntactic analyses for certain characterizations of these data—e.g., the decomposition of more into much and -er (Chapter 3), the assimilation of the surface form many to plural much (Chapter 5), and the assumption that a morpheme, κ, breaks up regular comparative formation (Chapter 7). The ontological assumptions required by the theory were motivated semanticsinternally, however, even if they were based on distributional and interpretive evidence

12

introduction

outside of my focus on comparatives specifically. Yet the dependence of my theory on independently-specified ontological assumptions raises the question of whether it makes the right predictions, given an ontology. But how should we understand this, independently of semantic analysis? It turns out that this is a difficult question, one only briefly touched on in contemporary writing in semantics. It connects, inevitably, with questions in language acquisition, cognitive psychology, and the philosophy of mind and language. I consider a broad range of research relevant to how people understand comparative sentences, how children acquire them, and how adults evaluate them in context, to motivate a view of our semantic ontology which relates directly to representations and operations in extralinguistic cognition. Some of that research includes: (i) the acquisition pattern for the much/many distinction in English (Gathercole 1985); (ii) early knowledge of the meaning of more (Barner & Snedeker 2005, 2006, Odic et al. 2013, Wellwood & Farkas under review a); and (iii) the verification procedures employed in understanding comparatives in context (Pietroski et al. 2009, Lidz et al. 2011; cf. Odic & Halberda 2015, Kotek et al. 2015, Hunter et al. 2017). Connecting formal semantic description with cognition helps to directly make sense of these results. Making sense of the results and predicting them are two different things. Thus, I also emphasize research into how people determine how novel stuff or things fit into a particular ontological category. Understanding this conceptual determination (cf. Prasada et al. 2002, Rips & Hespos 2015, Wellwood et al. 2018a,b) can be used to predict the assignment of meanings to novel lexical targets, how such classifications can be overridden by further grammatical information, and how decisions made at these levels should impact how dimensionality is resolved with more as in (27)–(28). (27) a. Ann bought more blick than Bill did. b. Ann bought more blicks than Bill did. (28) a. A and B gleebed around a little. A gleebed more than B did. b. A and B gleebed every second or so. A gleebed more than B did. But; this is all to come. For now, let’s talk about more!

2 Measurement and degrees

One of the ways in which we can think about things involves comparing their extents along various dimensions. We can note that Bill is taller than Ann, but that Ann is more intelligent, and we can acknowledge that Ann’s five kilometer run was faster than Bill’s, and so on. In formal semantics, the analysis of sentences expressing such thoughts typically begins by interpreting tall, intelligent, and fast as relations between entities and degrees—formal objects representing extent along a given dimension— and comparative morphemes like -er, as, and too as expressing relations between degrees. For example, -er expresses a strictly greater-than relation, as a greater-thanor-equal-to relation, etc. Ordered collections of degrees are called ‘scales’. The development of degree-based theories has focused almost exclusively on the distribution and interpretation of adjectives. In English, expressions of this category are unique in their ability to combine directly with comparative morphology (cp. taller and ∗ waterer etc.). Within the class of adjectives, though, we can distinguish between those that are plainly acceptable and interpretable in the comparative from those that aren’t. For example, we can easily say that one tall person is taller than another, but it is strange to say that one wooden chair is more wooden than another. Degree-based theories thus differentiate gradable adjectives (GAs) like tall as those which conventionally associate with a particular scale, while non-gradable adjectives do not. In this chapter, I present the major data motivating degree-based theories, contrast such approaches with their major alternatives, and present the basic formal toolkit that I assume throughout the book. Along the way, I propose straightforward applications of the core degree-semantic toolkit to attributive adjectival comparatives involving expressions like hotter coffee, and to their adverbial counterparts (e.g., run faster). We see there that the distinction between gradable and non-gradable is evident with adverbs as well (cp. faster and ?more twice). Incorporating an analysis of the adverbial data allows me to introduce an event semantics, which will be useful later when I discuss the semantics of verbal comparatives. At the end of the chapter, I set up a question of central importance for how we understand our degree-semantic theories. That is: what do we mean, exactly, when we say that the semantics of comparatives involves ‘measurement’? Based on ideas in neighboring fields, I discuss two ways of understanding this, and how these ways distinguish between the theory that I advance from that which we’ve inherited. Our inheritance tells us that a ‘measure’ is just an assignment of degrees to entities, and that one and the same thing may be measured in very many different ways; for example, hotter coffee and stronger coffee involve different ways of measuring some coffee. On my The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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measurement and degrees

understanding, measurement is more discriminating: hotter coffee involves measuring heat and stronger coffee strength, both by way of the coffee. This distinction is subtle, but it is also important, and it has interesting consequences for how we think about the meaning of comparatives. To appreciate these points, we must first remind ourselves of what we’ve inherited. Let’s start with the data.

2.1 The empirical landscape 2.1.1 Adjectives Gradable adjectives (GAs) canonically appear in English with the comparative morphemes -er/more and as, and without any apparent mediation by further functional morphology. On the face of it, adjectival comparatives like these indicate comparisons between extents along a dimension specified by the GA: (29a)–(29b) express that Al’s height or intelligence exceeds Bill’s, and (29c)–(29d) express that Al’s height or intelligence meets or exceeds Bill’s.1 (29) a. b. c. d.

Al is taller than Bill is. Al is more intelligent than Bill is. Al is as tall as Bill is. Al is as intelligent as Bill is.

comparative equative

In this book, I mainly focus my attention on comparative constructions that roughly take the form of those in (29), although anything I say about them is intended to apply equally well to sentences like those in (30), with the requisite alterations. As their listed labels suggest, (30a)–(30b) express that Al’s height or intelligence is excessive for some purpose, (30c)–(30d) express that Al’s height or intelligence is sufficient for some purpose, and (30e)–(30f) express that Al’s height or intelligence is of the highest extent, among those in a relevant comparison class. (30) a. b. c. d. e. f.

Al is too tall to get on this ride. Al is too intelligent to date Bill. Al is tall enough to get on this ride. Al is intelligent enough to solve this puzzle. Al is the tallest girl in her class. Al is the most intelligent girl in her class.

excessive assetive2 superlative

Adjectives appear to represent a distinguished class in their morphological patterning in comparatives: for example, nouns like coffee are highly unacceptable combined with -er, (31). This type of anomaly suggests that a grammatical rule has been broken, a conclusion supported by intuitions about the combination of non-gradable adjectives 1 See Schwarzschild 2008 for discussion and references on the ‘at least as great’ semantics for the equative form, as opposed to ‘exactly as great’. 2 The constructions with enough have long gone without their own label. The term I list was coined by J. Foulks (p.c.), during a talk I gave at Stony Brook University on April 4, 2014. Foulks cites the OED etymology for inspiration: asset, n., “Legal Anglo-Norman as(s)etz from Old French asez (modern assez = enough), ultimately from Latin ad to + satis enough, sufficiency”.

2.1 the empirical landscape

15

with comparative morphology. (32) feels importantly different, suggestive not of ungrammaticality but of a category error: the question of how one wooden thing can be more wooden than another is invited, but we don’t know how to answer it.3 (31) a. ∗ That is coffee-er than this is. b. ∗ That is as coffee as this is. (32) a. ?This piece of wood is more wooden than that piece. b. ?This piece of wood is as wooden as that piece. GAs also occur outside of comparative constructions, of course; or at least, they occur in constructions that fail to show comparative morphology. They occur unmodified (at least on the surface) in copular constructions like (33a), which intuitively express that Al’s height or intelligence stands out among the individuals in the relevant comparison class. When they occur modified in the copular construction, the interpretation is quite similar: the sentences in (34) mean what (33) do, except that the standards for ‘standing out’ are higher. (33) a. Al is tall. b. Al is intelligent. (34) a. Al is very tall. b. Al is very intelligent. Nouns like coffee and non-gradable adjectives like wooden also occur outside of the comparative form, of course. Here, though, questions of comparison class or standards don’t seem to arise: intuitively, the sentences in (35) just mean that the stuff demonstrated is coffee, or that the piece is made of wood. (This description simplifies the picture somewhat, since (35a) may be judged infelicitous when said of a barely perceptible amount of coffee, and the same with (35b) if not enough of the piece is made of wood; cf. Schwarzschild & Wilkinson 2002). Nouns do not combine directly with very, (36b), and such modifiers are odd with non-gradable adjectives, (36). (35) a. That is coffee. b. That piece of furniture is wooden. (36)

a. ∗ That coffee is very coffee. b. ?That piece of furniture is very wooden.

2.1.2 Adverbs Some adverbs pattern much like gradable adjectives, both with respect to their distribution and interpretation, while others pattern more like non-gradable adjectives. In the comparative form, fast and loudly can be used to express that the speed of Al’s run 3 This example is well-chosen, of course. Many adjectives classified as non-gradable aren’t as obviously bad as this in the comparative form, or, at least, it is easier to conjure up a meaningful interpretation for them.

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measurement and degrees

or the loudness of her talking exceeded the corresponding values for Bill, (37a)–(37b), and we get the same overall interpretation in the equative form, (37c)–(37d), just it is left open whether Ann’s speed or loudness was the same as or greater than Bill’s. (37) a. b. c. d.

Al ran faster than Bill did. Al talked more loudly than Bill did. Al ran as fast as Bill did. Al talked as loudly as Bill did.

comparative equative

And so with the other comparative constructions when combined with these (what we might call) gradable adverbs: (38a)–(38b) express that Al’s speed or loudness was excessive for some purpose, (38c)–(38d) that they were sufficient, and (38e)–(38f) that they were of the highest extent. (38) a. b. c. d. e. f.

Al ran too fast to get caught. Al talked too loudly to be understood. Al ran fast enough to catch him. Al talked loudly enough to be heard. Al ran the fastest of the group. Al talked the most loudly of the group.

excessive assetive superlative

Canonically, these adverbs occur bare as verbal modifiers, (39). Intuitively, (39a) means that Al ran at a speed sufficient for it to count as fast, and (39b) that she talked at a high enough volume for it to count as loud. On the face of it, it isn’t obvious that these understandings are relative to comparison classes, at least not consisting of individuals like Al and Bill. Just like gradable adjectives, though, they can be comfortably modified directly by very, (40), with the understanding that the speed or volume is substantially higher than that required for (39). (39) a. Al ran fast. b. Al talked loudly. (40) a. Al ran very fast. b. Al talked very loudly. Here too we see parallel contrasts to those we observed between gradable adjectives, on the one hand, and nouns and non-gradable adjectives on the other. It is highly unacceptable to combine a verb like run with -er, (41a), or very, (41b). Meanwhile, an adverb like hourly (i.e., on an understanding where work hourly means being contracted by the hour) in the comparative form, (42), suggests a similar sort of category mistake as the non-gradable adjective wooden; it is simply not clear what it would mean for one’s hourly work to count as more hourly than another’s. (41) a. ∗ Al ran-er than Bill did. b. ∗ Al very ran. (42) a. ?Al works more hourly than Bill does. b. ?Al works very hourly.

2.2 degrees and scales

17

In sum, comparative constructions reveal deep parallelisms between the nominal and verbal domains. Just as we can morphosyntactically distinguish adjectives and nouns in this grammatical context, we can distinguish adverbs and verbs; and just as we can discern a difference in gradability within the class of adjectives, we can discern this split with adverbs. These distinctions—structural and semantic—characterize the major empirical basis for the development of a modest extension of a standard degree semantics that I develop directly.

2.2 Degrees and scales 2.2.1 The approach The core assumption of a degree semantics is that gradable adjectives express relations between individuals and degrees, formal objects that represent extent along different dimensions. Very often, they are taken to be the kinds of things that expressions like three inches refer to.⁴ The set of (ordered) degrees along a certain dimension is called a scale, and the mapping to degrees is performed by a measure function. These assumptions are the primary defining characteristics of degree-based theories. Degree-based theories contrast with delineation-based theories (building on Lewis 1970; see Wheeler 1972, Kamp 1975, Klein 1980, 1982, 1991, Larson 1988, Doetjes 2009, Van Rooij 2011, Burnett 2012, 2016, among others). Delineation approaches begin with mechanisms designed to resolve the vagueness of GAs like tall in a context c: delineations are, roughly, ways of ‘drawing a line’ between the individuals that are definitely tall in c, and those that aren’t. Thus, Al is tall expresses that Al is in the positive extension of tall in c, while Al is taller than Bill expresses merely that there is a way of delineating the extension of tall such that Al lands in the positive extension but Bill doesn’t. The two types of theories differ markedly in their starting points, which ultimately leads to complementary empirical challenges. First, appealing to degrees in the lexical semantics of GAs suggests a ‘crispness’ of interpretation that is in fact characteristic of comparative constructions like (43a), but which raises questions when applied to the non-comparative form of GAs, like (43b).⁵ In contrast, the appeal to contextsensitive extensions in delineation-based approaches applies very well to the noncomparative forms like (43b), but can run into some trouble with at least some of the comparative forms. (43) a. Al is taller than Bill. b. Al is tall. ⁴ Degree-based approaches may be found in various forms in Bartsch & Vennemann 1972, Seuren 1973, Cresswell 1976, Hellan 1981, von Stechow 1984, Bierwisch 1989, Heim 1985, 2000, Kennedy 1999, 2001a, Bale 2006, 2008, among many others. One important cleavage is between the degree relation approach that I assume, and the so-called ‘A-not-A’ analysis; see Schwarzschild 2008 for an overview, also McConnell-Ginet 1973, Kennedy 2006, and Beck 2011. ⁵ See Fults 2006, ch. 4 for detailed discussion of the distribution of vague versus crisp judgments with GAs.

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measurement and degrees

On degree semantic theories, GAs are typically assigned the role of relating individuals to their extents along the relevant dimension, and the comparative morphology relates those extents in some way: (43a), for example, would then express that Al’s degree of height exceeds Bill’s. The trouble with GA occurrences like that in (43b), on such an approach, is that there does not appear to be any element that introduces the requisite relation between degrees. The standard fix for this is to posit the existence of a covert morpheme, which relates Al’s degree of height to a degree representing the standard for tallness in the context (though cp. Rett 2015). It is widely considered a problem for this approach that, despite extensive cross-linguistic searching, such a morpheme is never overtly realized (see especially Grano 2012, Grano & Davis 2017). Delineation-based approaches have no need to posit a covert morpheme for (43b), since tall merely expresses a context-sensitive property of individuals. On the flip side, however, lacking degrees or comparable formal objects, such approaches can run into difficulty in the analysis of certain classes of comparative constructions. This difficulty, in part, makes it challenging to see how the approach might be extended to comparatives targeting other than GAs.⁶ I turn now to a brief discussion of these cases in order to motivate my assumption of the degree-based framework.

2.2.2 Why degrees? Theories that appeal to degrees, and theories that appeal to delineations, have both theoretical benefits and drawbacks. Since the focus of this book is the semantics of comparatives across categories, however, insofar as the degree-based framework is better-suited to the analysis of those constructions, it will be more appropriate for my purposes. Thus, I sketch four cases where degree-based theories appear to have the upper hand. Each of the four cases involves comparatives with a distinct GA in its matrix and than or as clause, constructions which have become known as ‘subcomparatives’. An example of an uncontroversially acceptable and interpretable subcomparative is given in (44).⁷, ⁸ This sentence appears to be naturally interpreted as expressing that the extent of Al’s height is greater than the extent of Bill’s width. In a delineation-based approach like Klein’s, the sentence should be judged true just in case there is a possible context in which Al is in the positive extension of tall, but Bill is not in the positive extension of wide. Because the standards for tallness and wideness aren’t necessarily

⁶ Burnett 2015 extends delineation semantics to some of these troublesome cases, as well as to nominal comparatives involving expressions like more beer and more beers. ⁷ The term ‘subcomparative’ comes from the syntactic literature, and relates to the hypothesis that sentences like (44) involve elision of a covert element—roughly, the analogue of how as it occurs in forms like how much— from the than or as clauses in sentences like (44) below. This same element is posited to be elided in (43a), but such sentences furthermore involve the elision of a secondary instance of the matrix GA (see for example Bresnan 1973, Kennedy 2002, and Lechner 2004). ⁸ That the best arguments involve comparatives with two adjectives is not trivial: Beck et al. 2010 report that there are languages in which the equivalent of (43a) is grammatical, but not the equivalent of (44).

2.2 degrees and scales

19

linked across contexts, though, such an approach leaves it open that (44) could be true in one context but not in another, which is not expected if (44) expresses a comparison of simple extents. (44) Al is taller than Bill is wide. A different worry arises when we survey different pairings of GAs across the two clauses of the subcomparative (Kennedy 1999). The delineation theory wouldn’t directly expect that any such pairing should be anomalous, since the calculation is the same regardless of the GA: find a context in which the first individual exceeds the relevant GA standard but the second individual doesn’t. Yet sentences like (45) do seem odd, and such examples can be multiplied. Degree-based theories can explain cases like this by stipulating that the relation expressed by -er may only be evaluated if the two GAs relate to degrees on the same scale, which is intuitively the case for tall and wide, (44), but not for tall and punctual, (45). (45) ?Al is taller than Bill is punctual. Degree-based approaches thus appeal to interactions between comparative morphology, scale structure, and ‘evaluability’ to provide explanations for oddities like (45) and others. For example, the two GAs in (46) plausibly relate to the same scale, but may take conflicting perspectives on it (e.g., Rullmann 1995a,b). Kennedy (1999, 2001b) formalizes this effect by appeal to ‘positive’ and ‘negative’ degrees: positive degrees are intervals beginning at the bottom of a scale and extending up to a point (e.g., Al’s height), while negative degrees begin at that same point and extend up to infinity. If -er can only evaluate (now) subset relations between intervals, it can furthermore be stipulated that it will only consider degrees which could, in principle, stand in such a relationship, which is impossible for a positive and negative degree.⁹ (46) ?Al is taller than Bill is short. Sometimes, a GA pairing looks like it should lead to a sense of anomaly, but this is not observed; for instance, (47). For Kennedy, such examples involve comparison of itervals, too, but ones representing the distance between a simple measure of extent and the relevant scalar standard. On this interpretation, (47) expresses that Team A exceeds the standard for legitimacy to a greater extent than Team B exceeds the standard for fraudulence. Delineation-based approaches, in contrast, would seem not to have the representational resources to ensure, at least, that (46) and (47) differ in intuitive acceptability and interpretability.1⁰ (47) Team A is more legitimate than Team B is fraudulent.

⁹ As observed by Büring 2007, Kennedy’s analysis as given fails to predict that sentences like The ladder was shorter than the house was high are not anomalous. See Büring’s paper for an analysis, based around morphosyntactic decomposition of antonymic adjectives, that can preserve Kennedy’s analysis in the general case. 1⁰ I consider the generality of Kennedy’s approach to such cases in Chapter 7.

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measurement and degrees

Perhaps the most direct challenge to delineation-based approaches comes from Bale (2008). He considers pairs of examples like that in (48). First, it isn’t difficult to imagine an Al for whom (48a) is false, while (48b) is true. This is problematic for accounts like that of Klein (1980), which would interpret (48a) as, paraphrasing, ‘there is a delineator δ (e.g., very) that applies to wide such that δ-wide applies to Al but δ-tall does not’. This analysis predicts, minimally, that (48a) should be entailed by (48a), which doesn’t seem right. The challenge seems to arise, again, because the standards of wideness and tallness (plainly invoked by (48b), but not necessarily by (48a)) are not linked across contexts. (48) a. Al is wider than he is tall. b. Al is very wide but he is not very tall. Taken together, considerations of data like that sketched in this section suggest the descriptive viability of a formal system that appeals to degrees and scales. Such a system provides a rich enough theoretical vocabulary within which asymmetries in intuitive judgments across an array of comparatives and GAs can be captured. The challenges posed by such data may not be insurmountable for vagueness-based approaches, but to the extent that these challenges are straightforwardly met in a degree-based framework, I proceed assuming the viability of this framework for the purposes of the present project.

2.2.3 Scales Degree semantic theories tend to assume that scales are antecedently given and fixed, and that they reflect, in some sense, our ability to grade entities along various dimensions independently of language (e.g., Sapir 1944, Cresswell 1976, Kennedy 2007). On this view, our judgments of the truth or falsity of comparative sentences recruit knowledge of totally ordered sets of degrees, abstract objects that represent (roughly) increases in magnitude along dimensions like length, width, and temperature.11 Some theories depart from these basic assumptions in various ways: for example, for Bale (2008, 2011), scales are, in general, generated on the basis of antecedently given relations between individuals (see Chapter 7); Anderson & Morzycki (2015) generate them from relations between sets of kinds of states (cf. Scontras 2017); and Moltmann (2009) does similarly with tropes (i.e., particularized properties). Assuming that there is a stock of antecedently available scales, how should we model them? Apart from encoding information about a certain dimension δ, scales are thought of as sets of ordered degrees, the ordering Rδ of which is at least transitive, reflexive, and antisymmetric. This is given as a definition in (49), where the domain 11 Many degree-theoretic theories traffic not only in degrees but in convex sets of degrees (i.e., intervals). As far as I can tell, the question of whether we should state the interpretation of degree morphemes in terms of points or as sets of points will be orthogonal to questions I ask in this book. See Kennedy 2001a (citing Seuren 1984, von Stechow 1984), Schwarzschild & Wilkinson 2002, Büring 2007, Heim 2008 for relevant discussion.

2.2 degrees and scales

21

of the relation Rδ is a set of degrees Dδ . For example, given this definition, the scale representing the dimension of length, η, might be represented as ⟨Dη , ≤η ⟩ where Dη is the set of (possible) lengths. (49) A relation, ⟨Dδ , Rδ ⟩, is a scale if Dδ is a set of degrees and Rδ is a total order on Dδ . The interpretation of a sentence like (50) below, then, will involve relating the degree to which Al is tall against the degree to which Bill is tall—both degrees in a scale of length. Evidence for the claim that ⟨Dη , ≤η ⟩ is a scale, given (49), would consist in demonstrating that the relation ≤η is a total order on Dη : it requires evidence, in particular, that this relation is reflexive, transitive, anti-symmetric, and connected. (50) Al is taller than Bill is. A reflexive relation pairs each element in its domain with itself. The relation ‘be selfidentical to’ is reflexive, since everyone is self-identical, but the relation ‘be in love with’ isn’t, since love can be unrequited. The relation ‘be a sibling of ’ is irreflexive, since no one is their own sibling etc. Usually, degree semanticists understand the fact that equative sentences like that in (51) which target tall are intuitively true, whoever Al is, as evidence that the length scale associated with tall is indeed reflexive. (51) Al is (at least) as tall as herself. A transitive relation between individuals x and y is one for which it’s true that if x bears the relation to y, and y bears the relation to z, it follows that x bears the relation to z. The relation ‘be stacked above’ is transitive: imagine some plates, one stacked on top of the other, such that p1 is stacked above p2 , and p2 is stacked above p3 ; it follows that p1 is stacked above p3 . That the scale associated with tall is transitive underwritten by the intuitive validity of the inference pattern in (52). (52) Al is taller than Bill. Bill is taller than Carl. Therefore, Al is taller than Carl. An anti-symmetric relation is one for which, if x bears the relation to y and y bears the relation to x, then it must be the case that x and y are the same.12 The relation ≤ on the natural numbers is anti-symmetric: for any n, m ∈ ℕ, if n ≤ m and m ≤ n, then indeed m = n. Establishing the evidence that the length scale is transitive requires some care constructing the example. The most straightforward seems to be the inference pattern in (53), which strikes me as acceptable. (53) Al is as tall as Bill. Bill is as tall as Al. Therefore, Al and Bill are the same height.

12 The anti-symmetry property contrasts both with the symmetry property (if x bears R to y, then y bears R to x) and the asymmetry property (if x bears R to y, then y bears R to x).

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measurement and degrees

Lastly, a connected relation is one in which, for each distinct element of the domain x and y, it is the case that x bears the relation to y or that y bears the relation to x. ≤ on the natural numbers is connected, since for any distinct n and m in ℕ, either n ≤ m or m ≤ n. Again, it appears that the relation associated with tall has this property, since the sentence in (54) is intuitively true, whoever Al and Bill are. (54) Al is (at least) as tall as Bill, or Bill is (at least) as tall as Al. The same kinds of evidence that adverbs like fast (as it occurs adverbially in faster than, as fast as, etc.) associate with scales can similarly be found. For instance, if Al ran faster than Bill, and Bill ran faster than Carl, that it is certainly the case that Al ran faster than Carl. If Al ran (at least) as fast as Bill, and Bill ran (at least) as fast as Al, it seems that their running speeds must have been the same. Also, for any running by Al or Bill, one of them must have run at least as fast as the other. If these judgments are correct in the general case, then a degree-theoretic semantics will say that fast associates with a scale of degrees representing speed. Scales thus are structured very much like a number line, but they are not merely numbers, since they have dimension. Comparative morphemes express scalar relations between degrees and, on standard approaches, these objects enter into the compositional semantics via GAs: either because the GA directly expresses a mapping from entities to degrees (Bartsch & Vennemann 1972, Kennedy 1999, Bale 2008, 2011) or sets of degrees (usually, intervals; see Seuren 1984, von Stechow 1984, Kennedy 2001a, and Schwarzschild & Wilkinson 2002), or because such a mapping is packaged within a larger functional denotation (primarily Cresswell 1976, von Stechow von Stechow 1984, Heim 1985, 2000).

2.3 Basic degree semantics On standard approaches in degree semantics, scales are invoked by the lexical semantics of GAs. Thus, I will refer to any such approaches as the lexical theory of comparative language. In what follows, I present just one way of implementing the lexical theory, but my discussion is intended to apply to any of its variations. On this implementation, GAs lexically express ‘measure functions’—understood simply as functions that map entities to degrees—rather than ‘degree relations’—richer functions which themselves embed measure functions as a part. Such a semantics is rich enough to allow me to describe the kinds of data that I want to discuss.13 I will first set up some necessary technical background. Readers well-versed in the compositional process more or less along the lines of Heim & Kratzer (1998) could 13 The richer, degree-relational theory may be recruited in discussions treating of scope relations; see Heim 2000 in particular, also Cresswell 1976, von Stechow 1984, Heim 2000, Bhatt & Pancheva 2004. Later, the difference will be cast as one between interpreting GAs as type ⟨e, s⟩ (entities to degrees) versus ⟨s, ⟨e, t⟩⟩ (degrees to properties of entities).

2.3 basic degree semantics

23

skip ahead to §2.3.2. However, I shall wish to take a neutral position with respect to some of the foundational assumptions usually attending use of this framework, and so advanced readers interested in these cautionary notes should read on.

2.3.1 Formal preliminaries I assume a framework in which the interpretation of an expression is a type-theoretic object, either one of a distinguished class of basic entities or an n-place function. While my description of this system mostly tracks that of Heim & Kratzer (1998), I make use of an intermediate logical language rather than direct model-theoretic interpretation. Functions are named by λ-terms with the basic shape in (55), where ζ represents the argument, τ the type of the argument, and γ the value description. τ gives information about the domain of the function, and the value description the range. (55) Schema for λ-terms λζτ . γ I assume that we can talk about at least the types of things generated by the definition in (56). A proper name like Al denotes an entity of type e (individuals), a description like the destruction of Aleppo denotes an entity of type v (events), and a measure phrase like three feet denotes an entity of type s (degrees). The two truth values, ⊤ and ⊥, exhaust type t. A noun like cow denotes a function of type ⟨e, t⟩, a verb like run denotes a function of type ⟨v, t⟩, etc. Note that I will frequently shift between talk of types as classifying extensions—as I have just done—and as classifying expressions. (56) Semantic types a. e, v, s, and t are the basic semantic types. b. If σ and τ are semantic types, then ⟨σ, τ⟩ is a semantic type. c. Nothing else is a semantic type. Expressions are mapped to their interpretations by the interpretation function, J⋅KA , where A is an assignment of values to variables. I often omit reference to A, except when its use is important to the matter at hand. The basic set of composition rules that I assume are given in (57a)–(57c). One non-standard usage here is the variable name η, which indicates neutrality with respect to the basic types e, v, and d; normally, we see rule sets like these stated just for the basic type e. (57) Composition rules I a. Terminal Nodes (TN) If σ is a terminal node, then Jσ KA is specified in the lexicon. b. Functional Application (FA) If σ is a branching node, {β, γ} the set of σ’s daughters, and JβKA a function whose domain contains JγKA , then Jσ KA = JβKA (JγKA ).

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measurement and degrees

c. Predicate Modification (PM) If σ is a branching node, {β, γ} the set of σ’s daughters, and JβKA and JγKA are both of type ⟨η, t⟩, then: Jσ KA = λxη .JβKA (x) & JγKA (x) Two further rules are needed. I use the first for the interpretation of than- and as-clauses, (58a) (cf. Heim & Kratzer’s Predicate Abstraction rule). Following standard assumptions in degree semantics, such clauses contain an instance of wh-movement which is interpreted as an abstraction over degrees (i.e., a predicate of type ⟨s, t⟩; see Bhatt & Pancheva 2004 and references therein). The second, (58b), is used to interpret traces and pronouns at a level of generality that supports interpretation in various types (cf. Heim and Kratzer’s Traces and Pronouns rule). (58) Composition rules II a. Degree Abstraction (DA) If σ is a branching node, {β, γ} the set of σ’s daughters, and γ is an operator bearing index i, then: Jσ KA = λsd .JβKA[i→s] b. Indexed Expressions (IE) If σ is an expression bearing index i, then Jσi KA = A(i). For convenience, λ-conversion is stated in (59). (59) λ-conversion For any y of type τ, [λvτ . ϕ](y) ≡ ϕ′ , where ϕ′ is just like ϕ except every free occurrence of v in ϕ is replaced by y in ϕ′ . I assume a neodavidsonian semantics, following Castañeda’s (1967) generalization of Davidson 1967, with early developments by Parsons (1990).1⁴ On this view, verbs express simple properties of events, which are related to their participants by thematic relations (Schein 1993, Pietroski 2005, 2011, Landman 2000, and Champollion 2010).1⁵ I abstract away from the question of how the thematic relations are introduced by tagging the noun phrases in subject and object position (where relevant) with a thematic feature, and interpret such complexes as properties of events.1⁶ Finally, I assume a default rule of existential closure that applies at the top of a tensed clause, if that clause denotes a property of events. In a more articulated theory of the left periphery, at least up to the syntactic height relevant here, the role of binding the 1⁴ Ramsey 1927 and Reichenbach 1947 are cited as early precursors for event semantics. See also Fillmore 1970, Bach 1981, 1986a, Carlson 1984, Taylor 1985, Dowty 1989, Krifka 1989, 1992, Parsons 1990, and Landman 2000. 1⁵ I thus assume a neodavidsonian semantics that is total, rather than partial (e.g., Kratzer 2000). The latter relates subjects to verbs (often) via ‘little-v’ (see Marantz 1984, Chomsky 1995, Kratzer 1996, Pylkkänen 2002, among others), while objects are related to verbs directly. Schein 2003, 2011, Williams 2008, 2009, Laterza 2011, and others give arguments for total separation. My analyses are compatible with either approach. 1⁶ Some specific options include type-shifting (Landman 2000, Champollion 2010), silent heads in the syntax (Lin 2001, Schein 2003, Borer 2005a, Lohndal 2011), special composition rules (at least for subjects; see Kratzer 1996 and references therein), or certain correspondence rules (cf. Pietroski 2006).

2.3 basic degree semantics

25

event variable would be performed by aspectual morphology (see Ferreira 2005 and Hacquard 2006 for discussion and references). I simply mark this step in semantic derivations using ∃. Finally, some notational conveniences I assume are as in (60). (60) Notational conveniences a. x, y, z … range over entities of type e. b. e, e′ , e″ … range over entities of type v. c. d, d′ , d″ … range over entities of type s. d. v, v′ , v″ , … range over entities of type e and v.

2.3.2 The lexical theory As anticipated, I interpret GAs directly as measure functions (see Bartsch & Vennemann 1972, Kennedy 1999, Bale 2008, and others), here represented as expressions of type ⟨e, s⟩. For example, tall and intelligent are interpreted as in (61): they map individuals x to degrees d, where d ranges over values on a scale of height or intelligence, respectively.1⁷ (61) Gradable adjectives (to be revised) a. JtallK = λxe .tall(x) b. JintelligentK = λxe .intelligent(x)

⟨e, s⟩

In contrast, non-gradable adjectives like wooden are assigned functions of the property type ⟨e, t⟩ as in (62): they map individuals x to the value ⊤ just in case x has the property of being wooden. Following standard degree-theoretic approaches, this difference in type from GAs is meant to reflect the observation that adjectives like wooden are unnatural or difficult to interpret in comparative constructions. (62) Non-gradable adjectives (to be revised) JwoodenK = λxe .wooden(x)

⟨e, t⟩

Correspondingly, the interpretations of comparative morphemes are tied, typetheoretically, to those of GAs: in (63), the comparative and equative morphemes are specified to take a GA-type interpretation, that of a than- or as-clause (type s; see below), and that of the subject. Along with the assumption implicit in degree-theoretic frameworks, > and ≥ here are understood not as a particular degree relation, but as a stand-in for the scalar relation ordering the GA’s range. (I return to this assumption in Chapter 4.)

1⁷ One may wish to put very explicit domain conditions in the λ-terms given in (61). Perhaps along the lines of Cresswell’s lexical specification for JtallK: “[its] domain contains only physical objects”, and further, here, “> is the relation whose field is the set of all v such that v is a spatial distance, and ⟨v1 , v2 ⟩ ∈ > iff v1 is a greater distance than v2 , and u is the distance between a’s extremities … , and … this distance will typically be vertical” (1976:267). I return to the question about this way of thinking about adjectival orderings in Chapter 4.

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measurement and degrees

(63) Comparative morphemes (to be revised) a. J-er/moreK = λg⟨e, s⟩ λds λxe . g(x) > d b. JasK = λg⟨e, s⟩ λds λxe .g(x) ≥ d

⟨⟨e, s⟩, ⟨s, ⟨e, t⟩⟩⟩

Clauses headed by than or as are interpreted as a degree, derived by mapping their complement clause, the characteristic function of a set of degrees, type ⟨s, t⟩—itself derived via an operator-variable configuration1⁸—to the largest degree in that set via the description operator ι (Heim 1985), or via max, itself defined in terms of ι (von Stechow 1984 and Rullmann 1995b). I assume the latter implementation here, with max defined as in (65) (modified from Heim 2000).1⁹ (64) than/as morphemes Jthan/asK = λD⟨s,t⟩ .max(D)

⟨⟨s, t⟩, s⟩

(65) The maximum of a set D, max(D), is the unique degree d such that d ∈ D, and for all d′ , if d′ ∈ D then d is at least as great as d′ . i.e., max(D) =df ιd(P(d) & ∀d′ (P(d′ ) → d ≥ d′ )) Specifically, the abstraction operation relates a trace of type s to the measure function expressed by the GA via the morpheme abs (for ‘absolute’, see Kennedy 1999; Bale 2008 calls an equivalent morpheme comp), interpreted as in (66). Such a morpheme is posited not only in order to avoid certain compositional worries; according to Kennedy (1999), such an element is required, also, in order for such clauses to meet the relevant identity conditions on ellipsis, when those are applied in comparatives (see Bresnan 1973). Although I make nothing of it here, it is worth noting that (66) is identical to the interpretation of the equative morpheme as. (66) Absolute morpheme (to be revised) JabsK = λg⟨e,s⟩ λds λxe .g(x) ≥ d

⟨⟨e, s⟩, ⟨s, ⟨e, t⟩⟩⟩

2.3.3 Composition: adjectives I illustrate the process of composition given the assumptions so far laid out focusing on (29a), repeated as in (67). (67) Al is taller than Bill is. Beginning with the dependent clause, I represent its internal structure as in (68). This structure ignores any contribution of the copular verb or tense, and uses syntactic 1⁸ Chomsky 1977, building on observations by Bresnan 1973, discusses syntactic evidence suggestive of covert wh-movement in the dependent clause of a comparative. This syntactic analysis dovetails with the generalization (widely accepted since at least Heim & Kratzer 1998), that wh-movement corresponds to λ-abstraction. In the present context, this abstraction must be over the degree type, s; see Izvorski 1995, Kennedy 1999, Bhatt & Pancheva 2004, among many others; cp. Grimshaw 1987, Corver 1993. See the rule in (58a). 1⁹ See Schwarzschild & Wilkinson 2002 and Fleisher 2016 for issues related to the use of ι or max once comparatives with quantificational noun phrases occur inside the dependent clause.

2.3 basic degree semantics

27

category and type labels for convenience. The head of the clause, than, takes as its complement a function of type ⟨s, t⟩, itself derived via Degree Abstraction (see (58a), and footnote 18). This operation is triggered by opi when it raises to merge with S; thus, the node labeled opP is not annotated with a type. Noteworthy in this structure is the assumption that a silent instance of tall occurs in the dependent clause (cp. Kennedy 1998, 1999). (68)

thanP s than/as ⟨⟨s, t⟩, s⟩

opP ⟨s, t⟩ opi

S t Bill e

DegP ⟨e, t⟩ ti s

Deg′ ⟨s, ⟨e, t⟩⟩ AP tall ⟨e, s⟩

Deg abs ⟨⟨e, s⟩, ⟨s, ⟨e, t⟩⟩⟩

Given these assumptions, the bottom-up compositional interpretation of (68) is presented in simplified format as in (69). Here and below, I indicate the most relevant compositional steps on the right-hand side, and for conciseness I omit reference to the Terminal Nodes rule and instances of λ-conversion. The result in (69e) is, as desired, equivalent to a degree representing Bill’s height. (Following convention, (69e) represents the input to max as the characteristic function of the set on which max operates.) (69) a. b. c. d. e.

Jabs tallKA = λdλx.tall(x) ≥ d JDegPKA = λx.tall(x) ≥ A(i) JSKA = tall(b) ≥ A(i) JopPKA = λd.tall(b) ≥ d JthanPKA = max(λd.tall(b) ≥ d)

FA FA, IE FA DA FA

With this part of the derivation complete, my representation of the syntactic structure for (67) can be truncated at thanP as in (70).2⁰ 2⁰ This constituency (and consequently, the order of the λ-prefixes that I have assumed for the comparative morphemes) corresponds to what Bhatt & Pancheva 2004 calls the ‘classical’ constituency for comparatives (citing Chomsky 1965, Selkirk 1970, Bresnan 1973, and Heim 2000), which tends to go along with type ⟨e, s⟩ semantic analyses of GAs. The ‘non-classical’ constituency (Bhatt cites Abney 1987, Larson 1988, Corver 1990, 1993, and Kennedy 1999, 2002) tends to be paired with the degree relation analysis of GAs, type ⟨s, ⟨e, t⟩⟩.

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measurement and degrees

(70)

S t Al e

DegP ⟨e, t⟩ Deg′ ⟨s, ⟨e, t⟩⟩ tall ⟨e, s⟩

thanP d

-er ⟨⟨e, s⟩, ⟨s, ⟨e, t⟩⟩⟩

The interpretation of the structure in (70) is derived as in (71), abbreviating the interpretation of the than-clause (itself derived in (69)) as δ. The only substantive difference between this and the derivation of the dependent clause, up to node S, is that in (71) the than-clause provides the degree argument to the comparative morpheme, whereas a degree trace performs this role in the dependent clause. The result in (71) says that (67) is true just in case Al’s height exceeds Bill’s height. (71) a. JDeg′ KA = λdλx.tall(x) > d b. JDegPKA = λx.tall(x) > δ c. JSKA = tall(a) > δ

FA FA, abb. FA

Putting these pieces together, the semantics of the comparative in (67) is given in (72a), and that of the corresponding equative is given in (72b). The same compositional process derives both of these interpretations, modulo the identity of the comparative morpheme (-er vs as). (72) a. tall(a) > max(λd.tall(b) ≥ d) b. tall(a) ≥ max(λd.tall(b) ≥ d) Before proceeding to the next section—the interpretation of attributive occurrences of GAs, like tall woman—we should consider briefly how the lexical theory interprets cases in which a GA occurs without overt degree morphology, (73). As discussed above, sentences like this are are generally understood to mean that Al is ‘positively tall’, or ‘taller than the average’. (73) Al is tall. On many accounts, this standard-relative understanding is linked to covert comparative morphology. Implementing such an idea while making minimal modifications to the current set of assumptions, I can simply posit that structures like (73) include an instance of abs and an element, call it ∅, interpreted as a contextually-provided

2.3 basic degree semantics

29

degree, ds .21 Thus, (73) is interpreted as in (74), meaning ‘Al is (at least) as tall as the contextual standard for tallness, ds ’. (74) JAl is ∅ [abs tall]KA = tall(a) ≥ ds

2.3.4 Attributive adjectives I will not be able to offer anything close to a complete account of the syntax-semantics of adnominal GAs. My more modest goal will be to present a functioning semantics for comparatives like (75), making minimal additional assumptions. I doubt that things are as simple as my sketch will suggest (see e.g.). However, setting up some of the details for a simple extension of the lexical theory to these cases—in particular, details about how direct objects compose with verbs—will help prepare the way for further straightforward extension to gradable adverbs. (75) Al drank hotter coffee than Bill did. Before getting to (75), we need to say something about (76). How are VPs like drink coffee to be interpreted? On some accounts, NPs like coffee are interpreted as expressions of type e (e.g., they denote material fusions; Higginbotham 1994) or type k (i.e., kinds; Parsons 1970, Carlson 1977b, Chierchia 1998b, 2010). On others, they express predicates of type ⟨e, t⟩ (Pelletier 1974, Cartwright 1975, Gillon 1992, McNally 1995, van Geenhoven 1996, Koslicki 1999, and Krifka 2003, cf. Partee 1987). They might compose with the interpretation of the verb by a type shift (e.g., Chierchia 1998b, 2010, Krifka 2003) or a covert determiner (e.g., Gillon 1992). (76) Al drank coffee. In the system I’ve set up, the object NP must end up of type e before it is thetamarked (see §2.3.1), i.e., an expression of type ⟨v, t⟩. But, given that sentences like (76) seem to be about certain instances of coffee, it is straightforward to assume that coffee is of predicative type ⟨e, t⟩, and that the stuff it is true of can be mapped to degrees by GAs like hot. Concretely, I will follow Krifka (2003) in assuming that bare mass nouns (and, later, bare plurals) express properties of type ⟨e, t⟩; however, I depart from Krifka in assuming that the mapping from ⟨e, t⟩ to e is effected by a silent determiner (cf. Gillon 1992). The silent determiner could be interpreted as a quantifier (equivalent to some) or as a choice function that supplies an entity of type e from the relevant property term’s domain. I take the latter route, as it will simplify my logical forms, as well as their derivation. In (77), I call the relevant determiner ‘little-e’, and use 𝜖 in its interpretation 21 There are several variant proposals on how the relevant morpheme, usually called pos for ‘positive’, should be interpreted; these details don’t concern us here.

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measurement and degrees

to suggest Hilbert’s (1921[1922]) operator, the indefinite counterpart of ι which doesn’t presuppose uniqueness.22, 23 Along the lines suggested by Hintikka (1974; cf. Kamp 1981, Heim 1982), 𝜖x prefixed to an expression of type ⟨e, t⟩ is a term of type e. Then, 𝜖x P(x) generally is read, ‘some x such that P(x)’, and 𝜖x coffee(x) is read ‘some x such that x is coffee’. (77) little-e JeK = λP⟨e,t⟩ .𝜖x P(x)

type ⟨⟨e, t⟩, e⟩

And so coffee expresses a property of portions of coffee (with more to be said in the next chapter), which can combine with a silent determiner to indicate some portion of coffee or other. Along with our assumptions about the semantics of verbs and thematic role introduction, it is natural to assume that the sentence in (76) has a structure like that in (78), where little-e combined with coffee projects a DP. This DP, of type e, has type ⟨v, t⟩ after theta-marking. (78)

S Al[θAg ]

VP drank

DP[θTh ] e

coffee

These new steps for the interpretation of the direct object are indicated explicitly in (79), and this is folded into the derivation of the rest of the sentential interpretation as in (80). The result can be paraphrased, (continuing to ignore tense), ‘there is an event of Ann drinking some portion of coffee’. All else equal, this seems a good result. (79) a. JDPK = 𝜖x coffee(x) b. JDP[θTh ] K = λe.Th(e, 𝜖x coffee(x)) (80) a. JVPK = λe.drink(e) & Th(e)(𝜖x coffee(x)) b. JSK = λe.Ag(e)(a) & drink(e) & Th(e)(𝜖x coffee(x)) c. ⇝ ∃e(Ag(e)(a) & drink(e) & Th(e)(𝜖x coffee(x)))

FA θ PM PM ∃

By design, extending this semantics to attributive adjectival comparatives like (75) is straightforward. (81) hypothesizes that the adjective combines directly with the comparative morpheme, as before, then with the than-clause, and the expression contributing the measurand—in this case coffee. This much reiterates the structure

22 In making this choice, I abstract away from the problem of empty domains (A. Williams, p.c.). 23 This formulation echoes Bierwisch 1989, for whom 𝜖 is understood as equivalent to an existential quantifier. According to von Heusinger 1997, Schröter 1956 proposed the interpretation of Hilbert’s 𝜖 as a choice function, and Asser 1957 formulated this in detail; Slater 1988 argued that the interpretation of Hilbert’s 𝜖 as an indefinite as opposed to definite operator is misguided. Von Heusinger 1997 uses 𝜖 for a definitely-interpreted choice function operator, and η for the indefinitely-interpreted. In all other respects, my discussion follows that of von Heusinger 1997.

2.3 basic degree semantics

31

of a predicative adjectival comparative, except the DegP and noun will combine by Predicate Modification rather than Functional Application; see (82). (81)

DP[θTh ] e

NP DegP Deg′ hot

(82) a. b. c. d.

coffee

thanP

-er

JDegPK = λx.hot(x) ≥ δ JNPK = λx.coffee(x) & hot(x) ≥ δ JDPK = 𝜖x(coffee(x) & hot(x) ≥ δ) JDP[θTh ] K = λe.Th(e)(𝜖x(coffee(x) & hot(x) ≥ δ))

FA PM FA θ

The overall result, in (83), can be read, ‘there is a drinking event by Ann whose theme is some portion of coffee x, where the temperature of x is greater than δ’. In (75), that δ will be understood as the maximal degree of temperature of any coffee Bill drank. This, too, seems right. (83) ∃e(Ag(e) (a) & drink(e) & Th(e) (𝜖x(coffee(x) & hot(x) ≥ δ)))

2.3.5 Extension: adverbs The lexical theory can be straightforwardly extended to comparatives targeting gradable adverbs, especially in the neodavidsonian framework that I assume. All it requires is a small generalization in the interpretation of the comparative morphemes, e.g., (84) and (85): instead of specifying the final argument as type e, as we did in (63), we can indicate that this argument is neutral as between entities of type e or type v—I mark this sort of type neutrality using η.2⁴ (84) Comparative morphemes (final version) a. J-er/moreK = λg⟨η,d⟩ λds λvη .g(v) > d b. JasK = λg⟨η,d⟩ λds .λvη .g(v) ≥ d

⟨⟨η, d⟩, ⟨s, ⟨η, t⟩⟩⟩

(85) Absolute morpheme (final version) JabsK = λg⟨η,d⟩ λds λvη .g(v) ≥ d

2⁴ Thus, the relevant comparative morphemes express polymorphic functions—ones whose specific interpretation depends on the types of their inputs. Strictly speaking, then, I am assuming a polymorphic lambda calculus as my intermediate logical language (K. Rawlins, p.c.; i.e., System F, Girard 1972, Reynolds 1974).

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This change anticipates the interpretation of gradable adverbs as functions from events (or eventualities) to degrees, as in (223). Otherwise, we may assume that they are just like gradable adjectives on the lexical theory: they denote functions whose range consisting of scalar elements.2⁵ Plausibly, the scale associated with fast is a set of degrees representing speeds, e.g., ⟨Dξ , ≤ξ ⟩, where the elements of Dξ are speeds like 40 km/h. Evidence that the ordering ≤ξ is total on its domain can be shown by running through the paradigm in §2.2.3, mutatis mutandis. (86) Gradable adverbs (to be revised) a. JfastK = λev .fast(e) b. JloudlyK = λev .loudly(e)

⟨v, d⟩

As was said for non-gradable adjectives, the adverbs like hourly that display little comfort in the comparative construction can thereby be assigned interpretations like that in (87): they express simple properties, in particular functions from events to truth values. (87) Non-gradable adverbs JhourlyK = λev .hourly(e)

⟨v, t⟩

Thus, the sentence in (37a), repeated in (88), is assumed to have relevant structure as in (89), again simplifying the internals of the than-clause. As anticipated earlier, I minimally assume that the subject of an eventive predicate is theta-marked,2⁶ a step in the compositional interpretation I continue to mark using θ. (88) Al ran faster than Bill did. (89)

S Al[θAg ]

VP ran

DegP Deg′ fast

thanP

-er

The subscript on θ indicates what type of thematic relation a given theta marker introduces; in the case of the verb run, I assume that this is the Agent role.2⁷ Thus, the theta-marked subject is interpreted in two steps as in (90), resulting in a predicate of events of which Al is Agent. 2⁵ This analysis underdetermines several important aspects of the syntax-semantics of adverbs, focusing as it does on just the adverbials and the assumptions I need to get an analysis of adverbial comparatives off the ground. For relevant background and discussion, see Taylor 1977a, Ernst 1984, 2000, Tenny & Pustejovsky 2000, Piñón 2005, and Rawlins 2013. 2⁶ See footnote 16 for discussion. 2⁷ There is considerable debate and even controversy about how specific we should assume the content of these roles to be. See especially Dowty 1989, Schein 2002, and Williams 2015.

2.4 ‘measurement’, and the thesis

(90) a. JAlK = a b. JAl[θAg ] K = λe.Ag(e)(a)

33

θ

The interpretation of (89), then, is derived as in (91), ignoring tense, and abbreviating the contribution of the than-clause using δ. (91) a. b. c. d. e.

JDeg′ K = λdλe.fast(e) > d JDegPK = λe.fast(e) > δ JVPK = λe.run(e) & fast(e) > δ JSK = λe.Ag(e)(a) & run(e) & fast(e) > δ ⇝ ∃e(Ag(e)(a) & run(e) & fast(e) > δ)

FA FA, abb. PM FA ∃

The than-clause has an exactly parallel structure, differing only in the clauseinternal abstraction over the analogous position of the thanP in (89). Its compositional interpretation delivers (92) in the expected way. (92) J than [opi Bill ran ti abs fast ]KA = max(λd.∃e(Ag(e)(b) & run(e) & fast(e) ≥ d)) Putting the two clauses together, we derive (93), which says ‘there is a running event whose Agent is Al, the speed of which was greater than that of any event of Bill’s running’. This semantics, too, seems to accord with intuition. (93) JAl ran faster than Bill didKA = ∃e′ (Ag(e′ )(a) & run(e) & fast(e) > max(λd.∃e(Ag(e)(b) & run(e) & fast(e) ≥ d)) One question, though: Is it too weak? What if only the tiniest stretch of Al’s running was faster than any of Bill’s, but was otherwise slow? My own intuitions here are not so clear. If more is required, the semantics in (93) may be elaborated to include some form of maximization in the selection of permissible truth-making events in the matrix clause. This could perhaps be effected by perfective aspect, which is often conflated with past tense in English (see e.g. Filip & Rothstein 2005, Filip 2008). For now, for simplicity, I proceed assuming the semantics in (93). These simple extensions amount to a picture on which adverbial DegPs combine with their target—the expressions introducing measuranda—conjunctively, just like adnominal DegPs do. In setting up this picture, then, we can see that the lexical theory and its degree-theoretic setting is admirable both for its simplicity and for its extensibility.

2.4 ‘Measurement’, and the thesis On the lexical theory of comparatives, some expressions lexicalize measure functions (e.g., gradable adjectives and adverbs) and others don’t (e.g., non-gradable adjectives and adverbs, nouns and verbs). And what is meant by ‘measure’, here, echoes a certain practical understanding found in philosophical discussions of measurement theory:

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we apply various measuring devices to a given entity and record various types of values, depending on the device. An alternative requires greater transparency; to be properly called a ‘measure’, a function must preserve certain structural properties of the measuranda in the structure of scales. This latter understanding grounds the alternative, compositional theory that I advance in this book.2⁸ In Berka’s (1983) terms, measurement theory understands measurement in terms of homomorphic, or structure-preserving relationships between a given empirical structure—i.e., a set of entities and an observable ordering relation between those entities, (94a)—and a numerical structure—i.e., an ordered set of numbers or magnitudes, (94b). Abstractly, then, the concept of measurement ℳ may be represented as a relation like (95a) or a structure like (95b), where Φ is a set of homomorphic functions from ℰ to 𝒩. On either formulation, measurement is understood strictly as the representation of observable empirical relationships in numerical relationships.2⁹ (94) a. ℰ = ⟨E, RE ⟩ b. 𝒩 = ⟨N, RN ⟩ (95) a. ℳ(ℰ, 𝒩) b. ⟨ℰ, 𝒩, Φ⟩ To delimit the conceptual from the practical understanding of measurement, consider a simple case. Suppose that we want to find out how hot some coffee is; to do so, should we measure the coffee, or its heat? The practical answer, and the one expressed by the lexical theory of comparatives, is ‘the coffee’. This answer ties the question (and, thus, the object of measurement) to the measuring behavior—sticking a thermometer in the coffee. The conceptual answer, the one I will tie to the theory I advance, is ‘the heat (of the coffee)’. This understanding ties the object of measurement directly to the property represented by the temperature scale.3⁰ The lexical theory directly encodes an analogue of the practical conception of measurement. To see this concretely, consider how the lexical theory interprets a GA like hot, as in (96). In a phrase like hot coffee, the xs will be identified with portions of coffee. If that stuff happens to have some interesting inherent structure (i.e., if coffee happens to introduce a particular ordered set), that structure plays no role in determining the output of hot. Rather, hot is, if anything, sensitive to some other ordering—one imposed on coffee portions, based on the quantity of heat they manifest. Put differently: if one supposed that coffee ‘brings along’ certain mereological structure, that structure is ignored in the mapping to degrees. 2⁸ Neither here nor elsewhere do I attempt a systematic integration of semantics with measurement theory. See Klein 1991 for early discussion, and Sassoon 2007, 2010, Lassiter 2011a, and Cariani et al. under review. 2⁹ According to Berka, the development of this thought proceeded in three major phases, of which we are presently in the third: first, developments in Helmholtz 1887/1921 and Russell 1903/1964; second, Campbell 1920/1957, in his focus on applications in physics; and third, Stevens (especially his 1946), in his focus on psychology, sociology, and economics (see also Scott & Suppes 1958, Suppes & Zinnes 1963, and Krantz et al. 1971; cf. Roberts 1985). 3⁰ As Berka writes, “Often, there exist very complex connections between the measured objects, on which or with the help of which we measure something … and the features which we measure or with the help of which we measure these objects”, however “that which we measure, and that on what or by means of which we measure, are not to be identified” (Berka 1983, 29).

2.4 ‘measurement’, and the thesis

(96) Lexical theory λxe .hot(x)

35

⟨e, s⟩

What if, instead, degree introduction involved the kind of representational role indicated by Φ in (95b)? This is the view I will advance. In the case of nominal and verbal comparatives (e.g., more coffee, run more), evidence for such a view is plain and abundant. Consider that coffee is generally taken to express a property of coffee portions ordered by a part-of relation (cf. Cartwright 1975), and that more coffee can only be understood to express a comparison by volume or weight, not by temperature; only the former dimensions preserve strict part–whole relations between the portions (Schwarzschild & Wilkinson 2002, Schwarzschild 2006).31 Consider the verbal parallel: run expresses a property of running activity ordered by inclusion (e.g., Bach 1986a), and run more can express a comparison by duration or distance but not speed (cf. Nakanishi 2007, Wellwood et al. 2012). For the core cases motivating the degree-theoretic approach (Chapter 4)—the case of adjectival comparatives, and by extension, adverbial comparatives—more argument is needed. However, I suggest that the evidence here too is substantial. What would it mean for a compositional semantics to tell us that hotter coffee involves measurement of heat, rather than measurement of coffee? I will suggest that it involves reification of ‘heats’ as neodavidsonian states, and interpret hot as a property of such states, (97).32 Assuming that the states are ordered in the right way (i.e., very much in a way that is reflected by the temperature scale), the mapping to degrees can be seen as representational in the desired sense. (97) Compositional theory λsv .hot(s)

⟨v, t⟩

Instead of GAs introducing measure functions, I posit that they are introduced by a covert analogue of much. much, then, is interpreted as essentially a variable over measure functions, the particular values of which must be structure-preserving, in the right contexts, in the right ways. This analysis builds on but departs from Schwarzschild (2002, 2006), for whom a null head Mon∘ introduces the semantics of degree;33 I impose an additional condition on the selection of measure functions by Chapter 5. The analysis also builds on Bale and Barner’s (2009), for whom structuresensitivity was built into a non-decomposed more, but I underwrite that sensitivity in terms of structure preservation.3⁴

31 Schwarzschild attributes this pattern to a ‘monotonicity’ constraint, as I will; Krifka 1989 discusses similar patterns in terms of ‘extensivity’, and Higginbotham 1994 in terms of ‘additivity’. Compare Champollion 2010, 2017. 32 To stave off one potential worry, note that this move won’t bar our access to the individuals that bear, hold, manifest, or instantiate the heat, since these can be recovered via thematic functions. 33 Similar proposals are compositionally implemented by Rett 2008 and Solt 2009, 2015. 3⁴ My account furthermore shares with Bale 2006, Bale & Barner 2009 the explicit appeal to homomorphic mappings. However, the relevant functions are part of the lexical semantics of GAs for Bale, and the structures preserved in such cases are orderings on individuals, rather than on states.

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Thus the lexical and compositional theories interpret GAs in different types, which affects the sorts of explanations they can offer for the core data animating degree semantics. By assigning a special type to GAs, the lexical theory rules out examples like (98a) as a type-mismatch between the comparative morphology and the non-gradable adjective. The compositional theory, instead, rules out all of (98) via the selection of measure functions by much: only domains with non-trivial structure can be measured. Non-gradable adjectives (98a), like count nouns (98b) and singularly-interpreted telic VPs (98c), are naturally understood as lacking such structure. (98) a. ?A is more hexagonal than B is. b. ?Ann drew more hexagon than Bill did. c. ?Ann drew one hexagon more than B did. The lexical theory straightforwardly captures the morphological asymmetries between comparatives with adjectives and adverbs and those of other categories, where the compositional theory has to say something special. Unlike GAs, nouns and verbs can’t combine directly with -er; e.g., (99). The lexical theory can again rule out such direct combinations due to a type mismatch: -er requires a measure function type, but milk and run give only property types.3⁵ On the compositional theory, explaining the anomaly of such combinations is assigned to the morphophonological component, which determines the distribution of the surface form much and the analytic comparative form, more. (99) a. ∗ Ann drank milker than Bill did. b. ∗ Ann ranner than Bill did. A central question for the compositional theory is: what are the empirical relational structures ℰs suggested by semantic competence? The distinction I will elaborate, between ‘measurable’ and ‘non-measurable’ predicates, distinguishes predicates that invoke relevant ℰs from those that don’t. For better or worse, this position echoes Carnap’s view on measurement, which “considers every ordering (inasmuch as it permits a mutual comparison of different objects with respect to some common property) to be a sufficient condition of measurability” (cited in Berka 1983, 215). The important difference, in my view, sweeps across lexical category, to diagnose whether a predicate has non-trivial structure on its domain. I will be more precise about this. But if correct, we can use comparatives to learn about the order-theoretic properties on the domains of different predicates, based on whether they felicitously combine with more, and which dimensional interpretations they therein support.

3⁵ It is worth considering whether, intuitively, the ‘mistakes’ represented by (98) and (99) have the same feel. To me, the former ring of category mistakes, while the latter are simply uninterpretable. Despite what I think is a real phenomenological asymmetry, the lexical theory offers the same sort of explanation for both.

3 Measuring stuff and process

I have presented one detailed approach to the semantics of adjectival and adverbial (GA) comparatives, using standard tools from degree semantics with minimal extensions supported by event semantics. I called this the lexical theory, as its central posit is that there are some lexical items—the GAs, in particular—which directly encode measure functions (i.e., mappings from entities or events to degrees). With this chapter, I take my first initial steps towards an alternative, compositional theory of degree introduction, in which no adjective, noun, or verb, etc. lexically expresses a measure function. Instead, measure functions are introduced into the semantics by the comparative morphology itself. This exploration begins with the question of how comparatives that target nouns and verbs like (100) are interpreted. Answering this will depend, of course, on what we take the parts of the sentences to be, and how those parts are interpreted. Outside of any focus on comparatives, mass nouns like coffee and atelic verbs like sleep are analyzed as particular sorts of property terms. Inside comparatives, entities satisfying those properties are mapped to degrees by an expression like much. After all, this expression makes an asymmetric difference in grammaticality between GA and N/V comparatives: it is necessary for nominal and verbal equatives, (101), but unacceptable with GA equatives, (102). (100) a. Al bought as much coffee as Bill did. b. Al ran as much as Bill did. (101) a. ∗ Al bought as coffee as Bill did. b. ∗ Al ran as as Bill did. (102) a. ∗ Al is as much tall as Bill is. b. ∗ Al ran as much fast as Bill did. That much plays the role of the GA in N/V comparatives is thus a natural hypothesis that is often assumed, but rarely argued for (see, among others, Heim 1985, 2000, Bhatt & Pancheva 2004). If it is correct, how should we formalize the interpretation of much? Notice that (100a) is naturally interpreted as a comparison between the volumes of two portions of coffee, and (100b) between the distances of two stretches of running activity. Thus, the meaning of much can’t be hardwired for a particular measure function. Furthermore, given that (100a) additionally supports a comparison of weights, and (100b) of durations, the specific interpretation of much can’t be defined deterministically based on the N or V targeted in the comparative. The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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This chapter surveys some reasons for believing that much, overtly or covertly, introduces a measure function in nominal and verbal comparatives. In the theory I develop, the variability in the selection of measures both within and across predicates is captured by interpreting much as a variable over measure functions. What is interesting about this sort of meaning is not its context-sensitivity, but in how that contextsensitivity is restricted: as Schwarzschild (2002, 2006) and Nakanishi (2007) observed, N/V comparatives may only involve measures that are monotonic with respect to the measured domain, DP —that is, they only permit comparisons along dimensions that preserve the ordering ≺P . I thus build on Schwarzschild’s and Nakanishi’s initial insights in order to offer a general theory of the interpretation of the much that appears overtly in equatives like (100), and more or less covertly in comparatives with more—i.e., much (cf. Bresnan 1973). The key semantic property of this morpheme is that it is always structure-preserving on the domain targeted for measurement. This property will play a prominent role in the explanation of the semantics of a wider array of comparative constructions in subsequent chapters. In this chapter, I follow these other authors in stating the monotonicity constraint as sensitive to just mereological ≼P s, but I will undo this assumption later. It is in virtue of the structure-preservation property of much that we can say that my compositional theory of more introduces the concept of ‘measurement’ familiar from measurement theory, and discussed at the end of the last chapter. Comparatives that involve a mapping to degrees by much may only invoke scales that ‘represent’ the measured domain in the appropriate way. With this idea on the table, Chapter 4 revisits the lexical theory, looking at its target data through the lens of lessons learned in this chapter. This leads me to re-envision those core cases, and to apply the compositional theory here and more broadly.

3.1 The empirical landscape 3.1.1 Noun phrases Unlike gradable adjectives (GAs), nouns in English appear with -er and as only via the mediation of much—overtly with the equative form as much, and covertly with comparative more.1 Intuitively, the comparative sentences in (103a) and (103b) express that the amount of coffee Al drank, or rock she found, strictly exceeds that of Bill, while (103c)–(103d) express that Al’s amount meets or exceeds Bill’s. The overlap—both morphological (-er/more and as) and semantic (> and ≥)—between such constructions and those discussed in the previous chapter suggest the familiar labels. 1 Linguists have tended to assume, since at least Bresnan 1973, that nominal more, at least, hides semanticallysignificant internal structure: i.e., it decomposes morphosyntactically into much and -er. Such an assumption raises the question of how nominal and adjectival occurrences of more are related (cp. more coffee and more intelligent). I address this question directly in Chapter 4.

3.1 the empirical landscape

(103) a. b. c. d.

Al drank more coffee than Bill did. Al found more rock than Bill did. Al drank as much coffee as Bill did. Al found as much rock as Bill did.

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comparative equative

The other comparative forms also manifest with nominal targets. Some noteworthy morphosyntactic differences here include the fact that much surfaces in the excessive form, (104a)–(104b), assetive enough surfaces before the noun, (104c)–(104d) (where it appears following GAs),2 and if an expression surfaces specifying the comparison set for the superlative, it is here preceded by of (cp. the tallest girl in her class, ∗ the tallest girl of her class). (104) a. b. c. d. e. f.

Al drank too much coffee to sleep now. Al found too much rock to carry home. Al drank enough coffee to stay awake. Al found enough rock to be able to share. Al drank the most coffee of anyone. Al found the most rock of anyone.

excessive assetive superlative

The behavior of mass nouns like coffee and rock in the comparative contrasts with the behavior of count nouns like idea and traffic cone: while mass nouns are perfectly acceptable and have a stable interpretation in this form, count nouns are marked here. Consider that although one can imagine a world in which more idea relates to the relative profundity of an idea, such a reading is not available to (105a) and (105b). This problem is not specific to abstract nouns like idea; examples with concrete traffic cone are similarly marked, (105c)–(105d), although nouns like this support a kind of re-interpretation wherein they label a kind of stuff. These observations support the generalization that the comparative form disallows characteristically ‘count’ interpretations. (105) a. b. c. d.

?Al has more idea than Bill does. ?Al has as much idea as Bill does. ?This street has more traffic cone than that one does. ?This street has as much traffic cone as that one does.

Importantly, idea and traffic cone are rendered perfectly natural and acceptable in nominal comparatives when they have combined with the plural morpheme, (106). In such cases, the comparative can only be interpreted as expressing a comparison between numbers of things—whether abstract like ideas, or concrete like traffic cones. I investigate this pattern in detail in Chapter 5. (106) a. Al has more ideas than Bill does. b. This street has more traffic cones than that one does. 2 Actually, enough can follow N, but may not precede A, e.g., Al ate soup enough to feel comfortable, but ∗ Al is enough tall to date Bill (Bresnan 1973). See Doetjes 1997 and Neeleman et al. 2004 for finer-grained explorations of the morphosyntactic details of degree constructions in English and other languages.

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Nominal comparatives are subject to a ‘monotonicity constraint’ that is found with a variety of measure-related constructions (Schwarzschild 2002, 2006), including partitives headed by much like (107).3 Schwarzschild observed two major properties of such constructions: (i) they support variable dimensions for comparison, but (ii) the variability is interestingly constrained. For example, (107) can be used to compare portions of coffee by weight or volume, but not by temperature, suggesting that the relevant constraint permits only dimensions that respect the part–whole relations holding between the portions. (107) Al didn’t buy much of our coffee. To see monotonicity in action, we need only consider examples like (103) and (104) against relevant cases like the following. Consider two portions of coffee, c1 and c2 . In point of fact, these portions instantiate some amount of volume, weight, and temperature. Now consider some proper subparts of c1 and c2 in Dcoffee (the set of portions of coffee, ordered by a part-of relation ≼coffee ), namely c′1 , c″1 , and c′2 , c″2 . Importantly, c1 has a greater volume and weight than either of c′1 , c″1 , and the same is true for c2 and its proper subparts. Yet c1 and c2 have the same temperature as all of their parts. According to Schwarzschild’s constraint, then, only volume or weight are possible for (103) and (104) since only these map greater portions in ⟨Dcoffee , ≼coffee ⟩ to higher degrees. (108) a. Al has more coffee than Bill does. b. Al has as much coffee as Bill does.

volume, ∗ temp volume, ∗ temp

Part of the meaning of nominal comparatives ensures monotonic dimensions for comparison relative to the order-theoretic properties of the measured domain. As we will see, Schwarzschild’s generalizations can be straightforwardly captured in mereology-based semantic frameworks that posit interesting structure in the extensions of nouns like coffee. Furthermore, the intuitive markedness of characteristically ‘count’ nouns can be keyed to the assumption of such frameworks that the extensions of those nouns lack relevant structure.

3.1.2 Verb phrases Atelic verb phrases (VPs) do not include, as part of their semantic content, what is required for the happenings they describe to come to an ‘end’ or telos. A long tradition in formal semantics ties this referential property to a general notion of ‘unboundedness’ that applies equally well to atelic VPs and mass NPs. And indeed, such VPs equally well surface with much in the comparative, but what they quantify

3 Schwarzschild mainly focuses on pseudopartitive (e.g., 20 ounces of water) in contrast to attributive measure phrase constructions (e.g., 20 degree water). I do not discuss these cases in any detail.

3.1 the empirical landscape

41

is different: (109) express comparisons between the amount of running or sleeping Al and Bill did, with (109a)–(109b) expressing a strict exceeding relation between those amounts, and (109c)–(109d) a meeting or exceeding relation. (109) a. b. c. d.

Al ran more than Bill did. Al slept more than Bill did. Al ran as much as Bill did. Al slept as much as Bill did.

comparative equative

As with NPs, VPs can be targeted by the other comparative forms, (110), and here too we can observe some differences in how these forms are realized. For the first time, as/too surface linearly adjacent to much, and in each case the verb phrase linearly precedes the whole complex of relevant comparative morphology. (110) a. b. c. d. e. f.

Al ran too much to feel refreshed. Al slept too much to feel refreshed. Al ran enough to feel refreshed. Al slept enough to feel refreshed. Al ran the most of the team. Al slept the most of her family members.

excessive assetive superlative

Telic verb phrases, those that indicate a completion in their described activity, are generally considered the verbal parallel of count noun phrases. And indeed, the interpretation of such VPs is marked in the comparative: while the sentences in (109) can be used to compare ‘what happened’ if Al and Bill did only one thing each, those in (111) cannot: (111) are only interpretable in contexts supporting multiple happenings of the described sort. Although it is conceivable that forms like (111) could be used to express comparisons of duration, such a reading is not available. (111) a. b. c. d.

?Al graduated high school more than Bill did. ?Al graduated high school as much as Bill did. ?Al ate her first cupcake more than Bill did. ?Al ate her first cupcake as much as Bill did.

Some suggestive evidence as to what might be going on in the English sentences in (111) is provided by languages that have richer systems of verbal aspectual morphology (Wellwood et al. 2012). In a language like Bulgarian, an atelic VP headed by play in the perfective aspect is perfectly acceptable in the comparative, and is interpreted as a comparison between amounts of playing activity. In contrast, a telic VP in the perfective aspect is ungrammatical in the verbal comparative: examples like (112b) have no interpretation (R. Pancheva, p.c.). (112) Minalata sedmica (‘last week’), a. Ivan igra poveče ot Maria. Ivan play-pfv.past more from Maria ‘Ivan played more than Maria.’

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b. ∗ Ivan izkaĉi vrâh Musala poveče ot Maria. Ivan climb-pfv.past top Musala more from Maria ‘Ivan climbed Musala more than Maria.’ These data are important. In Chapter 5, I will suggest that they echo the facts for count NPs, and I will provide a correspondingly paralel analysis. In brief, perfectivemarked telic VPs are true, one at a time, of events of the described sort; in the imperfective, though, the interpretation that there were multiple such events (i.e., a plurality; cf. Ferreira 2005) becomes available. As (113) illustrates, not only are such VPs grammatical in the verbal comparative but they are naturally interpreted as a comparison between numbers of events. (113) V onezi dni (‘in those days’), Ivan izkaĉvasê vrâh Musala poveče ot Maria. Ivan climb-impf.past top Musala more from Maria ‘Ivan climbed Musala more than Maria.’ The English comparatives in (111) can be read in one of two ways, both of which are odd, and for reasons that depend on whether the telic VP is read as singular or plural. If the VP is read as singular, it corresponds to a perfective telic predicate in Bulgarian, which is uninterpretable. If the VP is read as plural, it corresponds to an imperfective telic predicate in Bulgarian, yet this interpretation runs afoul of what we know about events like graduating high school, or eating one’s first cupcake—namely, that these are the sorts of things that an individual can do only once. Returning to atelic VPs, we can see that their occurrence in verbal comparatives is subject to the same constraint identified for their nominal counterparts (cf. Nakanishi 2004, 2007, Wellwood et al. 2012).⁴ To see this, consider (114), and suppose that Al’s run is r1 and Bill’s run is r2 . Both r1 and r2 have some non-zero measure of duration, spatial distance, and speed. Yet (114) can only be understood to compare duration or distance, both of which ensure that r1 and r2 measure greater than any of their proper subparts; that isn’t guaranteed for a measure of speed. The available dimensions for comparison must be monotonic with respect to running activity. (114) a. Al ran more than Bill did. b. Al ran as much as Bill did.

duration, ∗ speed duration, ∗ speed

The monotonicity generalization that Schwarzschild identified applies equally well to nominal and verbal comparatives. Stating the relevant constraint on the selection of measure functions has so far appealed to preservation of mereological structure— part–whole relations holding between portions of stuff or happenings (e.g., Link 1983, Bach 1986a). Thus, approaches that posit such structure support stating the relevant constraint, as well as explaining the marked comparatives—those targeting count NPs and perfective telic VPs—in terms of extensions that lack such structure. ⁴ See Doetjes 1997, Schwarzschild 2008, and references therein.

3.2 stuff and process

43

3.2 Stuff and process 3.2.1 Noun and verb reference I tie the observation of variable but constrained dimensions in nominal and verbal comparatives to the nature and structure of the entities the target NP or VP is true of. A crucial assumption about those entities is that, at least sometimes, they bear intrinsic mereological relationships to one another: coffee is true of portions of coffee and subportions thereof, just like run (in the park) is true of running activity and substretches thereof. A target NP or VP that is true of atomic entities—e.g., single ideas or graduations—is not permitted in the comparative. This section sketches the independent motivations for these assumptions. In the nominal domain, mass noun contexts (e.g., this is N, a lot of N) reveal mereological structure, whereas (singular) count noun contexts do not (e.g., this is a(n) N).⁵ One pertinent demonstration involves whether N displays cumulative reference in either context: that is, if N applies to two distinct entities, does it also apply to their sum? A noun like mud in a mass context shows cumulative reference, (115a), while cup is simply odd in such a context, (115b). In contrast, cup in a count context does not show cumulative reference, (116a), and mud is odd here.⁶ (115) a. This is mud, that is mud; taken together, it’s mud. b. ?This is cup, and . . . (116) a. This is a cup, that is a cup; taken together, it’s a cup. b. ?This is a mud, . . .

??

Patterns like these suggest that mud should be categorized as a mass noun, and cup as a count noun. On many approaches, the lexical difference between these nouns is characterized by the kinds of things that the nouns are true of: mud applies to portions of mud, arbitrary subparts of which are also mud; cup applies to objects, arbitrary subparts of which are not instances of a cup. This difference can be modeled by assuming that count nouns like cup are true of atomic entities but none of their parts, while mass nouns like mud are true of entities and any of their parts (i.e., their extensions are anti-atomic).⁷

⁵ Other tests look for divisiveness, or homogeneity; e.g., if mud applies to a portion of stuff, it also applies to any proper part of that stuff. For relevant discussion and criticism, see Bunt 1979, Wiggins 1980, Zucchi & White 2001; also, Rothstein 2010, Landman 2011, Grimm 2012, and Sutton & Filip 2016. ⁶ These examples are well-chosen, since some nouns flexibly appear in both contexts, cp. some rock, a rock (see Gillon 2012 for an overview, also fn.5). ⁷ Superordinate mass nouns like furniture, in contrast, do have atoms in their extensions (the individual chairs and tables, etc.). I assume what Gillon 2012 calls the ‘neutral’ theory of the correspondence between mass NP syntax and semantics (Pelletier 1974, Gillon 1992, Fox & Grodzinsky 1998, Fox 2000, Nicolas 2002, 2008, Bale & Barner 2009): mass contexts carry no specific implications about atomicity. Alternatives are the anti-atomic theory, which bars atomicity in the extension of any mass noun (Ter Meulen 1981, Link 1983, Roeper 1983, Bunt 1985, Lønning 1987, Landman 1989, Eschenbach 1992, Ojeda 1993, Higginbotham 1994, a.o.), and the atomic theory, which holds that all mass noun extensions are, utimately, atomic (Chierchia 1998a, 2010). Again, see Gillon 2012 for discussion and overview.

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Just as the intuitive difference between mass and count nouns is encoded as a difference in their domains of application, so will we locate the difference between atelic and telic predicates (Taylor 1977b, Mourelatos 1978, Hoepelman & Rohrer 1980, Bach 1986a, Link 1987, Krifka 1989, Landman 2000, Rothstein 2004, Borer 2005a, a.o.; cp. Bennett & Partee 2004[1972]).⁸ To show the asymmetry in cumulative reference, I use the modifier for an hour to induce an atelic context on the predicate, and in an hour a telic context (cf. Dowty 1979). We see that a VP headed by run is comfortable in atelic contexts and shows the characteristic inferential pattern of a cumulative predicate, (117a), while graduate high school is not comfortable in such contexts in the first place, (117b). The reverse is true in telic contexts, where graduate high school is comfortable but fails cumulativity, (118a), run is uncomfortable here, (118b). (117) a. If Al ran for a year, and then again for a year, then what happened was Al ran for two years. b. ?If Al graduated high school for a year . . . (118) a. If Al graduated H.S. in a year, then again in a year, then what happened was Al graduated H.S. in two years.

??

b. ?If Al ran in a year . . . Such patterns support categorizing run as an atelic predicate and graduate high school as a telic predicate. At least since Bach (1986a), many authors render the difference between these predicates roughly as follows. The satisfiers of run are stretches of a certain sort of activity or process, all of which have substretches of the same type. In contrast, graduate high school applies to ‘events’, proper—entities that, like objects, are conceived of as indivisible wholes—that is, atoms. Following Bach and others, I assume that (singular) telic VP extensions are wholly atomic; and, extending the analogy between the nominal and verbal domains, that the extensions of atelic predicates (i.e., those that are true of processes; see Vendler 1957, Taylor 1977b) are anti-atomic.⁹ Positing entities of various sorts—what we might call substances and objects, on the one hand, and processes and events, on the other—is important not only for linguistic semantics but also for cognitive psychology. I return to potential intersections in Chapter 9. For now, I simply assume that there are such differences in the domain, and that they matter for understanding the semantic commitments of lexical items and certain grammatical contexts. The formal properties that these entities can display (or fail to display) are very important for how I analyze nominal and verbal comparatives, and so I turn now to one way of modeling those properties.

⁸ See Ryle 1949, Vendler 1957, Kenny 1963, Verkuyl 1972, Mourelatos 1978, Dowty 1979, Parsons 1990, Filip 2004, 2011 for discussion of telicity. Ramchand 1997, 2003, Borer 1998, 2005b, Ritter & Rosen 1998, van Hout 2000, and Kratzer 2004 discuss structural factors in determining telicity. ⁹ I do not assume that atelic syntax imposes anti-atomicity; rather, it is neutral with respect to this question, just as mass syntax is. C.f. footnote 7.

3.2 stuff and process

45

3.2.2 Parts and joins If a predicate shows cumulative reference, this is evidence that its domain of application is structured. The extension of mud consists not only of the totality of the mud on my desk (itself the ‘sum’ of many smaller portions that themselves satisfy mud) but also the sum of the mud on my desk and the mud on my office floor. That portions, their parts, and their sums are all in the extension of a noun like mud underwrites modeling the domains of such predicates as mereologically structured; in particular, as having the structure of a join semi-lattice. When I say that a given domain is structured, I have in mind abstractions like this. Substance mass nouns or atelic VPs, P, apply to entities ordered by a part-of relation, ≼P , as essentially laid out in §1.2.3 of Champollion 2017 (see Cartwright 1975, Link 1983, Chierchia 1998a, among others). ≼P is a primitive binary relation which is such that the following hold: for all v, v′ , v″ : v ≼ v (reflexivity); if v ≼ v′ and v′ ≼ v″ , then v ≼ v″ (transitivity); and, if v ≼ v′ and v′ ≼ v, then v = v″ (antisymmetric). Attempts at showing that natural language understanding supports such axioms usually involves reasoning with the part of construction, which doesn’t obviously support the relevant inferences (Champollion 2017 cites Moltmann 1997, 1998). This shouldn’t deter us, however, since ≼P is a theoretical posit, not a semantics for part of clauses (Champollion 2017).1⁰ Assuming that the domains of expressions like mud and run are ordered in this way, it is worth asking how their order-theoretic properties compare with those of scales as outlined in Chapter 2. One difference is just that between partial and total orders: the part-of relation ≼P on a substance or process domain DP is not connected (i.e., it is not generally the case that any two things in DP , x and y, are such that x is a part of y or y is a part of x), whereas scalar ordering relations are. Another difference is that we assume DP to have a unique least upper bound—an element which had all other elements in the structure as a part—whereas any given scale needn’t have such an element, and usually doesn’t.11 The kinds of part-of orderings we are considering, then, are join semi-lattices meeting the definition in (119), where the relevant operation ∘ is join, which I notate using ⊔.12 As an abstraction, this is one way of recording our intuitions about the sorts of things that are in DP , and the part–whole relationships that those entities show to one another, i.e., ⊔P records that a given P is cumulative. (119) A structure ⟨D, ∘⟩ is a join semi-lattice iff ∘ is idempotent, commutative, associative, and closed. 1⁰ This move recalls discussion (and controversy) surrounding the decomposition of sentences like A moved B into representations with an implicit cause predicate. Fodor (Fodor 1970) famously objected that such sentences don’t mean the same as any putative paraphrase A caused B to move. Later, Thomson 1987, p. 110 gives us reasons to doubt that we should expect such correspondences between implicit predicates and English words. 11 See Rotstein & Winter 2004 and Kennedy & McNally 2005 for recent influential discussion of finer-grained properties like ‘boundedness’ for particular scales. 12 An operation, for our purposes, is just a function that maps a pair of entities from the cross-product, D × D, of domain D, to an entity in D. In the present case, the relevant join operation maps any entities a and b in DP to their join, a ⊔P b. This operation is often characterized directly in terms of mereological summation (see e.g. Simons 1987) and notated ⊕ (e.g., Link 1983).

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An idempotent operation is one that, when a given entity is taken with itself, the output is itself. For instance, the operation max on two natural numbers returns the greater of the pair; taking any two numbers together, the output will be that number (since no number is greater than itself). The operation of addition on the natural numbers is not idempotent, since the pair of 1 with itself returns the number 2. The join operation ⊔ applied to portions of mud is idempotent, since taking a portion of mud with itself gives you no more, no less than that portion. A commutative operation is one for which the order of the elements in the input fails to affect the operation’s output. Addition is commutative on the natural numbers, since the sum of n and m doesn’t change whether we consider +(n, m) or +(m, n). Subtraction on the integers is not commutative, since −(1, 2) has a different value than −(2, 1). The operation ⊔ on portions of mud is commutative, since arbitrary portions of mud x and y, considered together, is the same mud regardless of the order in which x and y are considered. An associative operation is one that, applied iteratively to the same entities, always yields the same result. For example, addition is associative on the natural numbers, since for any m, n, p ∈ ℕ, m + (n + p) is the same as (m + n) + p, but subtraction is not associative on the integers, since, for example, the result of subtracting (3 − 2) from 5 is not the same as subtracting 2 from (5 − 3). That ⊔ is associative with respect to portions of mud can be intuited by considering three portions of mud together, taken in different orders—the result is always the same mud. Finally, an operation is closed if it always gives an output for any pairing of inputs from its domain. Addition is closed on (at least) the positive integers, and subtraction is closed on the positive and negative integers. That ⊔ is closed with respect to mud can be seen by from the fact that it is always possible to consider two portions of mud together. Since all of what we have said about mud can be said about running activity, I assume that the domain of run has the same kind of structure. For predicates P like these, their domain is partially ordered by ≼P , and, equivalently, closed under join ⊔P ; this equivalence is stated in (120). (120) Equivalence between ≼P and ⊔P For all x, y ∈ DP , x ≼P y just in case x ⊔P y = y.

3.2.3 Anti-atomicity Formally, then, mass NPs like mud and atelic VPs like run are treated on a par: their domains are non-trivially structured, differentiating them each within their respective lexical categories from count NPs like traffic cone and telic VPs like graduate high school.13 It is common to say that, while mass and atelic expressions apply to parts and

13 See Pelletier 1974, Cartwright 1975 for nouns like coffee, and Parsons 1990, Kratzer 1996 for verbs like run.

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wholes (just of different types of things), count and telic expressions apply to whole, indivisible entities, or atoms. To properly delimit the mass and atelic from the count and telic, then, requires a definition based on which we can say that some predicates are atomic, and others are anti-atomic. Atomicity can be defined in terms of the part-of relation, simpliciter, as in (121)—i.e., an atom is something that has no proper parts—and an atomic predicate can be defined as one for which every one of its satisfiers is an atom in this sense, (122).1⁴ (121) Atom For all v, v is an atom if there is no v′ such that v′ ≺P v. (122) Atomicity1⁵ A predicate Q is atomic if, for all v ∈ DQ , v is an atom. Mass nouns like mud are different: anything that satisifies mud has at least one proper part that also satisfies mud; such nouns are anti-atomic in the sense of (123). There has been much debate in the literature about whether we should think that any mass noun in fact has this property (see e.g. Chierchia 1998a for an opposing position). I follow Bunt (1979) and Gillon (1992): as far as the language is concerned, there are no atomic parts in the extensions of substance mass nouns like mud.1⁶ (123) Anti-atomicity A predicate Q is anti-atomic if, for all v ∈ DQ , there is a v′ ∈ DQ such that v′ ≺P v. By extension, I assume that the verbal correspondents of substance mass nouns— atelic VPs like run—are also anti-atomic, just in this case we are talking about process rather than stuff.

3.3 Nominal and verbal comparatives The NPs and VPs that are natural in the comparative—those true of stuff or process— predicate of entities whose measure is introduced compositionally. In particular, those entities are measured by some function introduced by the morpheme much, part of more, which surfaces overtly in as much coffee, run too much, so much sleep, etc. This morpheme is underspecified in the sense that it does not introduce a constant measure function (as tall does, at least on the lexical theory); however, any value for its measure 1⁴ These definitions assume that the relevant understanding of ≼P is in terms of unstructured parthood. That is, while we are factually aware that the satisfiers of traffic cone have parts—e.g., the square plastic base, the top plastic cone—these are structured parts which, I assume, are not relata of ≼P ; see Champollion 2017 for discussion. 1⁵ Also called ‘quantization’; cf. Krifka 1989, and more recently Husband 2010. 1⁶ That is, again, not to suggest that mass syntax simpliciter implies anti-atomicity. Mass syntax must permit the coexistence of substance nouns like mud and superordinate nouns like furniture, which have atomic minimal parts. This suggests an overall theory in which mass syntax is neutral with respect to atomicity; see the authors cited in the text, and footnote 7.

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function variable, μ, must adhere to certain conditions with respect to the domain targeted for measurement, DP . Whatever the conditions, they must support Schwarzschild’s monotonicity generalization, as well as the awkwardness of (singular) count NPs and telic VPs in comparative constructions. I tie the conditions to the types of properties just laid out: much presupposes a non-atomic domain for measurement, DP , and it introduces a measure function that preserves the structure of ≼P in the mapping to degrees. This ties the variability in dimensionality to the ontology in two ways: (i) stuff and process are different, and so are measured differently; and, (ii) only measures that preserve proper-part relations on such domains are admissible.

3.3.1 The proposal The mapping to degrees in nominal and verbal comparatives is variable both within and across predicates: recall that more coffee can be used to express a measure by volume or weight, while run more can be used to express a comparison distance or duration. But this variability is not unconstrained: run more can’t express a comparison by volume or speed, nor can more coffee express a comparison by duration or temperature. I presume that running can’t be measured for volume, and that coffee can’t be measured for duration, because of the sorts of entities that they are: existents take up space, and we can talk about how much space they take up; happenings take time, and we can talk about how much time they take. It seems that observations like these are plausibly captured by saying that, while there are a variety of measure of measure functions available to be exploited in the comparative, they may place different restrictions on their domains of application. For example, in (124), the measure function volume is restricted to the domain of existents, type e, and duration is restricted to the domain of happenings, type v. (124) a. volume : De → ⟨Dυ , ≾υ ⟩ b. duration : Dv → ⟨Dπ , ≾π ⟩ It is straightforward to interpret the morpheme that introduces measure functions in nominal and verbal comparatives as introducing a variable valued by such functions. In (125), much brings along index μ, which ranges over functions of type e or v to s (i.e., the measure function type; η indicates neutrality between e and v), the value of which is fixed by the assignment function A. On this approach, much functions semantically very much like a pronoun, except that it is valued by measure functions rather than basic entities.1⁷

1⁷ I inquire as to whether such an index-based approach is the most explanatory way of capturing the indeterminacy of much in §3.3.4.

3.3 nominal and verbal comparatives

(125) Interpretation of much (with restrictions) Jmuchμ KA = A(μ)

49

⟨η, d⟩

Some example values on different assignments are given in (126). (126) a. b. c. d. e.

A(μ) = volume A′ (μ) = duration A″ (μ) = temperature A‴ (μ) = speed …

The more interesting aspects of the interpretation of much concern the conditions imposed on the selection of these values, which are derived from the compositional semantics itself. First, only measures that are monotonic in Schwarzschild’s (2002, 2006) sense are admissible. That is, any A(μ), for assignment A, must preserve the structure of the measured domain, and the predicate that much combines with must have non-trivial structure to be preserved.1⁸ I discuss these aspects in turn. Requiring that the mapping be Schwarzschild-monotonic (or S-monotonic, for short) means that the choice A(μ) must, in whatever grammatical context in which it appears, be such that any strict part-whole relations holding between elements of its measured domain are preserved in their corresponding scalar degrees, (127). In the cases presently of interest, this means that any measurandum must be assigned a larger degree than that of any of its proper parts. This will exclude temperature as a measure with coffee, for example, since greater portions aren’t likely to have greater temperature, and the same for speed with run, mutatis mutandis (I generalize this condition in Chapter 4.). (127) S-monotonicity A measure function μ : Dη → Dδ is S-monotonic if, for all v, v′ ∈ Dη , if v ≺Part v′ then μ(v) d b. Jas muchμ KA = λds λvη .A(μ)(v) ≥ d

⟨s, ⟨η, t⟩⟩

I provide additional compositional details in relation to the nominal comparative in (136), assuming the (simplified) structure in (137). (136) Al drank more coffee than Bill did. (137)

S Al[θAg ]

VP drank

DP[θTh ]

e

NP DegP Deg′ muchμ

coffee

thanP -er

The composition of the DP in (137) is as in (138), with the semantic contribution of the than-clause abbreviated as δ. The composition is exactly like the derivation of the interpretation of hotter coffee in §2.3.4, modulo much. The type e variable introduced by coffee is bound by the interpretation of the null determiner e, and the whole phrase is bundled into its thematic role by [θTh ]. The result is a property of events that have coffee whose μ-measure is greater than δ as their Theme. (138) a. b. c. d.

JDegPKA = λv.A(μ)(v) > δ JNPKA = λx.coffee(x) & A(μ)(x) > δ JDPKA = 𝜖x(coffee(x) & A(μ)(x) > δ) JDP[θTh ] KA = λe.Th(e, 𝜖x(coffee(x)) & A(μ)(x) > δ)

(135a), FA PM FA θ

The remainder of the derivation is as expected, and just as anticipated in Chapter 2. The derivation of the than-clause interpretation parallels that of the matrix clause, modulo Degree Abstraction. The sentence’s interpretation is as in (139): it is an existential statement about drinking events e whose Agent is Al and whose Theme is some coffee measuring greater than δ, where δ = max(λd.∃e(Ag(e)(b) & drink(e) & Th(e, 𝜖x(coffee(x) & A(μ)(x) ≥ d))).

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(139) ∃e(Ag(e)(a) & drink(e) & Th(e, 𝜖x(coffee(x) & A(μ)(x) > δ))) To see the parallel with attributive adjectival comparatives on the lexical theory, compare (139) with the interpretation of Al drank hotter coffee than Bill did, repeated in (140). δ, in this case, is max(λd.∃e(Ag(e)(b) & drink(e) & Th(e)(𝜖x(coffee(x) & hot(x) ≥ δ)))). (140) ∃e(Ag(e)(a) & drink(e) & Th(e)(𝜖x(coffee(x) & hot(x) ≥ δ))) Similarly, the composition of the interpretation of (141) is parallel to that of adverbial comparatives. The simplified structure I assume is as in (142). The composition of DegP, again ignoring the internal composition of the than-clause, is the same as in (135). The composition of VP resulting in (143) is exactly parallel to the composition of NP in (138). (141) Al ran more than Bill did. (142)

S Al[θAg ]

VP ran

DegP Deg′ muchμ

thanP -er

(143) JVPKA = λe.run(e) & A(μ)(e) > δ

PM

With no surprises, the sentence is interpreted as in (144a): it is an existential statement about running events whose Agent is Al, and whose measure is greater than the measure of a running event by Bill—i.e., δ in (144a) is max(λd.∃e (Ag(e)(b) & run(e) & A(μ)(e) ≥ δ)). In comparison, the composition of the interpretation of Al ran faster than Bill did, on the lexical theory, looks as in (144b), with the parallel δ corresponding to max(λd.∃e(Ag(e)(b) & run(e) & fast(e) ≥ d). (144) a. ∃e(Ag(e)(a) & run(e) & A(μ)(e) > δ) b. ∃e(Ag(e)(a) & run(e) & fast(e) > δ) Nominal and verbal comparatives can thus be accommodated within a natural extension of the lexical theory, except here the measure function is introduced compositionally. The meaning of much is restricted in order to accommodate the fact that it is only interpretable with predicates that have structured domains (i.e., mass NPs and atelic VPs are in, singular count NPs and perfective telic VPs are out), and the measure functions it can be assigned must preserve that structure in the mapping to degrees.

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3.3.4 What kind of indeterminacy? The choice of dimension for a comparative sentence is variable, within limits, and the specific choice can make the difference between truth and falsity of the use of a comparative in context.1⁹ Cartwright (1975) demonstrated this sort of indeterminacy with examples like (145), wherein the comparative sentence is true along one of the admissible dimensions, but false along another. (145) There is more water than sand in these buckets by volume, but more sand than water by weight. Treating much, the part of more that introduces measures, like a pronominal element supports this kind of truth-conditional effect, (146a). So far, I have not argued for this sort of encoding over any other, and we haven’t seen the results of any tests to determine the sort of meaning indeterminacy much displays.2⁰ I’ll now show you that the evidence supporting a pronominal-type analysis is in fact mixed. But the only real alternative, that which I will tentatively count as a polysemy-based analysis along the lines of (i) or (ii) in (146b), is problematic for other reasons. (146) a. Jmuchμ KA = A(μ) b. JmuchKA = λv.μ(v) i. polymorphic: particular μ based on input type; or, ii. metavariable: μ is a variable in the metalanguage.

⟨η, d⟩ ⟨η, d⟩

Broadly, tests for a given variety of indeterminacy distinguish ambiguity and deixis, on the one hand, from generality and polysemy on the other. (See Gillon 2004 for detailed discussion, references, and other tests.) If an index-based treatment is appropriate for much, then the selection of dimensions in a comparative should pattern just like ambiguity resolution or pronoun resolution with respect to the relevant tests. I will consider whether this is so, comparing with uncontroversial examples of each: for ambiguity, the ‘financial institution’ and ‘riverside’ senses of bank; for deixis, values for the pronoun her; for polysemy, the ‘geographical region’ or ‘polis’ senses of France; and for generality, different subjects for teacher. The first test is distribution over conjuncts. A single instance of bank cannot, in unmarked usage, simultaneously invoke its two distinct senses, (147a), just as her cannot simultaneously refer to two distinct entities, (147b). In contrast, polysemous and general expressions allow for just this kind of mixing and matching: one instance of France can apply to two incommensurable aspects of that body, (148a),

1⁹ Many of the examples in this section arose in response to comments and notes from V. Hacquard and A. Williams, p.c. 2⁰ The present section focuses on classic tests for categorizing meaning indeterminacy. I resume the question of indeterminacy in a different light in Chapter 9, when I consider speaker understanding and acquisition of comparatives.

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and one instance of teacher can be truthfully applied to teachers of different subject matter, (148b).21 (147) a. ?Al and Bill are both into banks: Al likes financial institutions, and Bill likes riversides. b. ?Al and Bill are both into her: Al likes Susie, and Bill likes Mary. (148) a. Al and Bill are both into France: Al likes its governance structure, and Bill likes its shape. b. Al and Bill are both into teachers: Al likes philosophy teachers, and Bill likes physics teachers. For ease of comparison with comparatives, let’s consider the following context. Al is a landscaper with a large quantity of pumice, a light and porous rock. Bill is a freighter with a small quantity of iron ore, a heavy and dense rock. Suppose that Sue has a middling amount of pumice, which is greater in weight but less in volume than Al’s pumice, and which is greater in volume but less in weight than Bill’s iron ore. Can (149) be true in this context? I would say ‘true’ here, but I have heard this response as much as I’ve heard ‘false’. If the answer is ‘true’, this test supports polysemy or generality for more; if ‘false’, it supports ambiguity or deixis. (149) /? Al and Bill both have more rock than Sue. The second test involves negation; specifically, whether assigning otherwise contradictory properties using multiple instances of the indeterminate expression is sensical. This is so with two instances of bank, (150a), and with two instances of her, (150b). But it is not sensical to first deny something about France’s governance structure that is subsequently asserted of its geography, (151a), nor is it sensical to first deny one specific sense and then assert another, (151b). (150) a. Talking about Wells Fargo1 and the Chicago River2 . That bank1 is being dismantled, and that bank2 is being reinforced with steel girders. b. It sucks how annoying both Al1 and Sue2 are. It makes me hate her1 , but it doesn’t make me hate her2 . (151) a. On different countries’ governance structure1 and geography2 . ? France1 doesn’t have a shape, though France2 is hexagonal. b. Our favorite subjects are philosophy1 , followed by physics2 . ? Al isn’t a teacher1 , even though she’s a teacher2 . 21 Other tests give similar results: e.g., pronominalization, Al likes the bank, and Bill likes it, too, and ellipsis, Al likes the bank, and so does Bill; etc.

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For comparison, consider again the landscapers and the freighters. Suppose that Al’s pumice is ten times the volume of Bill’s iron, but Al’s pumice weighs far less than Bill’s iron. Can this situation be truthfully described using (152), where the intention is to understand more as being about volume in the first clause, but about weight in the second clause? My own judgments and those of my informants’ are again mixed. If (152) turns out fine and natural in contexts like this, though, that would suggests an index-based over polysemy-based account. (152)

Al’s rock is greater by volume1 , but less by weight2 . /? Al has more1 rock than Bill, but Bill has more2 rock than Al.

These results, such as they are, support only the inference that the precise nature of the indeterminacy of much remains a delicate matter. Perhaps this delicacy attends any cross-categorial functional item, or perhaps it has to do with the specific sort of content that more invokes; see Chapter 9. However, so far the implementation of a polysemybased account (at least as sketched in (146b)) would require more technical exposition than the data so far require. And so, for ease of exposition, I proceed assuming the index-based account.

3.3.5 Other occurrences of much The form much as it occurs transparently in comparative constructions along with the morphemes as, so, too, etc., and less transparently as part of more, contributes a variable over measure functions that is fixed in the context of use, in accord with certain conditions. But the form much occurs elsewhere, such as the predicative occurrence in (153a), the apparent determiner occurrence in (153b), and the ‘differential’ occurrence in (153c). I would be remiss if I didn’t offer at least a few remarks on such occurrences. (153) a. The soup wasn’t much. b. Much soup spilled. c. Ann ate much more soup than she expected. The simplest assumption I can make is that, semantically, all of the occurrences of much in (153) indeed contain much, but they also contain an instance of the abs morpheme (generalized version) introduced in Chapter 2, and the silent head I notated ∅ which introduces a contextual standard. I will sketch this sort of analysis as a live possibility, but I won’t bother to give compositional details. Any serious proposal will most assuredly require greater care than my sketch can provide. The simplest thing to say about (153a) may be wrong, but here goes. Taking the surface structure at face value, along with the assumptions just given about abs and ∅, the predicate would have the structure in (154). Without saying anything more, the interpretation of this predicate would be as in (155a). Making the usual assumptions

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57

about negation and the definite description, the interpretation of (153a) would then be as in (155b). This compositional interpretation appears straightforward, but I am not sure how well it would withstand scrutiny. (154) abs

much

∅

(155) a. J(154)KA = λx.A(μ)(x) ≥ dstd b. J(153a)KA = A(μ)(ιx(soup(x))) ≱ dstd For apparent determiner occurrences like (153b), my initial attempt doesn’t look much different, except I would say that the actual determiner is the silent little-e head, which binds the individual variable introduced by soup. So the structure of the relevant phrase would look as in (156), with the (simplified) interpretation in (157a). The usual compositional process will deliver (157b), which analyzes (153b) as asserting the existence of a spilling event with a portion of soup, the measure of which is greater than the contextual standard, as its theme. This appears at least a reasonable facsimile of the meaning of (153b). (156) e soup abs

much

∅

(157) a. J(156)KA = 𝜖x(soup(x) & A(μ)(x) ≥ dstd ) b. J(153b)KA = ∃e(spilling(e) & Th(e)(𝜖x(soup(x) & A(μ)(x) ≥ dstd ))) The last case in (153c) is more complicated. Differential comparatives involve an expression modifying the comparative complex that indicates some distance between the than-clause degree and the matrix clause degree. Often, this is encoded as the contribution of a ‘differential degree’, and the presence of such an expression shifts the analysis of more to a version with an additional lambda abstract over differential degrees (see discussion and references in von Stechow 1984). More concretely, instead of expressing a basic degree relation like d > d′ (for d the matrix degree and d′ the than-clause degree), the comparative would express d ≥ (d′ + d″ ), where d″ is the differential degree. In the present case, the addition of much conveys not a specific degree of difference, but merely that the difference is substantial. This suggests to me some role for abs in combination with much, but it seems to me that much cannot measure the same stuff that it does as part of more in phrases like much more soup.22 Instead, I would be tempted to suppose that the differential occurrence involves measurement of scalar objects themselves (this is related to but different from proposals made by 22 This assumption would lead to an interpretation in which the soup is said to measure greater than the thanclause degree and greater than the contextual standard—but that’s not what (153c) means.

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Schwarzschild 2006, Rett 2008 and Solt 2015; see below). Thus, minimally, I would need to assume that the μ indices on each occurrence of much are distinct, as the constraints on the selection of those μs will have to be calculated against different sorts of objects. Here is a sketch of the line a theory like mine could pursue. A sketch of the interpretation we want for (153c) is as in (158), abbreviating the than-clause degree as δ as before; it says that there is an event e and a degree d which is such that Ann was Agent of e, and the Theme of e is a portion of soup, the μ-measure of which meets or exceeds δ plus d′ (the differential degree), and the μ′ -measure of d′ is greater than the contextual standard. Such an interpretation makes sense if μ is understood as a volume measure, often so in cases like more soup, and if μ′ is understood as a measure of the distance between two degrees. Which specific scale d′ and dstd are drawn from is assumed to be appropriately fixed during the course of composition. (158) J(153c)KA = ∃e, d′ (Ag(e)(a) & eating(e) & Th(e) = 𝜖x(soup(x) & A(μ)(x) > (δ + d′ ) & A(μ′ )(d′ ) ≥ dstd )) There is more to be said. On Rett’s (2008) and Solt’s (2015) semantics, the basic meaning of expressions like much is a property of scalar intervals (i.e., convex sets of degrees; cf. Schwarzschild 2006). For Rett, much in particular maps scalar intervals to a set of degrees, i.e., the same scalar interval it takes as its first argument, (159a). Solt’s analysis is similar, except her much takes (point) degrees to intervals, and the null head that she posits to introduce degrees, Meas, has a simpler compositional interpretation than Rett’s corresponding Quantity.23 These differences are likely artifacts of their focus on different datasets, however.2⁴ (159) (From Rett 2008) a. Jmuch/manyR K = λD.λd′ .length(D) = d′ b. JQuantityK = λP.λd.λQ.∃x(P(x) & Q(x) & μ(x) = d) (160) (From Solt 2015) a. Jmuch/manyS K = λd.λI.I(d) b. JmeasK = λx.λd.μ(x) ≥ d

⟨⟨d, t⟩, ⟨d, t⟩⟩

⟨d, ⟨⟨d, t⟩, t⟩⟩ ⟨e, ⟨d, t⟩⟩

Both Rett and Solt give reasons for positing two covert heads. Extending my account to the kinds of data they were focused on will, too, depend on more than just much. However, it seems to me that a plausible compositional account that would deliver (153c) can be derived entirely from pieces otherwise required (much, abs, ∅) defined

23 In relevant respects, Solt’s Meas and Rett’s quantity are a lot like my much. Some differences (e.g., the order of λs) don’t matter for present purposes. Our accounts otherwise differ in that their items don’t explicitly note the assignment-relativity of μ, or they assume that μ is a metavariable; see my discussion of indeterminacy in §3.3.4. 2⁴ Rett 2008 primarily targets occurrences like Much soup spilled and How much soup spilled?, whereas Solt’s 2015 focus is broader. I do not discuss yet other alternative analyses; see Kennedy & McNally 2005, Svenonius & Kennedy 2006, or Grano & Kennedy 2012. In those cases, the motivating data and resultant analyses are yet more distant from the present targets.

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as I have defined them, along with some morpheme that introduces the role of the differential degree. This last, of course, is likely also independently required, in order to compositionally interpret phrases like two inches longer or two cups more soup. For now, I leave detailed comparison of these accounts for the future.

3.4 Conclusion I’ve extended the semantic theory outlined in the previous chapter so that it applies to comparative constructions targeting noun and verb phrases. On the surface, it might now seem as though there are no very big differences between the semantics of adjectival and adverbial comparatives, on the one hand, and nominal and verbal comparatives on the other. Both involve comparative morphemes that introduce degree relations, both involve measure functions contributed by a GA or much, etc. Yet there are a number of important differences. A major assumption of the lexical theory is that GAs fix a measure function as a matter of lexical specification: for example, hot expresses hot, and fast expresses fast. The monotonicity conditions that are relevant for much, in contrast, are not relevant there. In contrast, I have posited that much fixes a measure function as a matter of composition and context. The selection of its measure function is restricted to one among a class that is structure-preserving with respect to what is measured. To see the irrelevance of such a condition on the lexical theory of GA comparatives, consider again (161a)–(161b) with the sketches of interpretation given. The inputs to the GA measure functions are portions of coffee or stretches of running activity. How these entities are intrinsically ordered bears no relationship to the degrees hot and fast assign them. (161) a. Al drank a hotter coffee. ⇝ . . . hot(x) > δ & coffee(x) . . . b. Al ran faster. ⇝ . . . run(e) & fast(e) > δ. . . A precondition for the selection of measure functions with much is that the proferred measurand must be drawn from a ‘measurable’ domain—any x against which this condition is calculated must come from a set with particular ordering properties. This type of condition captures the fact that combining more, as much, etc., with singular count nouns like sandwich or with singular telic VPs like run to the store is odd. The fact that hot and fast are perfectly fine with such expressions, (162a)–(162b), could be taken as evidence that GAs comparatives are not sensitive in the same way. (162) a. Al bought a hotter sandwich than Bill did. b. Al ran to the store faster than Bill did. In Chapter 4, I ask whether the two classes of comparatives are really so different as has been supposed. There, I take another look at some of the distributional and

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semantic evidence to suggest that the answer to this question is ‘no’. My central claim is that GAs do not introduce measure functions; instead, following Parsons (1990), Landman (2000), and Fults (2006), among others, I suppose that GAs introduce properties of states. And furthermore, I suggest that what distinguishes GAs from nongradable adjectives is in their domains of predication, mirroring the possibilities for the relevant nominal and verbal domains: some stative domains are measurable, and others are not. On my account, much, or something just like it, introduces measure functions even for adjectival and adverbial comparatives, and the source of anomaly that arises in these comparatives is characterized in the same way as anomalies in the nominal and verbal domains. The lexical theory differentiates GAs from non-GAs via typetheoretic difference: GAs express measure functions (type ⟨η, d⟩), non-GAs express simple properties (⟨η, t⟩). On my account, any adjective or adverb expresses a simple property, and a given adjective or adverb is compatible with the comparative form just in case its domain has non-trivial structure. My theory, in its strongest form, holds that there is only one way of introducing degrees: much. Once we can discern how different adjectives might denote in structured vs unstructured domains, all of the pieces I need to advance this theory will be in place. The rest of the book explores its consequences.

4 Measuring states

At the end of Chapter 2, I distinguished ‘measurable’ and ‘non-measurable’ predicates as those whose domains display non-trivial ordering relations, and Chapter 3 showed how the interpretation of nominal and verbal comparatives is sensitive to these properties. There, the measurable predicates were those fully compatible with mass and atelic syntax, while the non-measurable were those preferring (singular) count and telic syntax. I characterized this divide, following many others, as between whether the relevant lexical items presume non-trivial mereological relations, in particular. I now revisit the treatment of adjectival and adverbial (GA) comparatives that is at the core of most degree-theoretic analyses of the comparative (Chapter 2). In particular, I revisit the question of whether GAs are special in the way that the lexical theory supposes. That theory differentiates GAs from non-gradable adjectives and adverbs type-theoretically: GAs express measure functions, non-GAs do not. If correct, such a theory sharply differentiates GAs and the phrases they head from NPs and VPs: the former introduce measurers and the latter measurables. This chapter presents my arguments against this sort of type-theoretic bifurcation. The first major hurdle for any such revision is the apparent morphosyntactic specialness of GAs. That we sometimes have forms like taller, but never like souper, has been taken to suggest that GAs compose directly with comparative morphology, a syntactic assumption dovetails nicely with a semantics specified directly in terms of measure functions. Here, I lean on Bresnan (1973), for whom such morphosyntactic differences are merely surface phenomena. The second major hurdle is the apparent semantic specialness of GAs. I aim to show that we can analyze adjectives, too, as coming in measurable and non-measurable varieties, and that much of their ‘specialness’ attends this difference (cf. Bale 2006, 2008). Incorporating GA comparatives into my general picture calls for some precisification of the monotonicity requirement on the selection of measure functions. Schwarzschild (Schwarzschild 2002, 2006) characterized this constraint directly in terms of the preservation of mereological structure. However, given a sufficiently finegrained ontology like that I’ll propose it is possible to say merely that measure functions must preserve whatever ordering relations hold of entities in the measured domain. That is, we needn’t assume that GAs are true of mereologically-structured states (cf. Moltmann 2009, Baglini 2015, Francez & Koontz-Garboden 2015). We can simply understand the tallness or intelligence states as ordered by how much of the relevant property they instantiate (see §4.1).

The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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The theory that results has a number of interesting properties. Of primary interest is that it supports the idea that comparative morphology encodes the conceptual understanding of ‘measurement’ described in Chapter 3. In any given comparative, the mapping to degrees involves considering a relational structure introduced by the lexical target, and mapping entities in those structures to scales in a way that reflects, or represents, certain quantitative relationships that they instantiate. On this view, non-gradable adjectives are naturally characterized as those which do not introduce relational structures in this sense, alongside (singular) count NPs and (singular) telic VPs. The account thus unifies the semantics of comparatives across categories. Such an account was briefly entertained by Cresswell (1976), but in the opposite direction (e.g., both mass NPs and GAs lexically introduce measure functions). I give reasons to prefer my direction of unification. If correct, though, we immediately face the question of why not just do away with degrees, now that we have non-degree ordering relations all over the place. Why this business about measuring and measurement? As we’ll see, Reichenbach (1947) sketched such an account, but it falters precisely on its lack of degree-theoretic resources (cf. Bartsch & Vennemann 1972).

4.1 Introducing states 4.1.1 Intensive and extensive GAs are often thought special in a number of ways. Perhaps, for example, only they allow ‘intensive’ dimensions for measurement.1 If GAs introduce measures, and the same stuff is measured in (163a) and (163b)—namely, coffee—then hot measures intensively in (163a), while permissible μs for (163b) do not. (163) a. Al has hotter coffee than Bill does. b. Al has more coffee than Bill does. Indeed, we can use GAs to express comparisons by intensive dimensions with respect to coffee (really, with respect to any material substance), like temperature, (164a), or hardness, (164b). These dimensions are barred in the nominal comparative, (165), as expected by the monotonicity requirement, since smaller portions of the stuff needn’t have smaller measures along these dimensions. (164) a. My coffee is hotter than yours is. b. My plastic is harder than yours is. (165) a. Al has more coffee than Bill does. b. Al has more plastic than Bill does.

A: temp. A: hardness N: volume N: weight

But considered as dimensions simpliciter, GA and nominal comparatives don’t divide extensive and intensive between them. Some GA comparatives involve 1 I think this is implied in many authors’ contrasting usage of ‘quality’ for adjectival comparatives vs ‘quantity’ for nominal (cf. Rett 2008, Bochnak 2010 for recent examples).

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comparison by volume or weight, (166), and some nominal comparatives involve comparison by temperature or firmness, (167).2 To be clear, the dimensions that are impossible for (165) are possible in (167); it just depends on the choice of target noun. (166) a. My glass is fuller than yours is. b. My plastic is heavier than yours is. (167) a. I have more fever than you do. b. My mattress has more firmness.

A: volume A: weight N: temp. N: hardness

We can observe the same pattern for verbal and adverbial comparatives. Speed and loudness are intensive with respect to driving or singing activity, since smaller stretches of the activity needn’t have smaller measures along these dimensions. These are permitted for the GA comparatives in (168), but not for the V comparatives in (169). As before, though, this pattern perfectly reverses when we switch around the adverbs and VPs, (170)–(171). (168) a. Al drove faster than Peter did. b. Al sang louder than Peter did.

A: speed A: loudness

(169) a. Al drove more than Peter did. b. Al sang more than Peter did.

V: distance V: duration

(170) a. Al drove farther than Peter did. b. Al thundered on longer than Peter did.

A: distance A: duration

(171) a. Al sped up more than Peter did. b. Al thundered on more than Peter did.

V: speed V: loudness

Given expressions like more heat and speed up as much, one might want to say that the relevant dimensions are intensive. This is puzzling only if we believe that much measures here, and that it must always measure extensively. That would be the case, for example, if one tied its S-monotonicity requirement to the preservation specifically of part–whole relations. Indeed, the appearance of such ‘non-quantity’-based N/V comparatives has occasionally led to the exceptional positing of lexicalized measure functions in such cases.3 But GAs aren’t obviously freer than nouns and verbs in supporting intuitions of intensive vs extensive measurement, and so there appears to be little argument so far that GAs are special, let alone that they should be assigned a different type. In other words, the implication that seems to be suggested in the literature—that intensive, or quality-based measurement signals a lexical measure function, and that this can only be found with GAs—isn’t well-grounded. The appearance of a distinction between quality and quantity is an artifact of the focus on a wide variety of GA comparatives but a narrower subset of N and V comparatives. 2 (167a) is based on an example from Champollion 2010, p.153. 3 Examples of such an approach include Morzycki 2005 (building on discussion by Bolinger 1972), Villalta 2008, and Lassiter 2011a, though the details (and the empirical domains) differ. I discuss these proposals in Chapters 7 and 8.

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If we can’t differentiate GA and N/V comparatives based on the sort of dimensions they introduce, perhaps we can differentiate them based on how many dimensions they can introduce.

4.1.2 Indeterminacy A sentence containing more coffee can be true based on the volume or weight of the coffee, and one containing run more can be true based on the distance or duration of the running. I and others have attributed this flexibility—both within and across predicates—to the context-sensitive selection of measure functions by much. If GAs never showed the same kind of flexibility, then there would be little reason to suppose that an account like that developed in Chapter 3 applies to GAs. Certainly, if the basic tenet of the lexical theory is that GAs express specific measure functions, we should not see multiple dimensions available for a given GA comparative. Yet there is some evidence that this is so.⁴ I illustrate such evidence using tall, red, and expensive. In each of these cases, I can imagine possible alternative analyses other than an extension of the analysis in Chapter 3, to be sure.⁵ Regardless, the lexical theory will need to say something special about such cases, while they are of course expected if GA comparatives are more like N/V comparatives than that theory typically supposes. I begin with the famous tall, though this demonstration is perhaps the least compelling. To set it up, consider Mount Everest on the border between Nepal and Tibet, and Mauna Kea in Hawaii. Mount Everest, usually regarded as the tallest mountain in the world, measures around 29,000 feet in height, while Mauna Kea comes in at nearly 14,000 feet. The latter value only tracks Mauna Kea’s extent above sea level, however; measured from its base, Mauna Kea comes in at around 33,000 feet. It seems to me that this state of affairs can be truthfully summarized as in (172). But if both (172a) and (172b) involve measures of the same objects, then they must also signal different measure functions.⁶ (172) a. Everest is taller than Kea (in extent above sea level). b. Kea is taller than Everest (in absolute extent). Next, consider the case of a color adjective like red.⁷ I focus on two aspects of its interpretation in the comparative, one that has been pointed out before and another that has not, so far as I know. First, we can use red to identify the particular ⁴ This discussion is adapted from Dunbar & Wellwood 2016. ⁵ Minimally, one could say that such GAs simply carry an index, just like much does. This echoes Kennedy & McNally 2010 approach to color adjectives, as I discuss presently. Dunbar & Wellwood 2016 outline theoretical reasons to disprefer such an analysis. ⁶ Perhaps (172a) and (172b) do not involve measure of the same objects; perhaps they reflect different ways of resolving ‘vague objects.’ For relevant discussion, see Evans 1978, Sainsbury 1989, and Morreau 2002, and citations therein. ⁷ For this demonstration, we can set aside Kennedy & McNally’s 2010 ambiguity analysis of red, since the alternative lexical variant they posit is non-gradable.

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quality of redness of an object, or the quantity of redness manifested by the object (Kennedy & McNally 2010). The possibility of thinking about ‘quality’ or ‘quantity’ here allows for opposite ordering relations to simultaneously hold: understood as describing the amount of red cover, the ordering in (173a) holds; understood as describing hue, that in (173b) holds. (173) a. This t-shirt is redder than that one (by area). b. That t-shirt is redder than this one (by hue). Yet we can observe flexibility even fixing on the ‘quality’ understanding of red. Imagine two patches of red lipstick, such that one exceeds the other in brightness, (174a), while the opposite is true in saturation, (174b). If both (174) can be true of the same patches, then it appears to be possible to use red to compare color quality holistically, while also isolating and comparing along the color’s component dimensions. As before, if the outputs can differ for the same inputs, it must be that red allows for more variability in the selection of measure functions than usually supposed. (174) a. This lipstick is redder than that lipstick (by brightness). b. That lipstick is redder than this lipstick (by saturation). But perhaps color adjectives are a corner case, perhaps because the semantic field they describe is special. But more mundane examples can be constructed. Imagine that you are considering purchasing either a case of the meal replacement beverage Soylent, or a pair of Camper Men’s 18304 Pelotas XL Sneakers, in size 41. You are able to make your purchase either in the US or in France. On Amazon US, a one week supply of Soylent costs $193.68 and the Pelotas cost $195.90. On Amazon France, the same amount of Soylent costs €370.49 and the Pelotas cost €139.00. Both (175a) and (175b) are intuitively true in this context. (175)

a. The Pelotas are more expensive than the Soylent (in the US). b. The Soylent is more expensive than the Pelotas (in France).

Taken together, cases like these suggest that at least some GAs support flexible measurement across a variety of semantic fields. Such a pattern is not expected on the lexical theory, though, since it holds that GAs directly express some particular measure function, not some family of measure functions. If instead much plays the role of degree introduction here, then we expect to see patterns like this as a matter of course.

4.1.3 Incommensurability Recall that Kennedy (1999) used data like (176) to argue against vagueness-based approaches, and in favor of the lexical theory. Given a degree semantics, it is possible to say that such examples are odd because they cannot be evaluated for truth or falsity, since the two GAs point to degrees which are ordered by no single antecedent scale. However, if such oddities recur across comparatives targeting non-GAs, then any

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such argument is better understood as evidence for the analysis of the comparative morphology itself rather than for the analysis of GAs. (176) ?The ladder is wider than the carpet is green. First, it’s important that the so-called ‘subcomparative’ form—comparatives with distinct lexical targets in each of their matrix and than-clause—is not itself illicit. An example like (177a) is directly interpretable as a comparison of the ladder’s width and the doorway’s height, and (177b) as a comparison between (say) the saturation levels of the curtains’ redness and the carpet’s greenness.⁸ The difference between (177) and (176), then, is that (177a) transparently involves comparing degrees representing length, (177b) degrees representing saturation levels, but there is no such common set of degrees for (176).⁹ (177) a. This ladder is wider than the doorway is tall. b. The curtains are redder than the carpet is green. Regardless of their ultimate explanation, it is easy to find analogous contrasts across domains. For example, we can transparently compare coffee and water for their volume, (178a), and whispering and shouting for their duration, (178b). But we can’t easily mix and match, say to compare the volume of the coffee to the duration of the shouting, (179). The same can be observed for comparing some running and walking by distance, (180a), and some love and hate for their intensity, (180b), in contrast to comparing the distance of the walking with the intensity of the hate, (181). (178) a. There was more coffee in the sink than water in the tub. b. There was more whispering inside than shouting outside. (179) ?There was more coffee in the sink than shouting outside. (180) a. Al walked in the race more than she ran. b. Al loved her mother more than she hated her stepfather. (181) ?Al walked in the race more than she hated her stepfather. Such examples can be multiplied. And so it does not seem that incommensurability phenomena distinguish GA semantics in particular. And perhaps we shouldn’t be surprised, since the initial degree-theoretic explanation of incommensurability ultimately depended on requirements for the interpretation of morphemes like -er. Such expressions resolve their semantics relative to some particular ordering on degrees (i.e., a scale). This resolution depends, of course, on the sorts of degrees demanding to be compared, and hence the measure functions involved. Just as plainly, though, it does not depend on which expressions introduce the measure functions. ⁸ I don’t know how, exactly, we should think about the dimension for comparing redness and greenness on the ‘quality’ interpretation of comparatives with color terms. Whatever the case, there is such a reading, in addition to a distinct ‘quantity’, or ‘extent of cover’ interpretation (see Kennedy & McNally 2010). ⁹ There are plausible alternative interpretations in the vicinity, e.g., ‘comparisons of deviation’ (Kennedy 1999), or perhaps even ‘indirect comparisons’ (Bale 2008; see also Van Rooij 2011). See Chapter 7.

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4.1.4 Reference and modification If GAs don’t express measure functions, what do they express? The balance of evidence suggests that they express neodavidsonian properties—predicates of entities that ordinary individuals can participate in or instantiate. Considering GAs like tall and hot, a natural ontological assumption is that these entities are states, the non-dynamic counterparts of events and processes. I consider the traditional sorts of evidence for a neodavidsonian analysis directly. First, GAs can be nominalized, and figure in definite descriptions that refer to something which can be surprising, (182a), or inflict pain, (182b). Those same referents can provide the antecedents for anaphors like it, as the pronominal in (183) can be used following either of (182a) or (182b) to recall the relevant height or heat.1⁰ (182) a. Al’s tallness/height was unexpected. b. The hotness/heat of the Scoville burned my mouth. (183) It surprised even John. We should think of the height and the heat as concrete, rather than abstract entities like facts, in light of patterns like (184) (Higginbotham 2000). As Higginbotham (2000) points out, explicit paraphrases using definite descriptions and talk of states seem semantically equivalent to sentences without such framing, e.g., (185). Higginbotham also points out that sentences with deadjectival nominal forms show a mutual entailment relationship with their bare adjectival correspondents; i.e., (186a) is true only if (186b) is. (184) a. The state of Mary’s happiness lasted awhile. b. ?The fact of Mary’s happiness lasted awhile. (185) (The state of) Ann’s happiness was threatened. (186) a. Ann was happy for 10 years. b. Ann’s happiness lasted 10 years. Moreover, Landman (2000) uses the example in (187) to show the same difference with the stative predicate be in love with Jocasta: if the it in the last clause of (187) referred to a certain fact, he suggests, then the dialogue as a whole should sound contradictory. If instead the pronoun picks out something else—like a particular state—then there needn’t be a contradiction: the fact that a certain state holds might be a burden, but being in that state can feel good. A parallel argument can be constructed for a GA like happy based on (188). (187) Oedipus was in love with Jocasta. Though the fact that he was in love with her was a burden on his conscience, he had to admit that it felt good. 1⁰ Moltmann 2009 discusses data like this, and ultimately argues that such GAs express properties of tropes (particularized properties). I think that my states are very much like her tropes, whereas she reserves the use of ‘state’ for entities that are more like facts than like events.

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(188) Al was very happy when Bill fell down. Though the fact that she was happy was a burden on her conscience, she had to admit that it felt good. Moroever, adjectival predications can be targeted in because-clauses, which have a semantics implying causal relations between eventualities (see Kawamura 2007 and references therein). That is, it was Ann’s particular height that motivated an architectural change, (189a), and her intelligence prompted a certain kind of emotional response, (189b). Given the right sort of adjectival predication, GAs can also be used to identify the effect of some cause, (190). (189) a. Because Ann was tall, the architects planned a higher ceiling. b. Because Ann was intelligent, the boys felt ashamed. (190) Because Sue willed it to be so, the coffee was hot. If GAs introduce something which can enter into causal relations, we furthermore have a tidy explanation for what look like attachment ambiguities with because clauses. For example, (191) has two readings: on one, Sue is just that kind of person who can make people want things—in this case, she succeeded in willing Al to desire hot coffee; on the other, Sue’s magic allows her to will coffee to be hot.11 These readings can be captured by positing causal relations between (the state of) wanting or being hot and a certain act of will, with different corresponding values of the pronoun. (191) Al wanted1 the coffee to be hot2 because Sue willed it1,2 to be so. More broadly, adjectival predications easily co-occur with modifiers that normally target predicates of eventualities. Some of these modifiers temporally locate the eventuality, (192), others spatially locate, (193), and still others specify the duration over which a certain eventuality took place or lasted, (194)—whether they are used to modify adjectival predications, as in the (a) examples, or verbal, as in the (b) examples. It is difficult to see how any simple analysis of these modifiers could be offered, if the verbal predications involve eventualities but the adjectival predications only involve measure functions. (192) a. Al is happy in the morning. b. Al runs in the morning. (193) a. It’s hot in the kitchen. b. Al dances in the kitchen. (194) a. Al was patient for fifteen minutes. b. They drove for six hours. And finally, GAs may be targeted by modifiers and interpreted within the scope of a comparative (Fults 2006): (195) expresses something about Al’s patience, as instantiated in a particular spatial location, namely that it is greater than any corresponding 11 (191) also militates against a fact-based analysis of GAs. It doesn’t seem possible to will a fact into existence, or at least that’s what the oddity of a sentence like Sue willed the fact that it rained into existence suggests to me.

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state of Bill’s—it does not comment on Al’s patience, simpliciter. Such modifiers must thus be ‘low’ enough to contribute to the sense of the GA that figures into what is compared. As before, it would be difficult to say what such a modifier is doing down there, if the GA merely contributed a measure function. (195) Al is more patient on the playground than Bill is.

4.1.5 Morphosyntax Of course, one could allow GAs to introduce states while also introducing lexicallyspecified measure functions. Then, the state argument could be recruited in any explanation of the modifier data just discussed, but the role that the GA plays in adjectival comparatives can remain more or less intact. Without addressing the morphological data that have been taken to suggest a much closer relationship between GAs and comparative morphology than that posited for Ns and Vs—which require the support of much—there will be little push to abandon the idea that GAs are special in how they interact with that morphology semantically. One of the earliest and most comprehensive analyses of the syntax of comparatives argues for a uniform analysis. In modern terms, this means that surface differences between cross-categorial comparatives are matters to be explained primarily by morphophonology (i.e., the theory of how syntactic structures are pronounced) to explain. Bresnan (1973) proposes that something like much is present even in GA comparatives; if there’s good reason to believe that she’s right—and given that GAs introduce something that can, in principle, be measured by like much—we have little reason to maintain that GAs themselves introduce measure functions. Bresnan highlights a class of morphemes that, intuitively, suggest a common semantics, and most of which occur with much, (196a).12 Her analysis assumes that, when much surfaces, it reflects something that is there out of some necessity; and in particular, if the class she’s identified is well-behaved, it must be necessary across the class. Thus, she supposes that more realizes much and -er, and thus it is not possible to hear more and much together, (196b). (This morphological conflation must happen prior to the rule that affixes -er to adjectives that take that simplex form; see below.) (196) a. as/too/so/that much soup b. ∗ more much soup Without saying more, the most puzzling aspect of Bresnan’s theory is why we do not then find forms like (197a) grammatical. More generally, GAs in English are not observed to co-occur with much, and while they do co-occur with more, (197b), such patterns could simply be used as evidence that Bresnan was wrong in her conflationbased analysis of more. 12 The exceptions, of course, are more and enough; cf. Neeleman et al. 2004.

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(197) a. ∗ as/too/so/that much delicious b. more delicious Bresnan’s predictions are more subtle than this, however. She derives the general absence of much with GAs by positing a deletion rule like (198). She orders this rule following that which produces the form more. Thus for her, what is underlying as much A will surface as as A, etc. These rules can be understood in modern terms as essentially morphophonological: they have no impact on semantic interpretation. (198) much-deletion much → / A Of course, any sufficient rule like (198) will need to be set in the context of a larger morphophonological theory (cf. Dunbar & Wellwood 2016). But the analysis sets up the possibility that while GAs and much don’t generally co-occur, they might under some structural conditions. In this light, consider (199) and (200), where much and the form more occur in the (b) examples but not the (a) examples. Importantly, the pairs do not seem to be semantically distinct. Bresnan’s theory can capture these data by positing extraposition of the prepositional phrase in the derivation of the (a) sentences, feeding the rule in (198), but no extraposition for the (b) sentences, bleeding that rule. (199) a. These plants may grow as high as 6 feet. b. These plants may grow as much as 6 feet high. (200) a. John is taller than 6 feet. b. John is more than 6 feet tall. Even Corver (1997) argues for a uniform underlying syntax of comparatives, but rather than positing deletion of much with GAs, he argues for insertion of much in the complementary environments. His “much-support” analysis is proferred as analogous to do-support in English, wherein tense morphology is borne by a dummy expression in certain structural environments (compare Mary met someone, with past tense met, and Did Mary meet someone?, with untensed meet). Thus, Corver posits a basically phonologically-null head which is occasionally ‘supported’ by the form much, as in (201). (201) John is generous, in fact he is too much so. Corver reasons as follows. If much is semantically active in the second clause of (201), and if so is an anaphor that picks up the meaning of its antecedent (as is uncontroversial)—in this case the GA generous—then (201) should be a semantic failure: too can’t take both a measure function introduced by much and the measure function introduced by generous. Given the evident success of (201), combined with an unwillingness to revise the central semantic assumption about GAs, it must be that much is meaningless. Yet, if much is generally present, and always semantically active, then any concerns surrounding such examples evaporate.

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4.1.6 Cross-linguistic sightings The reader may still not be convinced: GAs are distinct enough from expressions of other lexical categories that they should be assigned a different type-theoretic interpretation. Yet a small survey of languages turns up at least a couple in which an analogue of much surfaces overtly both in adjectival and non-adjectival comparatives. Furthermore, in some languages, the form that shows up in (the analogues of) much soup is the same as that which shows up in very tall. Such data evaporates what might otherwise appear to be a robust grammatical distinction for GAs. Consider the case of Serbo-Croatian (E. Dunbar, I. LaTerza, p.c.). Across an array of comparative constructions—amount questions (202b)-(202a), degree demonstratives (202c)–(202d), and equatives (202e)–(202f)—a complex morphological form plausibly decomposed into ko-, to-, and ono- plus liko surfaces.13 This is so regardless of whether we consider nominal targets—(202a), (202c), and (202e)—or adjectival— (202b), (202d), and (202f). Even without a complete morphological analysis, these facts are suggestive of my conclusion. (202) a. koliko kafe how.much coffee ‘how much coffee’ b. koliko srećan/kafe how.much happy ‘how happy’ c. Marija je prosula toliko vina Marija aux spilled that.much wine ‘Marija spilled that much wine’ d. Marija je toliko visoka Marija aux that.much tall ‘Mary is that tall’ e. Marija te prosula onoliko vina koliko je prosuo i Marija aux spilled that.much wine as.much aux spilled and Branko Branko ‘Marija spilled as much wine as Branko spilled’ f. Marija je visoka koliko i Branko Marija aux tall as.much and Branko ‘Mary is as tall as Branko’ In Greek (A. Giannakidou, p.c.), the form poly (‘much’) is obligatory in nominal comparatives, (203a), and optional in adjectival comparatives (at least those like (203b)). When it does surface with GAs, we find a pattern that is completely unexpected if much usually fails to appear in such contexts in English because the semantic 13 However, it does not appear that liko can surface on its own, the way much appears to in English (I. LaTerza, p.c.)

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work is already performed by the GA. And indeed, the meaning of the Greek sentences are the same, regardless of whether much is overt. (203) a. I Maria ipje pio poly krasi apoti o Janis the Maria drank.3sg more much wine than.clausal the John ‘Mary drank more wine than John did.’ b. To fagito tis Marias itan pio ( poly) nostimo the food the.gen Mary.gen was more much delicious apoti/aposo tou Jani. than the.gen John.gen ‘Mary’s food was more delicious than John’s was.’ Meanwhile, a number of languages show a formal equivalence between what appears to be two distinct morphemes in English—very and much (cf. Doetjes 1997). If modification by very in English should indicate that a given expression denotes a measure function, then it is instructive to consider cases where the same intensifier modifies both GAs and nouns. For example, we see this pattern in Greek (204) (A. Giannakidou, p.c.), in Czech (205) (Doetjes et al. 2011),1⁴ in Italian (206) (F. Panzeri, p.c.),1⁵ and in Macedonian (207) (I. Stojanovska, p.c.). (204) a. Poly krasi xythike. much wine spilled.passive,3sg ‘Much wine spilled.’ b. To krasi tis Marias itan poly nostimo. the wine the.gen Mary.gen was much delicious ‘Maria’s wine was very delicious.’ (205)

a. hodně vysoký Q tall ‘very tall’ b. hodně trpělivosti/peněz Q patience/money ‘a lot of patience/money’

(206)

a. Giovanni è molto alto Giovanni is much.adv tall ‘Giovanni is very tall.’ b. Giovanni ha mangiato molta minestra Giovanni has eaten much.fem soup ‘Giovanni ate a lot of soup.’

1⁴ Doetjes does not gloss the form hodně, so I have indicated this just as Q. 1⁵ F. Panzeri notes that molta agrees in feminine gender with minestra, which indicates it is behaving like an adjective (similarly for molti in combination with plural NPs). In the other cases, the form molto suggests realization as an adverb.

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(207)

73

a. Taa e mnogu visoka she is much tall ‘She is very tall’ b. Ne izede mnogu supa neg she.ate much soup ‘She didn’t eat much soup.’

Such observations will find easier explanations if the abstract syntax of GA and nominal comparatives are uniform, as I have argued; in fact, it is difficult to see how such data could be easily explained otherwise.

4.2 Adjectival and adverbial comparatives Here, then, is how I propose to re-imagine the semantics of comparatives targeting adjectives and adverbs. GAs like tall and fast express properties of neodavidsonian states; that is, they are expressions of type ⟨v, t⟩. As with nominal and verbal comparatives, adjectival and adverbial comparatives are interpreted in part via the contextual selection of measure functions by much—the element sometimes pronounced much in English. Everywhere that much occurs, it plays that same semantic role; i.e., everywhere that comparative morphemes like -er, as, too, etc., appear, much is there. I distinguish the gradable and non-gradable expressions here parallel to how mass and count NPs, and atelic and telic VPs are distinguished: the former case in each class has a domain with non-trivial ordering relations (i.e., they express ‘measurable’ predicates), whereas the latter does not (i.e., they are ‘non-measurable’). Unlike in the case of nouns and verbs, though, there is little independent literature to suggest what the properties are of the relevant state orderings (cf. Francez & Koontz-Garboden 2015, Baglini 2015). Since GAs are normally thought to associate directly with scales, the extent to which such structure has been detected it is usually attributed directly to the degree orderings. My proposal thus contrasts with the lexical theory set up in Chapter 2. There, the difference between gradable and non-gradable adjectives and adverbs is hardcoded in the type system: GAs denote in type ⟨e, s⟩ or ⟨v, s⟩, while their non-gradable counterparts have a simple property type. For NPs and VPs, the lexical theory need have no objection to the dependence on an element like much. And so the only really controversial move is that which I have motivated in up to now: that the relevant semantic distinction between gradable and non-gradable As are whether or not the states they predicate of show non-trivial ordering relations.

4.2.1 The proposal Whenever there is a comparative construction, measures are introduced not by lexical GAs, but by much. Its semantics remains unchanged from Chapter 5: it introduces a context-sensitive measure function, with constraints. I have presented some evidence

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for this variability even with GAs; just as with N and V comparatives, this variability is constrained such that any potential value of A(μ)(a) has the relevant entities in their domains (i.e., the same sort of entities predicated of by the GA, in the present case), and (b) is structure-preserving with respect to the ordering relations that obtain between those entities. Some presumed measure functions are listed in (208). These representations suppose different measures apply to different sorts of things—volume applies to (concrete) entities, while speed applies to (concrete) eventualities, etc. Further specification may be needed, since, I suppose, temperature may apply to states but not portions of matter or stretches of activity, etc. (208) a. b. c. d.

volume : X ⊂ De → Dυ duration : X ⊂ Dv → Dπ temperature : X ⊂ Dv → Dγ speed : X ⊂ Dv → Dσ

Any such measure function may, in principle, value the variable μ introduced compositionally by much, (209), provided its restrictions are met. First, any measurandum falling under P must be drawn from the domain of a non-trivial ordering relation, ≼P . Second, any measure must reflect how ≼P orders its entities in scalar structure. (209) Interpretation of much (with restrictions) Jmuchμ KA = A(μ)

⟨η, d⟩

So far, we have focuses explicitly only on mereological ordering relationships— portions of coffee or stretches of running activity ordered by a part-of relation. So, should the relevant restrictions on much then be specified with respect only to mereological structures? Chapter 3 focused on comparatives with substance mass nouns like (210). The import of mereological structure in the domains of nouns like this has been well-established independently, and indeed, only ‘extensive’ measures are possible when they are targeted by comparative morphology. Yet we equally well have access to intuitively ‘intensive’ measures as the comparative form targets other sorts of nouns, e.g., (211) (see Champollion 2010, p. 153). (210) a. Al drank more coffee than Bill did. b. Al made more soup than Bill did. (211) a. Bill suffered more fever than Sue did. b. Scientists say we can expect more warming than last year. Among other things, if states don’t have mereological structure, then any monotonicity restriction that presupposes mereological structure should not apply to stative predicates.1⁶ And so it may be tempting to assume that the stative orderings we need for GA comparatives are, despite any appearance to the contrary, also mereological in 1⁶ Pasternak 2017 assumes this version of Schwarzschild’s restriction in his analysis of verbs like want and hate. I discuss such constructions in Chapter 6.

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nature. However, given that we are talking about states, and not, for example, portions of coffee, perhaps we can find a way to see temperature as nonetheless monotonic (in this sense) with respect to stative orderings. Of course, smaller amounts of heat have smaller temperature measures than larger amounts. As Champollion (p.c.) points out, to think of heat or amounts of heat as mereologically structured requires thinking about those smaller amounts as parts of the larger amounts. If we did that, we could preserve the letter of Schwarzschild’s monotonicity restriction, which specifically relativizes the selection of measures to those preserving mereological structure. Then we would say that while measures of temperature do not preserve part–whole relations between portions of water, (212), they do preserve such relations between states of heat or global warming, (213). (212)

∗

Al drank 30 degrees Celsius of water.

(213) a. Al had 41 degrees Celsius of fever. b. We can expect two degrees Celsius of global warming. I do not think that I need to commit myself in this way. Consider this alternative characterization. Fever, type ⟨v, t⟩, is true of states, whereas water, type ⟨e, t⟩, is true of (mass) individuals. First, suppose that the temperature measure function has states, not individuals in its domain. Supposing that pseudopartitives involve measurement in the same sense as comparatives, then the mapping to degrees in those constructions will also only invoke measure functions that have the relevant entities in its domain, and that preserve whatever strict ordering relations hold between those individuals or states.1⁷ In my view, we needn’t further add that the structure preserved is mereological, if the entities measured are sufficiently fine-grained. That is, if the entities that satisfy coffee are in the domain of a unique ordering (which happens to have mereological structure), that is the ordering against which the monotonicity restriction is evaluated. The pseudopartitive and comparative facts demand explanation that explicitly invokes mereological structure just if we think that portions of coffee show up in all kinds of orderings, and so this selection has to be winnowed down before the appropriate measure function can be selected. However, we haven’t yet seen evidence that coffee is true of entities that can be ordered any which way. We have seen evidence that coffee is true of entities that are ordered mereologically. Thus, for concreteness, I hypothesize that GA domains DP are ordered by some relation, ≼P ; this may or may not be properly understood as some kind of mereological ordering.1⁸ All I need to assume is that ≼P orders states in terms of how much fever, global warming, etc. they instantiate; an assumption that is formally analogous

1⁷ Of course, if pseudopartitives and comparatives involve measurement ‘in the same sense’, one wonders whether those measures are introduced by covert much as well. I will not consider this question here. 1⁸ Wellwood 2014 assumes this, and Francez & Koontz-Garboden 2015 posit the availability both of a mereological ordering and one based on a more abstract notion of ‘size’, depending on the noun; cf. Baglini 2015.

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to saying that the entities satisfying coffee are ordered by how much coffee they are (cf. Rothstein 1999). Furthermore, such an understanding paves the way for a new understanding of the oddity of sentences like (214): states of woodenness (at least for pieces of wood) are absolute, or atomic—they raise no question of ‘how much’ woodeness they are.1⁹ (214)

? This piece of wood is more wooden than that piece is.

On this approach, more wooden fails for the same reason as more toy and die more: the entities introduced by the relevant lexical targets provide no native ordering relationships that can be tracked by much. The requisite generalization of Smonotonicity—Monotonicity—simply undoes the restriction to part—of orderings.

4.2.2 Mapping to degrees The lexical theory attributes any order-theoretic properties of GAs to their lexicallyassociated scales—i.e., to the range of the measure function expressed by a given GA. I assume, instead, that GAs express properties of ordered states. For example, the GA hot is true of states in the domain of a (unique) ordering that we may characterize as {⟨s, s′ ⟩ | s is as much heat as s′ } (cf. Anderson & Morzycki 2015). This reflects but departs from Cresswell’s (1976) conception, on which GAs associate orderings between individuals, which may be equivalently represented as {⟨x, x′ ⟩ | x is as hot as x′ } or {⟨x, x′ ⟩ | x has as much heat as x′ } (cf. Engel 1989, Moltmann 2009).2⁰ Those entities of which it is true to say ‘are hot’ or ‘have heat’ are, on my theory, the thematic participants in the relevant states.21 Thus, hot is true of states in Dhot , which is ordered by the relation ≼hot , (215); therefore, the extension of hot is the structure ⟨Dhot , ≼hot ⟩. Elements of such structures are mapped to degrees by much. Since the monotonicity condition on this morpheme can be understood simply in terms of strict order-preservation, I leave aside the potentially thorny question of what operations, if any, are defined for Dhot , and thence whether the mapping to degrees here, too, preserves operational relationships.22 (215) a. Dhot = {s | s is a state of heat } b. ≼hot = {⟨s, s′ ⟩ | s is as much heat as s′ } Here, an expression like hotter coffee involves measurement of (particular) states of heat, while more coffee involves measurement of portions of coffee; see Figure 4.1, 1⁹ In other contexts, of course, wooden supports a gradable or measurable understanding; e.g., This table is more wooden than this chair; see §4.1.2 for parallel discussion related to color adjectives. 2⁰ Cresswell 1976 conceived of degrees as labels for equivalence classes based on such orderings. Bale’s 2006, 2008 theory is similar; I discuss Bale’s his theory in more detail at the end of this chapter. 21 Given standard neodavidsonian assumptions, thematic relations are both exhaustive and unique; see Williams 2015 for discussion and references. 22 Berka 1983 discusses difficulties related to certain observables like differences in heat related to determining what the requisite ‘concatenative’ operation should look like. Ultimately, he suggests that any answer is likely to be at least a little theory-dependent; see especially his §8.2.

4.2 adjectival and adverbial comparatives hotter coffee

more coffee

MUCHμ

77

-er

coffee

coffee MUCHμ

… A(μ)(x) > δ & coffee(x) …

-er

hot

… A(μ)(s) > δ & hot(s) & Ho(s)(x) & coffee(x) …

Figure 4.1 Structure and interpretation of more coffee and hotter coffee; δ abbreviates the contribution of the than-clause. run faster

run more run

run MUCHμ

-er

… A(μ)(e) > δ & run(e) …

fast

MUCHμ

-er

… A(μ)(s) > δ & fast(s) & θ(s)(e) & run(e) …

Figure 4.2 Structure and interpretation of run more and run faster; δ abbreviates the contribution of the than-clause.

where θ[θHo ] abbreviates the thematic relation linking states to their bearers. As I’ve suggested, more coffee cannot invoke a comparison by temperature because such a measure fails to preserve strict ordering relations between coffee portions (i.e., such measures are not Monotonicity with respect to the part-of structure denoted by coffee). The reverse is also true: hotter coffee cannot invoke a comparison by volume because such measures do not preserve relationships of increasing heat. What about gradable adverbs? The simplest approach analogizes their treatment to that of gradable adjectives, as I did in my sketch of the lexical theory in Chapter 2. Thus, I assume that fast is true of states in Dfast (perhaps consisting of ones that increase at a good clip; cf. Higginbotham 2008), and that there is a (unique) ordering, ≼fast , on those states; see (216). Then, the extension of fast is modeled as the structure ⟨Dfast , ≼fast ⟩. (216) a. Dfast = {s | s is an amount of speed } b. ≼fast = {⟨s, s′ ⟩ | s is as much speed as s′ } In tandem with these assumptions, run faster involves the measure of ‘fastness’ states, while run more involves the measure of stretches of running activity; see Figure 4.2, where θ abbreviates the thematic relation linking running activity and fastness states. Given such assumptions, just as run more fails to invoke a measure of speed since this is not Monotonic with respect to the part-of ordering on Drun , run faster fails to invoke a measure of duration because such a measure fails to track increasing speed. I have suggested that incorporating GAs into my theory requires only (i) that GA domains consist of ordered states, and (ii) that S-monotonicity is calculated relative to whatever ordering relations there are on the measured domain, rather than specifically keyed to the preservation of part–whole relations. It may turn out that it is appropriate to talk about mereological structure with respect to such domains; yet, given some of the conceptual challenges here, I prefer to make do with the more general notion.

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4.2.3 New composition: adjectives and adverbs I will illustrate the theory using (217). (217) Al’s coffee is hotter than Bill’s is. On my account, (217) expresses that the measure of some heat state s instantiated by Al’s coffee (i.e., the Holder of s;23 cf. Kratzer 1996, Husband 2012), is greater than the measure of any such state of Bill’s coffee. I interpret GAs like hot as expressions of type ⟨v, t⟩, (218), the same as other lexical expressions targeted in the comparative.2⁴ (218) JhotKA = λs.hot(s) I assume that the (simplified) structure in (219) underlies the matrix clause of (217), and I continue to ignore the copular verb, and abbreviate the semantic contribution of the than-clause as δ. The contents of the subject DP and the DegP modifier are summarized in (220). Putting the DegP together with hot looks as in (221), supporting the sentential interpretation in (221b): this says that Al’s coffee is in a state of heat which is such that its μ-measure is greater than that of Bill’s coffee. (219)

S DP[θHo ] Al’s coffee

AP hot

DegP [muchμ -er] thanP

(220) a. JDegPKA = λv.A(μ)(v) > δ b. JDP[θHo ] KA = λs.Ho(s)(ac) (221) a. JAPKA = λs.hot(s) & A(μ)(s) > δ b. JSKA = ∃s(Ho(s)(ac) & hot(s) & A(μ)(s) > δ), where δ = max(λd.∃s(Ho(s)(bc) & hot(s) & A(μ)(s) ≥ d))

PM PM

Given these assumptions, the extension to attributive adjectival comparatives like hotter coffee is straightforward. A noteworthy difference, though, would be in the direction of the thematic relation. In (217), the subject DP is theta-marked, and it is interpreted as a mapping from individuals to states. In an attributive adjectival comparative, I assume that the AP is theta-marked, and it is interpreted as a mapping from states to individuals.2⁵ This pattern of theta-marking and direction of interpretation would track which phrase—AP or NP—is ‘in control’, so to speak.

23 Nothing should hinge on the choice of label ‘Holder’, as Kratzer notes; it is not straightforward to say how we should understand the specific content of any given thematic relation; see Dowty 1989. 2⁴ See Fults 2006 and Park 2008, who also separate the measure function from the adjective, and Husband 2012, Baglini 2015 for reference to states in the semantics of GAs. 2⁵ Kratzer 2000 posits dual ‘stativizing’ (event to state) and ‘eventizing’ (state to event) functions for use in the verbal domain; cf. Chapter 6.

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As before, the compositional interpretation of adverbial comparatives like (222) is similar. (222) Ann ran faster than Bill. For concreteness, I assume that fast expresses the stative property in (223). Assuming an underlying structure like that in (224), the derivational details are as in (225). With this representation, I’ve assumed that states are linked to activities via thematic relation; however, to distinguish the relevant relation in this case from that which links states to their (individual) bearers, I notate this relation simply as θ. (223) JfastKA = λs.fast(s) (224)

S Ann[θAg ]

VP ran

AP[θHo ] fast

DegP [muchμ -er] thanP

(225) a. JDegPKA = λv.A(μ)(v) > δ b. JAnn[θAg ] KA = λe.Ag(e)(a) (226) a. JAPKA = λs.fast(s) & A(μ)(s) > δ PM b. JAP[θHo ] KA = λe.∃s(fast(s) & A(μ)(s) > δ & Ho(s)(e)) θ A c. JSK = ∃e(Ag(e)(a) & ∃s(fast(s) & A(μ)(s) > δ & Ho(s)(e)), PM where δ = max(λd.∃e(Ag(e)(b) & ∃s(fast(s) & A(μ)(s) ≥ d & Ho(s)(e)))) The analysis straightforwardly applies to subcomparatives like (227a) as well, and to explain the markedness of (227b) nearly as before. (227) a. The ladder is wider than the couch is tall. b. The ladder is wider than the couch is green. The compositional interpretation of the sentences in (227) is entirely parallel to that of sentences like (217), except the adjectival contribution in the than-clause is different. I interpret the identical matrix clauses of (227) as in (228), and their distinct thanclauses as in (228a) for (227a), and (228b) for (227b). Here, as before, (227b) is odd but (227a) is not because different measures (in this case, different values of A(μ)) are defined for tallness and greenness states. Absent a single scale to represent both, the result cannot be evaluated for truth or falsity (cf. Kennedy 1999). (228) ∃s(Ho(s)(l) & wide(s) & A(μ)(s) > δ), where δ = a. max(λd.∃s(Ho(s)(c) & tall(s) & A(μ)(s) ≥ d)) b. max(λd.∃s(Ho(s)(c) & green(s) & A(μ)(s) ≥ d))

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4.2.4 Two alternatives I have offered a theory on which, so far, only much introduces measure functions. The theory leans on the assumption that some APs, NPs, and VPs distinctively introduce their own ‘primitive’ ordering. Why characterize the semantics of the ‘measurable’ predicates in these terms, rather than extending the lexical measure function theory from AP to these other categories? Or, why not dispense with reference to measure functions altogether, and interpret comparative morphemes directly in terms of the primitive orderings? The former approach was hinted at by Cresswell (1976; cf. von Stechow 1984), and the latter by Reichenbach (1947). I consider each of these possibilities in turn. Cresswell (1976) follows Bresnan (1973) in assuming that an item like much is present whenever there is a comparative construction with -er, as, etc. Importantly, though, he thinks that the role of that expression is to indicate the local relevance of degree-theoretic interpretation. In other words, much doesn’t invite the play with degrees, as on my account, but simply marks that such play is underway. After all, the action of a degree semantics here centers around the GA, as in most subsequent work. Near the end of his paper, though, Cresswell briefly considers whether that action shouldn’t be extended to nominal comparative targets. Maintaining that much is essentially vacuous, Cresswell is reluctant to assimilate the analysis of nominals to that he has advanced for GAs—i.e., in terms of lexicallyspecified degrees—because then we would expect pairs like (229a)–(229b) to be synonymous, which they are not. The clear difference in meaning here must have something to do with much, but this should be impossible if that expression is effectively meaningless (Cresswell 1976, pp. 290–1). Perhaps we can say something stronger: if much only serves to mark that a degree semantics is in play, and a noun like water lexically introduces degrees, then (229a) shouldn’t even be generable. (229) a. Drink this water. b. Drink this much water. On the account I’ve developed, much introduces degrees. Those degrees can be demonstrated, as in (229b), but not if they are never introduced in the first place, as in (229a). Perhaps the difficulty stems from having made a distinction between primitive orderings and degree orderings in the first place. Why not just dispense with degrees and measure functions, and state the semantics of comparatives directly in terms of the hypothesized ordering relations on the domains of the relevant lexical items? In this respect, it is instructive to consider the logical analysis of comparatives sketched by Reichenbach (1947). Instead of appealing to (first order) eventualities and degrees, he appeals to ‘specific properties’ f, unique to the individuals that bear them, and

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themselves the bearer of other (higher order) properties. For example, he would analyze (230a) as in (230).2⁶ (230) a. Al moves slowly. b. ∃f( f(a) & move( f ) & slow( f )) Crucial for the present discussion is how he extends this analysis to the case of comparatives, for example (231), and measure phrase constructions like (232). (231b) says, on this account, that ‘Al and Bill have specific properties f and g, where f and g are in the class of tallness properties, and f is greater than g’. (232b) says, ‘Al has specific property f, and f is equal to 50 mph’. Bartsch & Venneman (1972) raise concerns about these interpretations, asking: what is this ‘greater than’ relation between specific properties? And, even if such could be stated, how can a property both be unique to Al, and equal to 50 mph? (231) a. Al is taller than Bill is. b. ∃f ∃g( f(a) & g(b) & tall( f ) & tall(g) & f > g) (232) a. Al moves at 50mph. b. ∃f( f(a) & move( f ) & f = 50mph) I am not concerned with Bartsch and Venneman’s first worry, as I have supposed that adjectival domains can provide the relevant ordering relations. But their second concern is starker. To see the issue in the context of the comparative constructions proper, consider how Reichenbach’s analysis would extend to the equative sentence in (233). Suppose for the moment that equatives express an identity relation; the problem, then, is in any such statement of identity between f and g. If specific properties are unique to their bearers—much like states—how can f and g be proprietary to Al and Bill, respectively, yet nevertheless be identical? (233) Al is as tall as Bill is. ∃f ∃g( f(a) & g(b) & tall(f ) & tall(g) & f = g) Questions like this are easily avoided given a distinction between ‘primitive’ orderings and orderings on degrees. Adopting the overall structure of Reichenbach’s interpretive scheme, but quantifying over states rather than specific properties, I would assign the interpretation in (234) to (233). Here, Al and Bill are each uniquely related to some state of tallness, s and s′ , and the relevant identity is stated between the measure μ of those states—i.e., two degrees—rather than between the states themselves. (234) ∃s∃s′ (Ho(s)(a) & Ho(s′ )(b) & tall(s) & tall(s′ ) & μ(s) = μ(s′ )) 2⁶ (230b) may be read, ‘there is a specific property f that Al has such that f is in the class of movement properties and f is in the class of slowness properties’.

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4.3 Other adjectival occurrences I have offered a treatment of adjectival comparatives in which GAs express properties of states, and measure functions are introduced by the comparative morphology. But GAs occur in non-comparative grammatical contexts, many of which have been cited in support of the development of the lexical theory set up in Chapter 2. In particular, much has been made of the fact that GAs combine with modifiers like very and two feet, and of their threshold-relative dependent interpretation in the positive form. I discuss these data in §4.3.1 and §4.3.2, respectively, and offer some preliminary remarks on how the new theory might apply to such cases.

4.3.1 Degree modification GAs indeed show a distinct pattern from expressions of other lexical categories with respect to modifiers like very and two feet. With respect to the former, it certainly seems that GAs are special: they surface directly adjacent to very, (235a), and are ungrammatical if much intervenes here, (235b). The opposite pattern, meanwhile, is observed with nouns and verbs: both require much, (236) and (237).2⁷ (235) a. Al wasn’t very intelligent. b. ∗ Al wasn’t very much intelligent. (236) a. ∗ Al didn’t drink very coffee. b. Al didn’t didn’t drink very much coffee. (237) a. ∗ Al didn’t run very. b. Al didn’t run very much. However, examples from Corver (1997) suggest that, whatever ultimately explains the data in (235)–(237), the presence or absence of much does not correspond with a semantic difference. Consider first that (238), without much, seems equivalent in meaning to (239b), with much; and, (239a), without much, is ungrammatical. Assuming that anaphoric so resumes the semantics of intelligent here (an uncontroversial assumption), the fact that much is required with so but not with intelligent suggests that its distribution is independent of semantic interpretation. (238) Al is intelligent, in fact she is very intelligent. (239) a. ∗ Al is intelligent, in fact she is very so. b. Al is intelligent, in fact she is very much so. Rather, it seems to me that data like (235)–(239) suggest only that very is a comparative morpheme on a par with -er, as, etc. Just like those morphemes, it requires much. 2⁷ I have given negative-marked examples in (236) because the positive versions with much are odd: English speakers would prefer to say Al drank a lot of coffee to Al drank much coffee. See Bolinger 1972 for discussion of the fluidity of form (diachronic and synchronic) of such modifiers; see also Doetjes 1997, Solt 2009.

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83

If so, then the surface form of this morpheme, much, goes unrealized in cases like (235a) for the same reason that it goes unrealized in many other GA comparatives— obligatory much-deletion. Moreover, if much is always around, then any appropriate degree-theoretic treatment of very can be incorporated into the present theory with little difficulty.2⁸ With respect to measure phrases like two feet, it is indeed straightforward to analyze (240) by interpreting six feet as a name for a degree d, and relating d to a measure function introduced by tall, via abs.2⁹ Certainly, the easy work that the lexical theory makes of cases like (240) can and has been taken as strong support for that theory. (240) Al is 6 feet tall. But it is not at all clear that these cases should be considered central to determining the semantics of GAs. For one thing, very few GAs are grammatical in such a construction, even once any potentially confounding semantic factors have been controlled for (see Schwarzschild 2005, Bale 2006, and Beck 2011)—witness (241). This pattern of ungrammaticality is in fact contra-predicted by the lexical theory, which makes a degree argument available whenever a GA occurs. More impressively, in the cases where we have unambiguous evidence for a degree-based semantics—comparative constructions—these measure phrases are always licit, e.g., (242). (241) a. ∗ Al is 200 pounds heavy. b. ∗ That book is a thousand dollars expensive. c. ∗ The soup is 90 degrees C∘ hot. (242) a. Al is 200 pounds too heavy. b. That book is a thousand dollars more expensive. c. The soup is 90 degrees C∘ hotter than the water. For the few good cases of a measure phrase in the positive form, the present account could treat the exceptions as exceptions (see Schwarzschild 2005 for an analysis in this spirit). For instance, suppose that an expression like six feet indeed denotes a degree. For (240), I could posit a selective device that maps that degree to a property of states (or, to equivalence classes thereof, see below; cf. Anderson & Morzycki 2015). The general pattern exemplified in (242), meanwhile, can be accommodated as on standard accounts, by shifting from an interpretation of more that depends on two degrees, to one that depends on three. Thus, these data do not seem terribly problematic for my theory, and more can be said about GA modification. The semantics literature has not discussed, to my knowledge, a certain pattern of productive modification which is not obviously illuminated by a degree-theoretic interpretation of GAs. The general pattern is exemplified in (243), 2⁸ For discussion, proposals, and references specific to very, see Wheeler 1972, Lasersohn 1999, Katz 2005, Bale 2006, among others. 2⁹ That is, this is an available analysis for the version of the lexical theory I have been assuming, on which GAs are expressions of type ⟨e, s⟩. On the type ⟨s, ⟨e, t⟩⟩ variant, the degree denoted by six feet would saturate the first argument of the GA’s degree-relational predicate. See Chapter 2.

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which feature NPs that, intuitively, pick out an individual, event, or place that typify a high standard for the GA. It would be a stretch to say that such NPs are degreedenoting, especially if it’s not possible to find any other grammatical context in which that analysis would be required.3⁰ (243) a. Al is Andre the Giant heavy. b. Our meal was dinner at the Ritz expensive. c. It’s Arizona hot right now. Here is a suggestion about how such data might be handled; the devil will have to wait for the details. Suppose we paraphrase (243a) as follows: ‘Al is in a heaviness state s that is qualitatively similar with a state s′ that Andre the Giant is in’. The notion of qualitative similarity I have mind, such that s ≈ s′ , goes as follows: despite being particular to each of Andre and Al, under the right circumstances you wouldn’t be able to tell s and s′ apart. With g referring to Andre, this might be formalized as in (244).31 (244) ∃s(Ho(s)(a) & heavy(s) & ∃s′ (Ho(s′ )(g) & s ≈ s′ ))

4.3.2 The positive form So far, my theory interprets a sentence like (245) as a simple existential statement about states. If all that’s required for the existence of a tallness state s is non-zero vertical extent,32 then (245) should just be true so long as an entity going by the name Al physically exists. But this isn’t right. Uses of (245) are usually taken to indicate that Al’s vertical extent ‘stands out’ in the relevant context. On the lexical theory, this indication is typically recorded in the semantics by positing covert abs and a contextually-provided standard degree. (245) Al is tall. ∃s(Ho(s)(a) & tall(s)) Positing an occurrence of abs here thus does double-duty for the lexical theory: in addition to providing a convenient solution for the relevant context-sensitivity, it dispenses with the degree argument introduced by the GA. Since my theory reimagines the lexical semantics of GAs, I face no compositional worries here; moreover, the context-sensitivity could easily be handled by positing a non–degree-theoretic analogue of abs. However, as long as we’re in the business of re-evaluating the analysis of

3⁰ Tellingly, this type of modification is not possible in the differential comparative form, e.g., ∗ Ann is Andre the Giant taller than Bill. 31 This idea occurred to me after extended consideration of a suggestion briefly entertained by Bale 2006 for examples like (240), which was based on an equivalence class relation. See also Schmidt et al. 2009, who suggest that positive GA occurrences are interpreted relative to an ‘indifference’ relation with a contextually-provided exemplar of the GA category; if so, (243) would simply represent cases where the exemplar is explicitly named. 32 Notice: even the shortest x and y can be such that x is taller than y.

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familiar data, it is worth considering what other evidence there is for something like abs, and what other semantic analyses are possible. The fact is, there is little evidence on the surface, at least, for an obligatory morpheme that attends positive GA occurrences. It had seemed, at one point, that the functional morpheme hen in Mandarin might be a good candidate for abs/pos, but Grano (2012) has argued convincingly that it is not. Recently, Grano & Davis (2017) reached the same negative conclusion about another tempting candidate in Arabic. Interesting data from Navajo looks like it could go the same way: in this language, all comparative constructions require a certain ‘comparative aspect’, but the positive construction is ungrammatical with such morphology, requiring instead ‘absolute aspect’ (BogalAllbritten 2013a). The lack of degree morphology with positive occurrences of GAs correlates with a striking semantic difference between the positive and comparative forms (see especially Fults 2006; cf. Kennedy 2007). Comparative constructions are semantically ‘crisp’: any discernible difference in height, in the appropriate direction, is enough to say that x is taller than y. The positive construction is different: given the way same smidgen of difference, one feels some discomfort with saying that x is tall, compared to y. Considerations like these suggest that it would be better to not posit a covert degreetheoretic layer for positive occurrences of GAs if we don’t have to (cf. von Stechow 1984). One possibility is that sentences like (245) indeed do have an exceedingly weak semantics, and so are typically pragmatically strengthened (cf. Rett 2008). Panzeri & Foppolo (2012) and Panzeri et al. (2013) argue for such a view based on observations suggesting that the weak interpretation is available even if it is generally dispreferred. In their experiments, 3-year-old subjects freely labeled novel objects of any size as tall, and adults did so as well when it was made clear that literal truth, and not informativity, was at stake.33 Panzeri and colleagues thus attributed a weak literal meaning to the children, and the strengthened reading to later pragmatic development. A distinct possibility is that something about the copular construction itself is to blame. In this respect, it is worth contrasting the pattern of copular GAs versus their nominalizations with possessive have, (246). Intuitively, there is an apparently systematic difference here, such that the adjectival predications invite thinking relative thoughts about standards and so on, whereas the possessive nominalizations do not: surely Al can have (some) beauty, even if she’s not beautiful, etc. If the adjectives and their nominalizations have more or less the same semantics, though, it is difficult to see how the context-relativity could be lexical in the one case but not in the other.3⁴

33 Here’s how Panzeri and colleagues did this: they presented adults with an alien puppet who was new to the language, and instructed them to say whether the alien’s statements were correct. However, the subjects were told that they should not say that the alien was incorrect if what he said was true, but simply ‘not optimal’—for example, in a case where the alien uttered a true sentence with a false implicature. 3⁴ That is, all else equal, the pairs in (246) would either (i) express the same trivialities, and so should be subject to the same pragmatic strengthening, or (ii) require the same covert abs, and so show the same standard-relativity. Cariani et al. under review discuss the desirability of attributing the same semantics to GAs and their nominal counterparts, based on the observation that their corresponding comparative forms are semantically equivalent.

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(246) a. b. c. d.

Al has beauty / is beautiful. Al has intelligence / is intelligent. Al has tallness / is tall. Al has wideness / is wide.

Francez & Koontz-Garboden (2015) offer a solution based on domain restriction, which may require some delicacy in light of the contrasts just noted. However, these authors point out that there are at least echoes of the sort of context-sensitivity that we see with GAs all over the place, in particular almost anywhere that we think there is otherwise mere existential quantification (Francez & Koontz-Garboden 2015 cite Kratzer 1977, 1991 for similar patterns with epistemic modals, and Travis 1989 for examples involving mass nouns). As the spread of the phenomenon grows, it becomes all the less likely that a covert abs-type morpheme explains it. Indeed, simple examples suggest that boring nouns and verbs are not entirely immune from a contextual sensitivity to ‘how much’ of the relevant stuff is required for their use to be felicitous. The quantity of wood expected for (247a) to be judged true is normally going to be quite different from that expected for (247b) (cf. Schwarzschild & Wilkinson 2002, p. 12), as is the amount of running normally required for (248a) compared to (248b). (247) a. There’s wood in my eye. b. There’s wood in my truck. (248) a. Al ran a maze. b. Al ran a marathon.

4.4 Conclusion In this chapter, I have offered an alternative view of GA comparatives on which GAs do not, wholly or partially, denote measure functions; instead, they express properties of states. This theory unifies the semantics of comparatives across a variety of lexical targets, and holds that the lexical expressions themselves introduce things that can be measured rather than things that measure; the semantics of degree is uniformly introduced by much. I supported this uniform view by revisiting some of the data and arguments taken to suggest analytic moves specific to GA or N/V comparatives. Yet the relevant properties are detectable in comparatives across lexical targets, and so would be better attributed to the comparative morphology itself. One of the most interesting semantic consequences of the view I’ve offered is that it promises to unify the distinction between gradable and non-gradable adjectives with distinctions that otherwise ‘feel’ similar in other domains. That is, the lexical theory divides the gradable from the non-gradable type-theoretically, whereas the present theory divides them on the basis of the structure (or lack thereof) on their domains of predication: a GA like tall applies to states in the domain of an ordering by length,

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whereas a non-gradable adjective like dead applies (at least by default) to unordered states. This division is the same as that I have assumed for mass versus (singular) count nouns, or between (singular) telic versus atelic VPs. At a more theoretical level, it is interesting to consider how the view employs the notion of ‘measurement’ in contrast to the lexical theory. On my account, what is measured determines in a very direct sense how measurement can proceed: the functions properly called ‘measures’ are, on my view, just those that are structurepreserving with respect to the measured domain. On the lexical theory, these functions are essentially arbitrary; while it is possible, of course, that somewhere ‘under the hood’ we have something like the mapping from states to degrees as I have proposed (cf. Cresswell 1976). On my theory, the measurement-theoretic notion is called up directly by a functional morpheme. GA comparatives have been of central interest in the development of degree semantics, while those I have otherwise focused on—nominal comparatives targeting mass NPs and verbal comparatives, simpliciter—have tended to fly almost entirely under the radar. Nominal comparatives targeting plurals NPs have received more attention, and by now it is fairly standard to view degree introduction as the provenance of a distinct functional item, many. Thus, I focus next on these comparatives, and their analogues in the verbal domain. In Chapter 6, I discuss a class of examples—comparatives with postadjectival more—that, I suggest, share many of the same properties. If the theory developed in this chapter is correct, then the number of measure functions has been reduced by at least the number of gradable adjectives. If I am successful in re-analyzing many, then that number will have been reduced to one.

5 Measuring pluralities

With the semantics of gradable adjectives reimagined, comparatives are uniformly interpreted by means of a structure-preserving map from entities to degrees. The ‘measurable’ predicates are mass NPs, atelic VPs, and gradable APs—i.e., those that introduce an ordered domain—while the non-measurable predicates are (singular) count NPs, telic VPs, and non-gradable APs. Regardless of lexical category or domain, degrees are introduced via the constrained, context-sensitive valuation of much. So far, only this expression introduces measure functions into the compositional semantics. In a certain respect, the distinction between measurable and non-measurable predicates that I have drawn divides ‘lexical’ meanings. I have, for the most part, sidestepped talk of how the broader compositional process can affect the interpretation of comparatives. For instance, I have not examined how the interpretation of plural NPs in nominal comparatives, or on the affects of grammatical aspect on verbal comparatives. As we will these cases bring into relief the power and flexibility of the semantic theory that I offer. Thus, I now focus on just these sorts of cases. For example, consider (249) and (250). A characteristically count noun like idea, (249a), is odd in the nominal comparative for the same reason that a (‘once-only’) telic verb phrase like kill Peter is, (249b): such predicates fail to introduce the sort of non-trivial ordering relations required for the selection of a measure function by much, at least by default. However, the comparative succeeds when idea is pluralmarked, (250a), and when the telic VP ‘repeatable’, (250b). The latter comparatives are straightforwardly evaluated for truth or falsity based on number. (249) a. ?Al had more idea than Bill did. b. ?Al killed Peter more than Bill did. (250) a. Al had more ideas than Bill did. b. Al hit Peter more than Bill did. I suggest that such patterns depend on the semantic implications of plural-marking, whether overt (as in the nominal -s in English) or covert (as in the verbal domain). The resolution of number-based comparisons for sentences like (250) are due to how much is resolved when the domain for measurement has the structure of an atomic join semi-lattice (cf. Bale & Barner 2009). It does not, or so I argue, reflect the presence of a distinct lexical item, many, which introduces a cardinality function. Instead, the surface form many is characterized as a morphophonological realization of much in certain restricted grammatical environments. The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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To ensure that much will resolve to number in cases like (250), I propose an additional condition on the contextual selection of measure functions over and above Monotonicity, which I call A-invariance. Attributing the new condition to muchμ can capture the important semantic facts usually attributed to a hypothetical many, and, as I show, better accords with English-internal and cross-linguistic evidence suggesting that the many/much distinction is, again, a surface phenomenon to be explained primarily in the morphophonology.

5.1 The empirical landscape 5.1.1 Plural count (and mass) Plural-marked NPs are, of course, perfectly acceptable and interpretable in the comparative forms, (251)–(252), and reveal two important properties. First, in every case, the understood dimension for comparison is number (cf. Hackl 2000, Bale & Barner 2009). Second, the equative and excessive forms surface with many instead of much. Such observations have typically led to the assumption that the first property—restriction to number—is explained in terms of the second: degree introduction here must be performed by a morpheme many, instead of context-sensitive much. (251) a. b. c. d.

Al had more ideas than Bill did. Al bought more coffees than Bill did. Al had as many ideas as Bill did. Al bought as many coffees as Bill did.

(252) a. b. c. d. e. f.

Al had too many ideas. Al bought too many coffees. Al had enough ideas to fill a book. Al bought enough coffees for everyone. Al had the most ideas of her cohort. Al drank the most coffees of anyone.

comparative equative excessive assetive superlative

Before turning to the relevant analytic options, let us first focus on two interesting generalizations about how plural-marking and dimensional interpretation interact in nominal comparatives, and (in section 5.1.2) on how those same patterns may be observed in verbal comparatives. For NPs, the general pattern is summarized in Table 5.1. On the one hand, any non-measurable N becomes measurable when N is plural-marked, and on the other, any measurable N which normally makes accessible dimensions δ is only measurable by number when N is plural-marked. For the first generalization, recall that bare count nouns like idea are anomalous in the comparative form: strings like (253a) cannot be used to express any number of otherwise conceivable thoughts, for example a comparison of how profound two ideas are, or how many ideas the individuals have, etc. Adding the plural -s changes things:

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measuring pluralities Table 5.1 The effect of plurality on comparatives with nouns. category count mass

−plural +plural −plural +plural

example

measure(s)

idea ideas rock rocks

?? number volume, weight number

targeting the plural count noun ideas in (253b) is perfectly acceptable, and interpreted as a comparison between the number of Susie’s ideas and the number of Al’s. (253) a. ∗ Susie has more idea than Al does. b. Susie has more ideas than Al does.

∗

number number

And so the addition of plural-marking reveals otherwise inaccessible dimensions; it also rules out otherwise accessible dimensions. As discussed in detail in Chapter 5, targeting the bare mass noun rock is interpreted as a comparison of the volume or the weight of relevant portions of rock, (254a). Plural rocks, though, supports only a comparison by number. Indeed, in a formal experiment pitting dimensions like volume and number against one another, people choose the continuous dimension for forms like more rock, but number for more rocks (Barner & Snedeker 2005). (254) a. Al found more rock than Bill did. b. Al found more rocks than Bill did.

∗

number number

The restriction to number in these cases is usually taken to signal the presence of the morpheme many, interpreted as a function from pluralities to cardinalities. Yet of course, such an analysis fails to explain the fact that, in many languages, the same restrictions are observed, but there is no evidence for a much/many distinction. For example in Spanish, the only difference between the equivalents of (254a) and (254b) is singular or plural agreement morphology on a univocal form mucha; that is, (255a) indicates a lot of beer-drinking by volume, while (255b) indicates a lot of beer-drinking by the number of units consumed. (255) a. Silvia tomó mucha cerveza durante la cena Silvia took much beer during the dinner ‘Silvia drank a lot of beer at dinner.’ b. Silvia tomó muchas cervezas durante la cena Silvia took much.pl beer.pl during the dinner ‘Silvia drank many (bottles/cups of) beer at dinner.’ French is similar, where the difference in plurality isn’t audible on the noun phrase, but is detectable from agreement on the verb. In this language, the base form equivalent to much is beaucoup. In (256a), with the perfect form of have showing singular agreement, a comparison by volume is understood, while when that form shows

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plural agreement the comparison is understood in terms of number, (256b). (These examples from M. Gagnon, p.c.; see Doetjes 1997 for a broader cross-linguistic look at morphological patterning like this.) (256) a. Beaucoup de bière a été bue hier soir. much de beer have.sg been drunk last night ‘Much beer was drunk last night.’ b. Beaucoup de bières ont été bues hier soir. much de beer.pl have.pl been drunk last night ‘Many beers were drunk last night.’

5.1.2 Pluractional telic (and atelic) Like their nominal correspondents ‘plural count nouns,’ telic verb phrases like hit Peter and run to the store are comfortable in any of the comparative forms, (257)–(258), and all may only be interpreted as involving comparisons between numbers—in this case, counts of events of particular sorts. In this case, though, the equative and excessive forms surface with either much or the complex many times, although there appears to be little substantial semantic difference between these alternates. (257) a. b. c. d.

Al hit Peter more than Bill did. Al ran to the store more than Bill did. Al hit Peter as much/many times as Bill did. Al ran to the store as much/many times as Bill did.

(258) a. b. c. d. e. f.

Al hit Peter too much/many times. Al ran to the store too much/many times. Al hit Peter enough to kill him. Al ran to the store enough (times) this weekend. Al hit Peter the most of the attackers. Al ran to the store the most (times).

comparative equative excessive assetive superlative

Following discussion from Wellwood et al. (2012), such data are the result of a syntactic analysis involving covert plural-marking, and imperfective aspect. First, Ferreira (2005) proposes that VPs in English and other languages can be marked singular or plural covertly. In the perfective aspect, only singular marked VPs are possible; and indeed, just like singular count nouns are anomalous in the nominal comparative, telic verb phrases explicitly marked perfective are anamolous in the verbal comparative; see the data from Bulgarian and Spanish in (259a)–(259b), which explicitly mark perfective aspect. (259) a. ∗ Minalata sedmica (‘last week’), Ivan izkaĉi vrâh Musala poveče ot Maria. Ivan climb-pfv.past top Musala more from Maria ‘Last week, Ivan climbed Musala more than Maria.’

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b. ∗ La semana pasada (‘last week’), Juan subió al Mt.Tom más que María. Juan climbed-pfv the Mt.Tom more than María ‘Last week, Juan climbed Mt.Tom more than María.’ In the imperfective aspect, telic verb phrases are both acceptable and interpretable in the comparative in these languages, (260a) and (260b). Importantly for present purposes, the only available interpretation of these comparatives is as comparisons of numbers of events. These data are explicable if we assume that the imperfective aspect modifies a plural-marked verb phrase which usually results in a habitual or repeated action interpretation. Such an analysis renders these data perfectly parallel, then, to plural-marked NPs in nominal comparatives.1 (260) a. V onezi dni (‘in those days’), Ivan izkaĉvasê vrâh Musala poveče ot Maria. Ivan climb-impf.past top Musala more from Maria ‘In those days, Ivan climbed Musala more than Maria.’ b. En esos días (‘in those days’), Juan subía al Mt.Tom más que María. Juan climbed-impf the Mt.Tom more than María ‘In those days, Juan climbed Mt. Tom more than María.’ Though the analytic moves must be made carefully, such data can be seen as the verbal parallels of grammatical manipulations making available dimensions that were otherwise impossible—singular (perfective) telic verb phrases make no salient dimensions available, while plural (imperfective) telic VPs make only number available. Continuing to look at languages that show the relevant aspectual distinctions on the surface, imperfective-marked atelic VPs headed by verbs like play and run are naturally compared by number, (261a)–(261b), but also support comparisons by continuous dimensions like duration. Wellwood et al. (2012) interpret this flexibility as reflecting a structural ambiguity between imperfective singular VPs, and imperfective plural VPs, obscuring a difference that parallels the case of mass/count flexible NPs in the comparative (e.g., more coffee/coffees). See Table 5.2. (261) a. V onez dni (‘in those days’), Ivan igraeŝe poveče ot Maria. Ivan play-impf.past more from Maria ‘In those days, Ivan played more than Maria.’ b. En esos días (‘in those days’), Juan corría más que María. Juan run-impf more than María ‘In those days, Juan ran more than María.’ 1 Comparatives with VPs marked by imperfective aspect and the covert singular are interpreted with an ongoing event interpretation. These VPs are universally anomalous in the comparative; the best we can do in English is examples like Right now, Al is running more than Sue is, which is not straightforwardly interpretable.

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Table 5.2 The effect of aspect on comparatives with verbs. category telic atelic

pfv sg impf pl pfv sg impf pl

example

measure(s)

reach the top reach the top run in the park run in the park

?? number duration, distance duration, distance, number

In the aspectually-deficient English, though, constructing similar data requires recruiting contextual or world knowledge. For telic VPs, we can consider ‘singular’ those that describe events that are non-repeatable for a given agent, while those that are repeatable are, at least in principle, ‘plural’ (Nakanishi 2007); see (262) and (263). (262) with telic run to the store is straightforwardly interpreted as a comparison by number if uttered in context (262b), while (263a) with atelic run in the park is most naturally read as a comparson involving distance or duration in context (263a), but by number in context (263b). (262) Al ran to the store more than Bill did. a. Al and Bill each went to Walgreens once. b. Al went 3 times, and Bill went twice.

∗

number number

(263) Al ran in the park more than Bill did. a. Al and Bill each went on a single run in Grant Park. b. Al ran in Grant Park 3 times, Bill twice.

∗

number number

Relevantly plural interpretations in the verbal domain are often referred to as ‘pluractional’ interpretations. This type of semantics is marked explicitly in many languages; see Cusic (1981), Cabredo Hofherr & Laca (2012). Bach (1986a), Ferreira (2005), van Geenhoven (2004, 2005), Nakanishi (2007), and Henderson (2012) for discussion and references.

5.2 Pluralities 5.2.1 Reference Comparatives exclude singular occurrences of the predicates that they target, but are indifferent with respect to non-singular occurrences (i.e., mass/atelic, plural count/ pluractional telic). As I have characterized it, singular predicates involve no (or, no non-trivial) structure on their domains, and hence are the non-measurable predicates. In contrast, the measurable predicates provide non-trivially structured domains, and the selection of measure functions is reflexive, in part, on the particular structures such predicates introduce. We saw this for mass and atelic predicates in Chapter 3, and I characterized the gradable/non-gradable distinction between adjectives in the same way in Chapter 4.

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A wealth of research suggests that the domains of plural and pluractional expressions have non-trivial structure, but they differ from those of at least substance mass nouns and process atelic VPs in that they plainly ‘bottom out’ in atomic entities. To see the non-trivial structure, it can easily be shown that plural NPs display cumulative reference. That is, if the predicate successfully applies separately to two distinct pluralities, this licenses the inference that the predicate applies to the sum of those pluralities, (264a). The concomitant, singularly-interpreted predicate, as before, fails in this regard, (264b). (264) a. These are cups, those are cups; taken together, they’re cups. b. ?This is a cup, and . . . The same can be shown for pluractional VPs. For example, the intuitive validity of (265a) suggests that identify Picassos, if it applies to two pluralities of events separately, it applies to the sum of those pluralities. In contrast, identify one Picasso, understood singularly, fails to support the cumulative inference pattern, (265b).2 (265) a. If Al identified Picassos for a week, and then again for a week, so Al identified Picassos for two weeks. b. ?If Al identified one Picasso for a year . . . The individual satisfiers of cups certainly seem to be the available referents for a cup, but there is debate in the semantics of nominal reference as to whether this intuitive plausibility amounts to positing atomic minimal parts for the extension of expressions like cups. The difference is between theories which are ‘inclusive’ in this sense versus those that are ‘exclusive’ (Farkas & de Swart 2010). They differ in whether the addition of the plural morpheme -s on N contributes a meaning like ‘one or more Ns’ (Krifka 1989, Sauerland 2003, Sauerland et al. 2005, Chierchia 2010) or ‘two or more Ns’ (Link 1983, Chierchia 1998b). I will assume the inclusive theory of nominal plurality, for reasons that will become clear directly, and the same for verbal pluractionality. First, both inclusive and exclusive theories are challenged by dependent plurals; see (266) (de Mey 1981; and Schwarzschild 1996, Champollion 2010). The inclusive theory should paraphrase (266a) as ‘Five girls grew one or more flowers’, and so the sentence is predicted to be judged true if the girls grew one flower total, which is intuitively wrong. The exclusive theory should paraphrase (266b) as ‘No girls grew two or more flowers’, which would be true if five girls grew one flower each, which also seems wrong. (266) a. Five girls grew flowers. b. No girls grew flowers. However, the inclusive theory can analyze such data as the result of pragmatic reasoning as follows: understand a plural NP as exclusive whenever that reading is 2 For discussion of the interaction between the object NP’s form and VP telicity, exploited in (265a) and (265b), see for example Krifka 1989 and Filip 1996.

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stronger than its inclusive reading (see Gillon 1992, p. 60, fn. 23, and Zweig 2008, 2009). To see how this helps, consider that Five girls grew one or more flowers would be true in any situation in which Five girls grew two or more flowers is, but the reverse doesn’t hold. In contrast with (266b), where the plural expression occurs in a downward-entailing context, No girls grew two or more flowers is true in more cases than would be No girls grew one or more flowers; here, the exclusive reading would not be stronger and hence not considered. Separate and apart from this question, there are two crucial properties of plural extensions that need to be captured, in order to formulate an explanation for why plural-marking (overt or covert) leads inexorably to number-based comparisons in nominal and verbal comparatives. First, plural NPs show limited divisiveness—if they apply to a plurality, they apply to some of its subparts but not all. Second, they show cumulativity. Thus, I will want to say that the domains of plural NPs are structured by a ‘plural part-of ’ relation, which has atomic minimal parts which are identical to those in the extension of their singular NP counterparts.

5.2.2 Imposing atomic parts Positing that the minimal parts of a plural predicate are the atoms of a corresponding singular predicate raises the question, of course, of how mass terms like coffee could come to have plural forms in the first place. As I assumed in Chapter 3 that substance mass nouns do not specify minimal parts in their extensions at all, let alone atomic minimal parts, where does coffees get its atoms from?3 I follow many authors in positing that mass nouns like coffee, when they surface as plural, must first have been ‘singularized’, atomized, or divided (cf. Greenberg 1972, Borer 2005a). My particular implementation follows the discussion and argumentation by Mathieu (2012); some of his examples of ‘singulative formation’ are given in Table 5.3, as revealed through gender shift (Russian and Breton), singulative suffixation (Classical Arabic), and animacy shift (Fox). Remnants of the same sort of process can Table 5.3 Singulatives. (Based on Mathieu 2012, references therein.) language

base N

Russian Breton Classical Arabic Fox

lyod geot teen owiiyaasi

singular N ‘ice’ ‘grass’ ‘mud’ ‘meat’

l’dina geot-enn teenah owiiyaasa

‘block of ice’ ‘blade of grass’ ‘a chunk of mud’ ‘a piece/cut of meat’

3 As a reminder, the assumption in Chapter 3 was that mass syntax is neutral with respect to atomicity. This allows for a given mass N to make available minimal parts—as nouns like furniture presumably do—but also to resist making such parts available—as coffee appears to. This ‘neutral’ view of mass syntax contrasts with atomic and anti-atomic theories, which posit either that mass noun extensions are always atomic or always non-atomic.

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measuring pluralities Table 5.4 Pluralized singulatives. (Based on Mathieu 2012, references therein.) language

base N

singular N

plural N

Hebrew Breton Fox4 Ojibwe5

se’ar ‘hair’ buzhug ‘worms’ zhooniyaahi ‘silver, money’ mikwam ‘ice’

sa’ar-a buzhug-enn zhooniyaaha mkwamiins

sa’ar-ot buzhug-enn-oú zhooniyaaha-ki mkwamiins-ag

be found in Hebrew, Syrian Arabic, German, Dutch, and Ojibwe (see Mathieu 2012 for examples). In many cases, the nouns that require singulative marking in the relevant languages show evidence of that process even after pluralization; some examples are given in Table 5.4. Mathieu (2012) draws on Borer’s (2005a) notion of semantic division for characterizing the effects of this process. For my purposes, I will represent the ‘singulativizing’ morpheme as sg as in (267), which represents the derivation of Ojibwe mkwamiins-ag (‘pieces of ice, icicles’). sg in Ojibwe is realized by diminutive morphology, and pl as a plural suffix. (267) mikwam ‘ice’

mikwam ‘ice’

-iins sg

mikwam ‘ice’

-iins sg

-ag pl

In my view, English coffees hides similar structure, as in the simplified derivation in (268). Bare occurrences of coffee correspond to bare N heads. Before combining with pl, it must first combine with sg. English morphology, of course, fails to distinguish derivations like these from derivations which produce the plural form of a count noun like toys, although one way of thinking about the atomicity of count nouns is that they lexicalize along with something like sg.⁶ (268) coffee

coffee

sg

coffee

sg

pl

What of the semantics? I have assumed so far that count nouns are ‘born’ true of atomic entities—individual cups, saucers, pens, etc. The function that sg expresses, here, maps anti-atomic domains DP to atomic ones DP′ , such that each atom x in DP′ is constituted by some y in DP (i.e., x is ‘materially constituted’ by y; see Parsons 1979, Link 1983, among many others). The derived DP′ is, then, semantically parallel to the domain of a characteristically count noun: a set of atoms. Such domains can be mapped, or so I will assume, by the interpretation of the plural morpheme, to deliver a property of pluralities, each atomic part of which is in DP′ . ⁴ The singulative form means ‘a coin, bill’, and the plural form ‘coins, bills’. ⁵ The singulative form means ‘ice piece, icicle’, and the plural ‘ice pieces, icicles’. ⁶ See Kratzer 2005 in this connection; also Krifka 1992, Landman 1996, and Chierchia 1998a.

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As before (cf. Bach 1986a, Krifka 1989), I assume that the same representational power available for talk of individuals like cups and pluralities thereof is also available for talk of events like identifying a Picasso and pluralities thereof. As with nouns, verbs can be ‘born’ singular: for instance, where (a) cup applies to atomic entities—the individual cups—jump (once) applies to atomic events—the individual jumps. And, too, I assume that it is possible to ‘atomize’ in the verbal domain: the verb run can be born true of (atomless) activities, and stretches of these activities can be existentially quantified and, in turn, be said to ‘temporally constitute’ the sorts of atomic events satisfying predicates like run to the park. More concretely, I assume that verbs like run can act as the V heads in derivations like (268), as in the schematic (269). (269) run

run

sg

run

sg

pl

5.2.3 Representing pluralities Even if there is broad agreement about what the extensions of count nouns look like (i.e., sets of unordered, atomic entities) there is little agreement about those of plural nouns. There are at least three distinct approaches. Either cups denotes the powerset of the set denoted by cup, minus the empty set (Scha 1981; Hoeksema 1983; van der Does 1992, 1993; Schwarzschild 1996; Winter 2001, 2002), or ‘aggregates’ thereof (Gillon 1992; Bale & Barner 2009; cf. Bunt 1985); or, it involves the ‘individual sums’ of the relevant entities, where sums are the values returned by the two-place operator ⊔ or ⊕ (Link 1983; Krifka 1989; Landman 1989, 1996, 2000, among many others).⁷ Suppose then that cup has the denotation in (270). Assigning an interpretation to the plural noun delivers (271a) on the sets-based approach, (271b) on the aggregates-based approach, and (271c) on the sums-based approach. The difference between (271a) and (271c) is, for present purposes, primarily ontological: the individual sums are treated as complex entities of the same basic type as the individuals comprising them, whereas sets are of a distinct sort. The aggregates-based approach differs in that it assigns something closer to a partition rather than powerset structure.⁸ (270) JcupK = {a, b, c} (271) JcupsK = a. {{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}} b. {{a, b, c}, {ab, c}, {ac, b}, {bc, a}, {ac, ab}, {ab, bc}, {ac, bc}, {abc}} c. {a, b, c, a ⊔ b, a ⊔ c, b ⊔ c, a ⊔ b ⊔ c} ⁷ A different approach uses plural variables (Boolos 1984; Schein 1993; Pietroski 2005, among others; cf. Yi 2005, McKay 2006, Liebesman 2016). ⁸ That is, where ab represents an individual aggregate (a set or sum of individuals), an aggregation is “a set of aggregates with the requirement that their join yields the greatest aggregate . . . and [which] is minimal,” i.e., “no aggregate in the set is a proper sub-aggregate of any other aggregate in the set” (Gillon 1992:619). This recalls the notion of a cover on sets: covers are partitions not restricted to disjoint sets; i.e., a set X covers set Y iff X ⊆ P(Y) ∧ ∅ ∉ X ∧ ⋃ X = Y (Gillon 1992:617, fn.15), where P indicates powerset and ⋃ generalized union.

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Regardless of how the representational question resolves, there is a natural ordering on the satisfiers of plural expressions that we may neutrally refer to as the ‘plural partof ’ relation, and one that defines (at least) a join semi-lattice. On the sets theory, x is a plural part of y just in case x is a subset of y. On the aggregates theory, x is a plural part of y just in case every aggregate in x is an aggregate in y. On the individual sums theory, x is a plural part of y just in case every atom in x is an atom in y. Because of the relative equivalence between the theories on this point—how the domains of plural expressions are structured—it shouldn’t matter too much which one I adopt. For concreteness, I assume the individual sums theory, simply because it is the most widely utilized at present. All I hope to take on board with this assumption is the idea is that cup applies to whole, atomic objects (and so has a set of such entities as its extension), while its pluralized counterpart cups applies to any of the possible joins/sums of those objects—i.e., ‘pluralities’. Such an extension is ordered by the plural part-of relation, which has as its minimal parts the atomic entities in the extension of cup. Semantically, then, the role of -s is to map the ‘flat’ structure introduced by cup to an ordered set of pluralities ordered, effectively, by inclusion. These representational resources, again, extend to the verbal domain: a verb like jump, true of atomic events, can be mapped to a set of pluralities, each of which has atomic jumps as their minimal parts (cf. Ferreira 2005). The verbal analogue of the plural morpheme has, then, exactly the same semantic effect as the nominal plural morpheme, just in the domain of events. Such a morpheme appears to have overt correspondents in languages that show pluractional morphology (see Henderson 2012 for recent description and formalization).

5.3 Plur(action)al comparatives Comparatives targeting plural NPs or VPs involve, just like the other comparatives I’ve analyzed, a mapping to degrees by much. If so, then there must be an explanation for the distinction between much and many, as well as for two key semantic facts: (i) otherwise non-measurable predicates (i.e., relevantly singular count nouns and telic VPs) are measurable when plural-marked; and (ii) otherwise measurable predicates supporting dimensions δ permit only number comparisons when plural-marked. I will suggest that the distinction between much and many reflects a morphophonological quirk of English which has, unfortunately, served to mask a profound regularity in how measurement is expressed in the language: which measures are possible depends on what is measured, not on which expression introduces the measure. (i) and (ii), then, are explained by thinking about pluralities as forming a richer structure from the atomic parts that make them up, and by imposing an additional condition on the selection of values for μ. That is, ensuring (ii) in particular requires more than just Monotonicity. Apparent counterexamples to (ii) come from the so-called ‘mass plurals’ like suds. I discuss these and related cases in §5.3.5.

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5.3.1 The proposal First, how to understand the much/many alternation in English, (272)? (272) a. Al drank more/as much coffee. b. Al had more/as many ideas. I suggest that the distinction reflects a process of allomorphy, such that many is the morphophonological reflex of the combination much plus the nominal plural. That is, for present purposes, I assume any sufficient variant of a rule like that in (273). Any such sufficient variant will capture the fact that much sounds like many when there is an overt plural morpheme, but will ensure that the structural conditions for the rule produce, for example, many long underappreciated books but not *much long underappreciated books. (273) many formation much → many /

-spl

I will not spell out the morphophonological analysis in any detail,⁹ the crosslinguistic picture suggests the viability of the approach: in any language I’ve looked at, where English has much/many, other languages display a univocal form paired with (broadly) some marker of plurality; see Table 5.5.1⁰ Importantly, across these languages the interpretive pattern is the same as it is in English: the base form that corresponds to much involves interpretation by weight or volume with a noun like soup, while it involves interpretation by number with a noun like cookie(s). Meanwhile, the observation that comparatives targeting plural nouns must be compared by number (Hackl 2001, Bale & Barner 2009) is usually attributed to a distinct

Table 5.5 Much and many correspondents across languages. language

volume

number

mode

English Spanish Italian Macedonian Mandarin Bangla

much soup mucha sopa molta minestra mnogu supa henduo tang onek sup

many cookies muchas galletas molti biscotti mnogu kolaci henduo kuai quqi onek-gulo biskuT

suppletion agreement agreement plural noun classifier classifier

⁹ Dunbar & Wellwood’s 2016 updated morphosyntactic implementation of Bresnan’s 1973 analysis would be a good place to start. 1⁰ See Biswas 2012 for Bangla. The other data was received by personal communication: A. X. He for Mandarin, I. Stojanovska for Macedonian, F. Panzeri for Italian. See Doetjes (1997) for discussion of categorial underspecification of comparative morphemes across languages.

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primitive, many, which introduces a function from pluralities to their cardinality (Heim 1985, 2000, Bhatt & Pancheva 2004, Hackl 2001, 2009; cf. Higginbotham 1994, Doetjes 1997, and Chierchia 1998a).11, 12 Since I reject the idea that the surface form many reflects the existence of a lexical primitive distinct from much, my task is to explain how its semantics interacts with that of plural nouns to guarantee comparisons by number. Recall that (274a) with idea expresses no stable comparison at all, whereas (274b) with ideas expresses a comparison by number; and while (275a) with coffee can express a comparison by volume, (275b) with coffees can only express a comparison by number. (274) a. ∗ Sue has more idea than Al does. b. Sue has more ideas than Al does. (275) a. Al drank more coffee than Bill did. b. Al drank more coffees than Bill.

∗

number number

volume, ∗ number ∗ volume, number

Such data are compatible with a theory of degree introduction constrained by Monotonicity; as Schwarzschild (2006) noted already, the ordering on natural numbers will reflect an ordering by the plural part of relation. However, many other dimensions along which it is conceivable to measure a plurality will also satisfy Monotonicity, yet these dimensions are not observed for sentences like (274b) and (275b). In assuming the individual sums representational theory of pluralities (e.g., Link 1983), I have supposed that they are complex individuals of type e—and so, of the same type, at least, as their atomic parts. Yet, whereas cup has only atomic entities in its domain, cup has those atomic entities as well as all of the sums that can be formed from those atoms. The latter domain is structured by the plural-part of relation; more specifically, it has the structure of a join semi-lattice with atomic minimal parts. Thus, feeding the satisfiers of a plural predicate to A(μ) will ensure that S-monotonicity is calculated relative to the plural part-of relations that hold between elements of the relevant domain. This sort of structure—an ordering by a plural part-of relation—is derived not directly from the domain of a noun like coffee (in the case of (275)), but from the domain of a property derived from that noun. As before, coffee expresses a property of portions ordered by inclusion; to derive coffees, one first applies the covert singulative morpheme to get a property that is true of atomic entities each ‘constituted’ by some portion of coffee. Thus, coffees has in its domain pluralities of entities that bear such a constitution relation. Then, coffees is semantically just like toys, and so any restriction to number that applies to one will apply to both. Turning to the verbal domain, a comparative with a telic VP like (276) is read as a comparison between pluralities—in this case, that reading is true if Ann and

11 Exceptions include Schwarzschild 2006, Rett 2008, and Solt 2009, 2015, for whom much and many denote predicates of scalar intervals. 12 The text assumes only strict ‘cardinal’ readings are possible; I thus set aside the question of ‘proportional’ readings; see Barwise & Cooper 1981, Partee 1989, and Tanaka 2006, among others, for discussion.

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Bill continually resurrect, for example. Under normal circumstances—one death per person—the sentence is unnatural. Extending the nominal analogy, I suppose that verbs like die are ‘born’ singular, just like idea is; here, though, we have a quieter derivation of a plural predicate. Atelic VPs like run aren’t born singular, but the asymmetry in (277) can be explained on a par with more coffee/coffees. (276) Ann died more than Bill did. (277) a. Ann ran in the park more/as much. b. Ann ran to the park more/as much/as many times. Importantly, restrictions to number here don’t correlate utterly with surface many; the form that shows up in the adverbial equative is much, although many can show up if it is attended by the plural nominal times.

5.3.2 Mapping to degrees I have assumed that the extensions of terms like toys and jump-pl share two important properties with their mass NP and atelic VP correspondents. First, plural domains show a limited form of divisiveness. Given, for example, any plurality of toys X, there are proper subparts of X which are also toys (i.e., the atomic minimal parts, or any subplurality consisting only of some of those atoms); however, arbitrary subparts of the atoms of X aren’t necessarily toys. The set of atoms upon which the domain of plural toys is based, then, corresponds to the domain of toy, as in (278).13 (278) a. JtoyK = {x | x is an (atomic) toy } b. e.g., { t, t′ } Second, plural domains are cumulative. Given any two pluralities of toys X, X′ , their sum X ⊔ X′ is also a plurality of toys. And, some plurality of toys X corresponds to that plurality which is proper part of no other plurality of toys. Thus, we may model Dtoys as the set of pluralities of toys, ordered by the plural part of relation ≼toys ; i.e., it’s structure is definable as in (280). (279) Dtoys = a. JtoysK = {X | X is a plurality of toys } b. e.g., { T, T′ , T ⊔ T′ } (280) ≼toys = a. {⟨X, Y⟩ | X is as many toys as Y} b. {⟨X, Y⟩ | X is a toys subplurality of toys Y}

13 Here and below, to keep the distinctions between our relevant domains as maximally transparent as possible, I will use capital letters for variables that range over entities in plural domains.

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I suppose that ‘pluractional’ domains are no different. First, they show the same limited form of divisiveness: for any plurality of jumpings E, there is at least one subplurality (E itself) which is a plurality of jumpings, and there may more (i.e., any E′ which is part of E but which consists only of atomic jumpings). Yet arbitrary subparts of single jumping events aren’t in there. Thus I suppose that the set of atoms upon which the domain of jump-pl is based corresponds to the domain of jump, as in (281). (281) a. JjumpK = {e | e is an (atomic) jumping } b. e.g., { j, j′ } But pluractional domains are also cumulative. Given any two pluralities of jumpings E, E′ , their sum E ⊔ E′ is also a plurality of jumpings. And, some plurality of jumpings E corresponds to that plurality which is proper part of no other plurality of jumpings. Thus, we may model Djump-pl as the set of pluralities of jumpings, ordered by the plural part-of relation ≼jump-pl ; i.e., as a structure definable as in (283). (282) Djumpings = a. Jjump-plK = {E | E is a plurality of jumpings } b. e.g., { J, J′ , J ⊔ J′ } (283) ≼jumpings = a. {⟨E, E′ ⟩ | E is as many jumpings as E′ } b. {⟨E, E′ ⟩ | E is a subplurality of jumpings E′ } This chapter began with the observation that comparatives with plural and pluractional predicates can only invoke comparisons by number. So far, my semantics for much doesn’t guarantee this. To see this, first recall the definition of Monotonicity as in (284). (284) Monotonicity A measure function μ : Dη → Dδ is Monotonic if, for all v, v′ ∈ Dη , if v ≺η v′ then μ(v) δ) b. Je [more [[coffee sg] pl]]KA = 𝜖X(∀x(X(x) → ∃y(coffee(y) & x ⊳ y)) & A(μ)(X) > δ) For completeness, the interpretations of (290a) and (290b) are given in (297a) and (297b), glossing over, as usual, tense information etc. Here I have written the equivalent of Th(e) = x instead of Th(e)(x) as previously. Given the assumption that thematic relations are exhaustive and unique (i.e., that they are functions), this difference is just a convenient notational variant, which makes some space for the additional functional material at play in the interpretation of plural comparatives. (297) a. J(290a)KA = ∃e(Ag(e)(a) & sharing(e) & Th(e) = 𝜖X(∀x(X(x) → idea(x)) & A(μ)(X) > δ)) b. J(290b)KA = ∃e(Ag(e)(a) & drinking(e) & Th(e) = 𝜖X(∀x(X(x) → ∃y(coffee(y) & x ⊳ y)) & A(μ)(X) > δ))

5.3.4 Composition: plural telic We find verb phrases which are natural in the comparative and those which are not (at least, not under certain interpretations). And, we find verbs that, in some grammatical contexts, support comparisons along various dimensions, but which in others only support comparisons by number. For the first, telic VPs like hit Peter are only licit in the comparative if interpreted as describing a plurality of events, and the comparison then is understood in terms of number, (298a). For the second, VPs headed by run allow multiple dimensions for comparison except when they occur with some telicityinducing modifier like to the park, in which case they can be compared only by number, (298b). (298) a. Ann hit Peter more. b. Ann ran (to the store) more. I have proposed that number-restricted readings of verbal comparatives involve pluralized VPs. Many authors have posited the existence of something like a plural morpheme in the verbal domain (see especially Ferreira 2005; cf. Sternefeld 1998, Sauerland 1998, Beck 2000, Beck & Sauerland 2000). Like the nominal plural morpheme, its semantics requires composition with atomic VPs. I assume that verbs like hit are the verbal analogue of count nouns—they are lexically atomic, and so can combine directly with pl, (299a). A verb like run is the verbal analogue of a mass noun—it combines with a singular morpheme prior to composition with the plural (cf. Ferreira 2005), (299b). (299)

a. hit

pl

moreμ

b. run

sg

pl

moreμ

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As in the case of count nouns like idea, I encode ‘lexical’ atomicity as a domain restriction on the function lexically expressed by hit, (300a). Just as there is no such restriction on the domain of application for a mass noun like coffee, it is absent from that of run, (300b). (300) a. JhitKA = λev : Atom(e).hit(e) b. JrunKA = λev .run(e) Verb phrases can be rendered atomic compositionally by the addition of the (now type-generalized) singular morpheme, sg: (301a) can apply to an anti-atomic properties of individuals or eventualities. In the case of the eventualities, v ⊳ v′ should be read ‘v is temporally constituted by v′ ,’ as a straightforward analogue of the material constitution relation that holds between (say) substances and objects in nominal denotata. Similarly, the (type generalized) interpretation for pl is in (301b); given a property of atoms v, returns a property of pluralities whose minimal parts are the vs. (301) a. JsgKA = λV⟨η,t⟩ : Anti-at(P)λvη : Atom(v).∃v′ (P(v′ ) & v ⊳ v′ ) b. JplKA = λP⟨η,t⟩ : Atomic(P)λV⟨η,t⟩ .∀v(V(v) → P(v)) Given these pieces, the phrase hit (Peter) more expresses a property true of pluralities consisting of atomic events, each of which is a hitting (of Peter), and the measure of which is greater than δ—as usual, the interpretation of the than-clause, when present. In tandem, run (to the store) more expresses a property of pluralities of events, each atomic part of which is constituted by some running activity, and the measure of which is greater than δ. Given Invariance, the only licit value for μ given properties of pluralities is number. (302) a. J[hit pl] moreμ KA = λE⟨v,t⟩ .∀e(E(e) → hit(e)) & A(μ)(E) > δ b. J[[run sg] pl] moreμ KA = λE⟨v,t⟩ .∀e(E(e) → ∃e′ (run(e′ ) & e ⊳τ e′ )) & A(μ)(E) > δ For completeness, I provide the interpretations of the sentences in (298a) and (298b) as in (303); these expand the interpretations in (302) just by the addition of the Agent thematic relation, and existential closure. (303) a. JAnn ran (to the store) moreKA = ∃E(Ag(E)(a) & ∀e(E(e) → hit(e)) & A(μ)(E) > δ) b. JAnn hit Peter moreKA = ∃E(Ag(E)(a) & ∀e(E(e) → ∃e′ (run(e′ ) & e ⊳τ e′ )) & A(μ)(E) > δ)

5.3.5 On ‘mass plurals’ There is a class of potential counter-examples to the claim that plural NPs must be measured and compared by number. There are occurrences of expressions that appear

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morphosyntactically plural but don’t obey this restriction; for example the occurrence of the ‘mass plural’ suds in (304a), which is most naturally read as a comparison by volume. Furthermore, certain occurrences of NPs like mashed potatoes in (304b) support both a mass plural-type reading (i.e., comparison by volume) and the expected regular plural reading (i.e., comparison by number). (304) a. There are more suds in the sink than in the dishwasher. b. Sue ate more mashed potatoes than Bill did. Accounting for the properties of mass plurals is challenging. But it seems likely that whatever may be said about them, independently of the comparative context, could extend to an account of the apparent ambiguity of expressions like mashed potatoes. Thus, I will briefly consider the data on ‘lexical’ mass plurals (see McCawley 1975, Ojeda 2005, Acquaviva 2008), and point to one direction for their analysis (Schwarzschild 2012). Some examples of mass plurals are given in (305). (305) belongings, fumes, preparations, directions, brains, dregs, suds, droppings, guts, valuables, outskirts Such nouns show similarities and differences from regular plural NPs both syntactically and semantically. First, they occur with overt much instead of many. As many speakers that I have asked find such combinations odd (at least at first), I provide naturally-occurring examples in (306). Also unlike regular plurals, mass plurals are odd with number words and other canonical modifiers of NP, e.g., (307). (306) a. How much belongings can I bring?22 b. If one purposely sniffs gasoline or glue, or accidentally gets too much fumes while painting inside a closet, he can get damage to the lungs, brain, etc.23 c. Too much suds push the door outward.2⁴ d. On average five hens produce as much droppings as one medium-sized dog and unlike dogs, chicken and rabbit droppings can be easily composted.2⁵ (307) a. ?a sud, ∗ several fumes, ∗ many dregs b. ?How many preparations did you make for the party? c. ?He gave me too many directions to your house. Yet mass plurals trigger plural agreement on the verb (308), and they require the plural form when used demonstratively, (309b). (308) a. The suds were spilling out of the machine. b. ∗ The suds was spilling out of the machine. 22 23 2⁴ 2⁵

https://answers.yahoo.com/question/index?qid=20130310170420AAnE04Q https://healthtap.com/topics/can-breathing-in-gasoline-fumes-get-you-sick http://skp.samsungcsportal.com/integrated/popup/FaqDetailPopup3.jsp?cdsite=in\&seq=211364 http://wetaskiwintimes.com/2013/06/27/backyard-ag-an-actual-boost-to-city-says-reader

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(309) a. I can’t take these fumes. b. ∗ I can’t take this fumes. Nouns like dregs, fumes, suds, etc. seem rigid enough in their behavior to warrant classification as mass plurals, simpliciter. Solt (2008) notes, though, that expressions like mashed potatoes can function either as regular or mass plurals. For instance, some speakers allow such an expression to surface both with much and many, (310). Importantly for my purposes, though, these questions are read very differently: (310a) reads as a request for a response like 2 scoops, whereas (310b) calls for a response like two. (310) a. How much mashed potatoes do you want? b. How many mashed potatoes do you want? The semantic differences between mass and regular occurrences of NPs like mashed potatoes can be detected elsewhere. Suppose there are two people, Al and Sue, that together are the referent of they in (311a).2⁶ Given just this, the most natural reading of (311a) is paraphrasable as ‘there are two directions such that Al and Chris went in those respective directions’—the regular plural interpretation. But (311b) means, instead, ‘there are some directions that Chris gave me which differ from those someone else gave me’—the mass plural interpretation. (311) a. They went off in different directions. b. Chris gave me different directions. Such regular and mass plural occurrences differ in whether they license reciprocals like each other as well (Gillon 1992, Schwarzschild 2012). Normally, coordinated plural NPs license a reciprocal, (312a), just the same as a simple plural definite, (312b). Whether a reciprocal is licensed with a noun like directions depends on whether it surfaces as a regular or mass plural. On the ‘two sets of different directions’ reading, the reciprocal is licensed with the coordinated subject in (313a) but not with the definite plural subject (313b). Along with (311), this suggests that mass plural occurrences have a different semantics from regular plurals. (312) a. The boys and the girls contradicted each other. b. The kids contradicted each other. (313) a. Your directions and her directions contradicted each other. b. ∗ The directions contradicted each other. Schwarzschild (2012; following Acquaviva 2008) suggests that surface realizations of the plural morpheme mask a potential ambiguity between an ‘inner’ and an ‘outer’ plural projection. In the Distributed Morphology framework, the inner plural corresponds to the combination of a root nominal with a plural morpheme, prior to that root’s categorization as an N head. The outer plural corresponds to the combination of 2⁶ This is a modified example from Schwarzschild 2012.

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the plural morpheme after this categorization. Syntactically, then, the combination of root and plural projects a noun phrase (NP), while the combination of N and plural projects a number phrase (NumP). For present purposes, I will assume that some version of Schwarzschild’s analysis is correct. Telling a satisfying story that will explain the comparative facts in (304a) and (304b) must await further developments, however.2⁷ What I want, of course, is for more suds to involve measurement of stuff (rather than measurement of pluralities), while more mashed potatoes is ambiguous between a parse involving measurement of stuff, and the other involving measurement of pluralities.

5.4 Conclusion Comparatives that obligatorily invoke comparison by number aren’t a challenge to the idea that a single expression—much—introduces degrees. On the contrary, strengthening the conditions on its selection of measure functions μ can guarantee such restrictions on dimensionality: plural predicates, whether ultimately involving individuals or events, introduce new structures against which those conditions are calculated. And indeed, as we have seen, however we ultimately understand plural reference, it will have the introduction of such structure as a consequence. More than mere compatibility, the cases surveyed in this chapter are expected by the present theory. They represent paradigmatic instances of how grammar—rather than merely lexicon—can set the agenda for measurement and comparison. I assume that no one wants to attribute the dimensional differences between more coffee and more coffees to a difference in the lexical expression of measure functions. On a view where the selection of measure functions is always context-sensitive, the difference can simply be attributed to the semantic effects of the kinds of functional structures that embed the relevant noun. Thus, my theory expects grammatical effects on dimensionality to run rampant. Indeed, such effects are detectable even in the adjectival domain. In Chapter 6, I focus my attention on dimensional differences that I have observed between forms like more patient and patient more. Where ‘gradability’ is relevant for semantic description in the former case, the distinction between stage-level and individual-level properties (e.g., Carlson 1977b, Husband 2010) is relevant for the latter case. And indeed, patient more is interpreted very much like a verbal comparative. My theory can capture these facts directly, as I show, by assuming that the difference in word order tracks additional functional structure. In the end, then, sentences with postadjectival occurrences of more are, both structurally and semantically, very much like occurrences of more targeting telic VPs 2⁷ The most pressing question from the perspective of grammar is how the inner/outer plural distinction interacts with the many-formation rule. A simple solution to try out would involve triggering that rule based not on the presence of pl but on the presence of NumP. This sketch leaves the important semantic questions unanswered, however.

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headed by an atelic V (e.g., run to the park more). The difference, of course, is that run introduces a property of process, while patient introduces a property of states. And so again, the entities that I posit multiply, and this allows me to preserve my uniform semantics for comparatives intact. However, in Chapter 6 just as in the present one, there is independent evidence available to motivate the ontological proliferation that the theory requires.

6 Measuring occasions

Grammatical context can systematically affect which dimensions are available for a given comparative, both in the nominal and verbal domains. Comparisons by number become available with count NPs and telic VPs when pluralized, where no dimension was stably available otherwise; and number is obligatory for mass NPs and atelic VPs when pluralized, though dimensions were otherwise available. This chapter is about related patterns in the adjectival and adverbial domains. I focus on grammatical contexts in which comparisons by number become available for non-gradable adjectives, just when they are compatible with stage-level readings; in the same contexts, gradable adjectives support only number readings, while their characteristic ‘degree’ readings are excluded. This study thus shifts from the traditional focus on the interpretation of adjectives in comparatives like (314a) to that in comparatives like (314b). The important interpretive contrast is that whereas (314a) involves a comparison between degrees of happiness, (314b) compares numbers of occasions of being happy. I will suggest that (314b) involves a distinct syntactic derivation in which the complex spelled out by more appears in a higher structural position than that same complex in (314a). In my semantic analysis, (314a) involves measurement of states, as before, while (314b) involves measurement of pluralities of ‘occasions’ (cf. Mourelatos 1978), or events. (314) a. Ann was happier than Bill was. b. Ann was happy more than Bill was. The primary data I consider in order to reach this diagnosis comes from consideration of structures like (315), on the indicated parse.1 (315a) expresses that the number of occasions of Ann’s being happy for a two-day stretch exceeds the number of such occasions for Bill. In contrast, (315b) expresses that the number of occasions on which Ann was happy simpliciter exceeds the number of such occasions for Bill, and that these occasions (Ann’s and Bill’s) took place over two days. I will suggest that (315a) involves the for-phrase combining with a property of states prior to a mapping to events, and that (315b) involves combining the for-phrase with the derived eventive property.

1 A salient alternative reading of the string in (315a) bundles the for-phrase with the comparative. Such a parse would function well in response to the question: How long was Ann happy, compared to Bill?. This chapter is not about that parse. On the intended parse, (315a) would function well in response to the question, How many times was Ann happy for two days, compared to Bill? The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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(315) a. Ann was [happy for 2 days] [more than Bill was]. b. Ann was [happy more than Bill was] [for 2 days]. This ‘double-eventuality’ analysis is motivated primarily by how stage-level gradable adjectives interact with temporal for-phrases in two classes of comparatives, which I differentiate as ‘low’ versus ‘high’ attachment of the comparative morpheme (cf. Rothstein 1999). As I show, individual-level GAs are not compatible with the ‘high’ attachment structure. Low attachment comparatives (e.g., more available), express canonical degree readings while high attachment (e.g., available more) involve comparing numbers of occasions. The relation that binds states and occasions is, I suggest— now on a par with my analysis of variable telicity in the verbal domain—one of temporal constitution. Low attachment comparatives, then, involve comparison of states, and high involve comparison of (pluralities of) events. This analysis depends on the stative analysis of adjectives from Chapter 4, and the possibility of mapping properties of states to properties of atomic events, very much like mapping properties of processes to properties of atoms from Chapter 5. Properties of the latter type meet the definedness conditions for the verbal plural; its presence, by A-invariance, guarantees comparisons by number. This analysis has some consequences for alternations between adverbial and verbal comparatives, as I discuss near the conclusion of this chapter. In the end, I show how these data could be captured on a modified version of the lexical theory. While it is far from impossible for that theory to address these data, the message will be clear: such an analysis would require greater abstraction, and broader appeal to covert elements, than the alternative I propose.

6.1 The empirical landscape 6.1.1 ‘Low’ versus ‘high’ attachment What I call the ‘low’ attachment of the comparative is exemplified in (316)–(317). These sentences indicate comparison of two degrees of happiness/availableness and tallness/aliveness. Acceptability and interpretability in the ‘low’ comparative form for a given adjective typically serves to distinguish that adjective as gradable. Focus on sentences like these initially motivated the lexical theory that interprets gradable adjectives as measure functions (Chapter 2). (316) a. Ann was happier than Bill was. b. Ann was more available than Bill was. (317) a. Ann was taller than Bill was. b. Ann was more alive than Bill was. What I call instances of ‘high’ attachment are different: (318) express comparisons between numbers of occasions of being happy/available. Here, the acceptable and interpretable adjectives are those that naturally support stage-level as opposed to individual-level interpretation (i.e., S- versus I-level; see Carlson 1977b). The examples in (319) are odd because we prefer to interpret tall and alive as expressing ‘once-only’

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measuring occasions Table 6.1 Independent effects of I-/S-level and gradability on dimensionality. measure(s) category I-level S-level

gradable non-gradable gradable non-gradable

example

‘low’

‘high’

tall wooden drunk pregnant

height

∗

∗

∗

drunkenness

number number

∗

or ‘long-lasting’ properties. This clashes with the construction’s suggestion that the property can hold on multiple distinct occasions. (318) a. Ann was happy more than Bill was. b. Ann was available more than Bill was. (319) a. ?Ann was tall more than Bill was. b. ?Ann was alive more than Bill was. These two distinctions—gradable/non-gradable and S-/I-level—are independent (see Table 6.1). To see this, first consider the contrast in comparatives with more preversus post-posed with respect to the adjective. While (320a) with more pregnant is odd, (320b) is acceptable, and interpreted as a comparison of numbers of occasions of being pregnant. The oddity of (320a) suggests that pregnant is non-gradable, while the interpretation of (320b) suggests that it is S-level. (320) a. ?Al is more pregnant than Sue is. b. Al is pregnant more than Sue is. Now consider the case of tall. With more pre-posed, (321a) is perfectly fine, and expresses a comparison between the heights of two individuals. In contrast, (321b) is odd; it implies that Al regularly goes in and out of being tall, which isn’t normally true, whomever Al might be—we usually understand that if one is tall on Tuesday, one is tall on Wednesday, etc. Thus the adjective tall is gradable, and I-level. (321) a. Al is taller than Bill. b. ?Al is tall more than Bill is. With more pre-posed, non-gradable adjectives are odd, and the dimension for comparison varies with the adjective (Chapter 4). With more post-posed, I-level adjectives are odd, and S-level adjectives here lead uniformly to comparisons by number.2 All of the ‘high’ attachment comparatives show this pattern, regardless of the comparative form, e.g., (322)–(323). To draw out the relevant readings, these examples include a modifier phrase that should encourage a habitual reading, which will help 2 Some speakers report feeling unsure about this judgment. Although, as R. Schwarzschild (p.c.) points out, it could be that these speakers are getting a potentially distinct interpretation, one easily detected with phonologically ‘heavy’ phrases. For example, He’s (very) interested in Renaissance art, more than most first-graders are is most naturally read as grading levels of interestedness. Thus there may be a grammatical role for to hearing more postadjectivally, even while it carries a meaning like its preadjectival correspondent.

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allow one to read the relevant time window as containing multiple instances of the described occasions. Without this support, it seems easier interpret these examples in a different way that is, yet again, orthogonal to the matter at hand.3 (322) Last week, a. Al was drunk more than Bill was. b. Al was drunk as much as Bill was. (323) a. Al was drunk too much/many times. b. Al was drunk there enough to name a stool after her. c. Al was drunk the most of her friends.

comparative equative excessive assetive superlative

I propose to explain these data by deriving the S-level interpretations of adjectives as involving pluralities of events. Like Kratzer (1995), I will posit that S-level adjectival predications involve eventuality variables, but unlike Kratzer I will suppose the same thing for I-level adjectives (cf. Higginbotham 1985, McNally 1994). In both cases, the ‘base’ understanding for the adjective is of a property of states, from which a property of events can be derived. This process will be very much the derivation of coffee from coffees, or run to the park from run. The oddity of I-level adjectives, then, can be attributed to the fact that any given individual is usually paired only with one relevant such event, and comparatives despise singular interpretations.

6.1.2 Stages versus individuals S-level predications apply to states that (normally) hold temporarily, while I-level predications apply to those that (normally) hold for a lifetime. We can test for such predications, then, by combining different phrases that imply an individual goes in and out of the state. Consider the predicates be my favorite number (S-level) and be prime (I-level). Suppose that the truths of mathematics always hold, but my preferences can change from time to time. Meanwhile, the VP modifier last year suggests that whatever activity its VP describes that activity is not ongoing. This is fine when reporting my preferences about numbers, (324a), but odd when reporting a mathematical truth, (324b). (324) a. The number 2 was my favorite number last year. b. ?The number 2 was prime last year. Surveying more mundane cases, it is clear that we can’t ultimately restrict I-level properties to just those that hold for a lifetime, or even a temporal interval lasting almost as long. As Kratzer (1995) points out, having brown hair seems to pick out a

3 The intrusive reading I have in mind in this instance is that which attends a ‘metalinguistic’ comparative. I understand such readings to involve grading how well an entity fits to a category (see Chapter 7). This reading is likely more plausible with the adjective drunk because being a ‘good fit’ to the relevant category may have a lot to do with how often one drinks.

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quintessential I-level property, but if we used it to describe every second time Ann dyeed her hair, we would deploy an S-level version of the property. Thus what is important are the temporal properties of the states that the predicate is true of, as understood in a context—these cannot be fixed “once and for all” in the lexicon.⁴ Still, there are robust generalizations about how grammatical context interacts with S- versus I-level interpretation, which can be detected by first fixing on certain default understandings of the adjective. Suppose we think that American names a property that a given individual instantiates once and for all, while an adjective like happy names a property that (hopefully) one sometimes instantiates. Given these understandings, we see that use of American in the past tense leads to the (defeasible) implication that Ann is dead, (325a), but use of happy does not, (325b). This correlates with the interpretative pattern observed by adding temporally-bounding modifiers, (326). ? (325) a. Ann was American. ⇝ Ann is dead. b. Ann was happy. ⇝̸ Ann is dead. (326) a. ?Ann was American on Tuesday. b. Ann was happy on Tuesday. The two types of adjectives show further contrasts. One of the earliest observations about the distinction (Milsark 1974) is that S-level predicates are natural in thereexistentials, unlike I-level predicates, (327). This grammatical context, whatever the ultimate explanation for why it imposes the interpretive restrictions that it does, implies an episodic or bounded timeframe during which the people or the doors are in a particular state that they likely aren’t in any longer. Such a reading is artificial when talking about being tall, (327c), or made of wood, (327d). (327) a. b. c. d.

There were people drunk. There were doors open. ?There were people tall. ?There were doors wooden.

Consider their embedding in the complement position of perception verbs like see (Carlson 1977b). The most natural understanding of the sentences in (328a)–(328b) is that Ann saw Bill or the firemen while they were in particular states, and that these are ones that they need not normally be in (S-level). Whenever it can be expected, though, that one sees Bill or the firemen in a state that they can reasonably be expected to be in all the time (I-level), the result is odd, (328c)–(328d). (328) a. b. c. d.

Al saw Bill drunk/healthy. Al saw the firemen happy. ?Al saw Bill tall/male. ?Al saw the firemen altruistic.

⁴ It is worth pointing out that similar observations could be made, and so something very similar could of course be said, for the gradable/non-gradable, mass/count, and telic/atelic distinctions.

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Finally, S-level predicates can induce an existential interpretation of bare plural subjects in the present tense, (329a), whereas I-level predicates only allow for generic interpretations of their subjects in the present tense ((329b); Carlson 1977b). Related contrasts can be observed with depictive predicates (Rapoport 1991, McNally 1994), post-nominal modification (Bolinger 1967, Larson 1998), embedding under perfect aspect (Martin 2015), etc.⁵ (329) a. Firemen are available. b. Firemen are altruistic.

∃, gen ∗∃, gen

Carlson (1977a) characterizes the S-/I-level distinction ontologically: I-level predicates express properties of individuals, while S-level predicates express properties of stages or temporal slices of individuals. Such an account will get in the way of a fully general account of the semantics of the comparative I am developing, and so I will not consider it in detail here. However, my own treatment depends on features of the ontology as well, except that I understand the adjective to, at root, express a property of states, and I- vs S-level predicates to express properties of events. I’ll suggest, next, that there are other reasons to prefer the neodavidsonian treatment, too.

6.1.3 Interaction with for-phrases We will get a feel for the demands of the ‘high’ comparative by considering its interpretation with differently-positioned temporal modifiers like for x time. First, observe that the syntactic position of such modifiers matters little for the interpretation of the ‘low’ comparative: that is, both (330a) and (330b) seem merely to express that Ann’s degree of availableness exceeded Bill’s over the course of two days. (Deriving the surface differences between the strings will depend on the syntax of than-clauses and ellipsis; see Bresnan 1973; Bhatt & Pancheva 2004; Lechner 2004; Alrenga et al. 2012; Larson & Wellwood 2015, among others.) (330) a. Ann was more available than Bill was for 2 days. b. Ann was more available for 2 days than Bill was. I will use the examples in (331) to show the effects of such modification on the ‘high’ attachment comparative, with the intended parses indicated. (331) a. Ann was [available more than Bill was] for 2 days. b. Ann was [available for 2 days] more than Bill was. First, consider the situation depicted in Figure 6.1. Here, Ann and Bill are counselors whose Monday and Tuesday schedules are divided into one-hour slots. Out of a total of 14 one-hour slots each, Ann has 5 filled, while Bill has 12 filled. This situation can be described truthfully using the sentences in (332). The sentence with the for-phrase ⁵ See Husband 2010, 2012 for a recent, more comprehensive review.

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measuring occasions Ann’s schedule

Bill’s schedule

Mo

Mo

Tu

Tu XXXX XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

XXXX

Figure 6.1 The counselors’ schedules on Monday and Tuesday. ‘XXXX’ indicates unavailability. Ann’s schedule Mo

Tu We

Th Fr

Bill’s schedule Sa

Mo

Tu We

Th Fr

Sa

XXXX

Figure 6.2 The contractors’ schedules last week. ‘XXXX’ indicates unavailability.

at the end of the sentence in (331a) accurately describes this state of affairs, and in fact follows as a natural inference from the conjunction of (332a) and (332b). (332) a. Ann was available for nine hours over Monday and Tuesday. b. Bill was available for two hours over Monday and Tuesday. In contrast, (331b) does not describe this situation.⁶ For one thing, knowing nothing more about Ann’s and Bill’s schedules, there is no period of time during which either Ann or Bill are ‘available for two days’. If we suppose that the rest of their schedules are booked, (331b) is false in this context. I illustrate the reverse—a case where (331b) succeeds where (331a) does not—using the situation depicted in Figure 6.2. Here, Ann and Bill are contractors who divide their six-day workweeks into two-day chunks. Last week, out of three possible twoday periods, 0/3 of Ann’s were booked, while 1/3 of Bill’s were. This situation can be summarized by the two sentences in (333). (331b) describes just this situation, and in fact follows as a natural inference from (333). (333) a. Ann was available for two days, three times. b. Bill was available for two days, twice.

⁶ Applying a certain parenthetical intonation to the string in (331b) makes it seem like it could, e.g., Ann was available (for two days) more than Bill was. This feels like a different parse, perhaps one indicating extraposition of the than-clause over the (higher) for-phrase.

6.2 states and their occasions Ann’s schedule Mo

Tu We

XXXX

Th Fr

119

Bill’s schedule Sa

Mo

Tu We

Th Fr

XXXX

Sa

XXXX

Figure 6.3 Non-equivalence. ‘XXXX’ indicates unavailability.

(331a) isn’t exactly false here, but when it is true it describes something different than (331b) does. That is, where (331b) captures the entire six-day period, (331a) requires narrowing our focus to two-membered subsets of Ann’s and Bill’s twoday chunks—for example, (331a) would be true given just Wednesday through Saturday. The sentences in (331a) and (331b) come apart truth-conditionally in the context depicted in Figure 6.3. Here again Ann and Bill are contractors, dividing their six-day workweeks into two-day chunks. Of three possible such divisions, Ann is available for one and Bill is available for two. (331b) is false, here, since one is not greater than two. But (331a) can be true, since Ann is fully available Friday/Saturday, but Bill isn’t—the number of occasions of Ann’s being available within that period has to be greater.

6.2 States and their occasions 6.2.1 A brief look at ‘low’ comparatives Temporal for-phrases are straightforwardly interpretable given an event semantic framework. Events and states and so on are temporal entities, and, intuitively, forphrases just specify how long the event takes or how long the state holds. Thus, in the simplified (334), τ is a function that maps an eventuality e to its ‘runtime’, and 2 days specifies its length (cf. Link 1987, Larson 2003, Rothstein 2004, Champollion 2010). (334) Jfor two daysK = λev .τ(e) = 2 days

⟨v, t⟩

This simplified presentation ignores, of course, facts discussed in detail by Rothstein (2004) and others, in particular those suggesting that for-phrases themselves impose semantic restrictions. That is, they are comfortable combining with stative, (335a), activity, (335b), and semelfactive VPs, (335c), but they are less comfortable combining with relevantly singular event predicates, (336). Such data minimally suggest that forphrases are semantically restricted very much like comparatives are; however, I will set consideration of these details aside for the moment. (335) a. Ann loved Bill for five years. b. Ann ran for two hours. c. Ann sneezed for five minutes. (336) ?Ann died for ten minutes. In general, though, it appears that for-phrases are eventuality modifiers, suggesting that the minimal interpretation given in (334) is appropriate. With just this much,

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we can get the semantics right for the ‘low’ attachment comparative given their states-based analysis in Chapter 4.⁷ I assume that the position of the than-clause itself has little semantic consequence (cf. Bresnan 1973, Bhatt & Pancheva 2004). Consider (337). (337) a. Ann was more available for two days than Bill was. b. Ann was more available than Bill was for two days. I assume that the essential structural properties of (337) for present purposes are as in (338). In (338a), the structure I assume to underlie (337a), the for-phrase merges low with the adjectival complex, prior to extraposition of the than-clause (Bresnan 1973), which I’ve indicated by coindexing that phrase and its trace. In (338b), the structure underlying (337b), the for-phrase merges higher than the extraposition site of the thanclause. (338) a. thanPi moreμ available ti

for two days

b.

thanP

for two days

moreμ available Deriving the equivalence in meaning between (337a) and (337b) is straightforward given these assumptions. The adjective available, interpreted as a property of states in type ⟨v, t⟩ (339), composes with the for-phrase and comparative morphology to deliver the same interpretation for (337), despite their syntactic differences: (340) reads, ‘Ann is in an availableness state s whose measure A(μ) exceeds δ, and s lasted for two days’, where δ abbreviates the degree introduced by the than-clause as before. (339) JavailableKA = λsv .available(s)

⟨v, t⟩

(340) ∃s(Ho(s)(a) & available(s) & A(μ)(s) > δ & τ(s) = 2 days) The challenge of for-phrases arises in the ‘high’ attachment comparative. Given just the pieces on the table so far, we would not expect that the alternation between more available and available more would show any difference in meaning. Yet the latter invites comparison by number, where the former doesn’t. Luckily, there is evidence that different aspects of the adjective’s interpretation are relevant in the latter case. The adjectives that are comfortable here behave, in many cases, as though they express properties true of occasions on which a certain state holds. ⁷ The analysis of the ‘low’ comparative data with for-phrases does not depend on my compositional theory; things will work out on the lexical theory, too, so long as that theory incorporates eventualities into its adjectival interpretations. See Wellwood (2016) for discussion, also §6.3.4.

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6.2.2 Introducing occasions A sentence like Ann was happy three times reads as an indication that there were three occasions on which Ann was happy. But what are ‘occasions’? The simplest thing to think is that they are events. More will have to be said, of course; it isn’t obvious that, whichever events these are, they are labeled by specific lexical items, like those that jump or die predicate of. However, plenty of evidence shows that S-level adjectives pattern like eventive predicates in general, supporting the simple hypothesis.⁸ Number-based interpretations are generally suggestive of domains with discrete, or atomic entities (Chapter 5). Stative predicates are not thought to be atomic; unlike eventive predicates, they don’t predicate of discrete entities (see Rothstein 1999 for extensive discussion). If a stative description is true of a given interval of time, then it is true at every moment of that interval; eventive descriptions, even if true of a given temporal interval, usually don’t describe events that occur at every moment of that interval. This difference is most easily brought out using relevant nominalizations: a discourse like (341a) with stative happiness can easily be both felicitous and true, but that in (341b) with eventive jumping is odd. (341) a. Ann’s happiness lasted an hour; you couldn’t identify a moment within that hour when she wasn’t happy. b. ?Ann’s jumping lasted an hour; you couldn’t identify a moment within that hour when she didn’t jump. Nominalizations like happiness thus seem to target the root, stative meaning of their adjectival counterpart (cp. Francez & Koontz-Garboden 2015). Bolstering this idea, consider the following paradigm. Eventive nominalizations targeted by cardinal number words directly indicate how many events of the relevant sort occurred, (342a). Such targeting with happiness, in contrast, does not involve counting occasions, but instead distinct sources for states of the relevant sort, (342b) (see Gillon 1999). An alternative nominalization, as in (342c), can get the occasion-counting reading, but this case is supported by the adverbial modifier three times. (342) a. Ann’s three jumps were awesome. b. Her three happinesses are a dog, a hammock, and a boat. c. Ann’s being happy three times last week surprised me. Adverbials like three times have been analyzed as eventive modifiers. For example, Rothstein (1995) analyzes every time in (343a) as introducing a matching relation between calling and jumping events. If we can quantify over events with S-level adjectives, then (343b) can be analyzed as involving a matching relation between calling events and occasions of being happy. Events are discrete; they start and end. If it isn’t natural to think of a certain sort of state as one which sometimes holds and ⁸ Husband 2010, considering a complementary set of data, distinguishes S-level adjectives as predicates of ‘quantized’ states (cf. Krifka 1989), which are formally analogous to what I have been calling atomic events. Collapsing the stative and ‘event-y’ properties of S-level adjectives renders certain other facts mysterious; for example, the felicity and interpretability of (341a), below.

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sometimes doesn’t, then the requirement of every time for (discrete, distinct) events can help explain the oddity of I-level adjectives in such contexts, (343c).⁹ (343) a. Every time Bill called, Ann jumped. b. Every time Bill called, Ann was happy. c. ?Every time Bill called, Ann was intelligent. The same pattern can be observed with when-modifiers (Kratzer 1989 and McNally 1994). The interpretation of (344a) doesn’t differ all that much from that of the good examples in (343): (344a) says that for each event of Ann playing the piano, there is a (temporally-coincident; McNally 1994) event of her singing a song. The same understanding can apply to (344b), if be happy is somehow about events, and we can see (344c) as odd because it implies that someone can quickly and easily slip in and out of being intelligent (cf. Condoravdi 1992). (344) a. When Ann plays the piano, she sings a song. b. When Ann plays the piano, she is happy. c. ?When Ann plays the piano, she is intelligent. Events give us the sort of anchors in time required by certain discourse-sensitive expressions, too. Glasbey (1993) observes an interesting pattern of interpretation for the modifier then illustrating just this point. When a sentence with initial then occurs following an uncontroversial eventive description as in (345a), it is understood to put two non-overlapping events in temporal sequence. The same type of interpretation is natural with S-level adjectives like happy, e.g., (345b), but not so for I-level adjectives like intelligent, e.g., (345c). (345) a. Ann jumped. Then Bill died. b. Ann was happy. Then Bill liked her. c. ?Ann was intelligent. Then Bill liked her.

6.3 ‘High’ adjectival comparatives I propose that the stative properties introduced by adjectives can be mapped to properties of (atomic) events in the syntax. The derived predicate can then be pluralized like any other eventive predicate. Where the ‘low’ comparatives receive the familiar interpretation comparisons between measures of states—the ‘high’ comparatives are interpreted just like plural verbal comparatives—as comparisons between numbers of events. One benefit of syntactically incorporating the elements that derive a plural eventive property from a stative property is the direct account it supports for the interactions between ‘high’ comparatives and temporal for-phrases. As we will see, the for-phrase can specify how long a state holds versus the time it takes for a plurality of events to occur, depending only on its structural position. ⁹ Although, I-level adjectives shouldn’t be so bad if the ‘occasion’ lasts a lifetime. For instance, if Ann continually reincarnates, then it is perhaps fine and maybe true that Every time Ann is reborn, she is intelligent (again).

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6.3.1 The proposal I posit that states can be ‘wrapped’ into events; just like a coffee is constituted by coffee, and a run to the store is constituted by running, an occasion of Ann’s being happy is constituted by Ann’s happiness during that time. I assume that the mapping from states to (atomic) events can be accomplished with little comment by the singular morpheme, sg, presented in Chapter 5.1⁰ The derived property can, in turn, be modified by the same plural morpheme, pl. The interpretation of sg is neutral between the basic types e and v. If we should furthermore understand v as including both processes (e.g., the lexical satisfiers of run; Chapter 3) and states (e.g., the lexical satisfiers of happy; Chapter 4), then sg can be recycled to accomplish the state to event mapping I need. This assumes, of course, that stative domains are anti-atomic, which, on balance, seems right (Rothstein 1999). (346) JsgKA = λP⟨η,t⟩ : Anti-at(P)λvη : Atom(v).∃v′ (P(v′ ) & v ⊳ v′ ) As with the shift from talk of running to talk of running in the park, I use the temporal constitution relation, ⊳τ , from Chapter 5. In this case, though, events e will be temporally constituted by states s rather than processes. I assume that, if e is so constituted by s, then e wholly coincides temporally with s—i.e., e starts the moment s holds, and e ends the moment s no longer holds (cf. the related notion of abutment in Kamp & Reyle 1993, p. 573; D. Altshuler p.c.). Thus, if there is a plurality of events which has such es as parts, this implies that the relevant ss are transitory. State to event mappings have been proposed elsewhere. Kratzer (2000) (cf. Parsons 1990; Piñón 1999; von Stechow 2002) notes that sentences with aufpumpen (‘pump up’) in German are eventive, but their combination with für-phrases reveals a stative layer: (347a) isn’t about how long it took to inflate the tires, only about how long that inflation will last; meanwhile, (347b) is ungrammatical, because begrüssen (‘greet’) doesn’t provide the states required by the für-phrase. Kratzer captures the dual nature of verbs like (347a) by lexical assignment of both a state and event argument, revealed as needed by a covert ‘eventizer’ or ‘stativizer’. (347) a. Wir werden das Boot für ein paar Stunden aufpumpen. we will the boat for a few hours up-pump ‘We will pump up the boat for a few hours.’ implies: the tires will remain inflated for a few hours b. ∗ Du kannst die Gäste für eine Stunde begrüssen. You can the guests for an hour greet ‘You can greet the guests for an hour.’ Derivational details aside, Kratzer analyzes das Boot aufpumpen as in (348). Depending on whether such a phrase combines with the stativizer or the eventizer (operations 1⁰ Wellwood 2014 posited a morpheme called ev to do this work, and Rothstein 1999 assigns a similar interpretation to the copular verb. Rothstein was responding primarily to interpretive differences between sentences like Ann made Bill happy and Ann made Bill be happy, which I do not address here.

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which can target either the state argument or the event argument), one or the other of these variables will be exposed for further modification, and the other existentially closed. My proposal differs from Kratzer in that, first, I assume adjectives are ‘born’ merely stative, though syntax can relate them to eventive predicates; and second, the relation between my states and events is one of constitution, rather than causation. (348) Jdas Boot aufpumpenK = λsλe.pump(e) & Event(e) & inflated(b)(s) & Cause(s)(e) Here, then, is how I characterize the gradability and S-/I-level distinctions. Consider Ann, who is in many different sorts of states at any given time, some of which she could have instantiated to a greater or lesser extent. If an adjective A picks out one of the variety that can show differences in extent, then A gradable (in my terms, measurable). But Ann can also be in different states at different times: some she regularly transitions in and out of, like being drunk; and some she doesn’t, like being American. Thus we can easily quantify the occasions on which she instantiates certain states (S-level) but not others (I-level).

6.3.2 Composition: eventized statives Given the hypotheses linking stative properties to eventive properties to plural properties, it is straightforward to derive the truth-conditional interactions between the ‘high’ comparative form and temporal for-phrases. I first illustrate the interpretation of this type of comparative without temporal modification. For the base case in (349a), I assume the structure in (349b). Ann combines low, in order to ensure that Ann bears the Holder relation, rather than whatever relation she would bear to the events introduced by sg. (On balance, this seems right, given no evidence for a difference in thematic assignment between the low and high comparatives, and the usual assumption that entities play different kinds of roles in states and events). Combining this core adjectival complex, then, creates the necessary pre-conditions for combination with pl. (349) a. Ann was available more than Bill was. b. DegP pl sg Ann available

moreμ thanP

Attaching DegP after pluralization supports the number-based interpretation of the ‘high’ comparative. To simplify the presentation of any derivational details, here and below I will abbreviate the interpretation of available as avail, the than-clause degree as δ, and eliminate reference to the assignment function A (and so μ should be read as shorthand for A(μ)). Thus, where the phrase headed by available is interpreted as

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in (350a), the phrase that combines with DegP is interpreted as in (350c), by way of (350b): (350c) is a property of pluralities of events (i.e., ‘occasions’), each atomic part of which is temporally constituted by a state of being available. (350) a. JAnn[θHo ] availableK = λsv .Ho(s)(a) & avail(s) b. J(350a) sgK ⇝ λev : Atom(e).∃s(Ho(s)(a) & avail(s) & e ⊳ s) c. J(350b) plK ⇝ λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & e ⊳ s)) (351) λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & e ⊳ s)) & μ(E) > δ (349a), then, is interpreted as in (352): ‘there is a plurality of events E, each atomic part of which is temporally constituted by a state of Ann’s being available, such that the measure of E is greater than δ.’ Since (349a) involves measurement of pluralities, the dimension for comparison will be number (Chapter 5). But for there to be such a plurality, of course, it must be that Ann has an associated interpolated period of being available and of not being available; those periods in which she was available correspond to the states that constitute the atoms of E. (352) ∃E∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & e ⊳ s)) & μ(E) > δ) Assuming this basic interpretive template for the ‘high’ comparative, incorporating the effects of for-phrase modification is straightforward. Recall that when this phrase appears between the adjective and more as in (353a) it indicates how long a state of being available lasted, and the comparative as a whole expresses that Ann instantiated more of such states than Bill did. To derive this interpretation, I assume that the for-phrase modifies the adjectival complex before the other pieces, as in (353b). (353) a. Ann was [available for two days] more than Bill was. b. DegP pl sg Ann available

moreμ thanP

for 2 days

Semantically, the composition of the for-phrase with the adjectival complex is the same as in the ‘low’ comparative; this is repeated in (354a). Combining that property with sg and pl delivers, as before, the property of pluralities E in (354b); any satisfier of this predicate has, as atomic parts, events that are temporally constituted by states of availability lasting two hours. Adding the comparative phrase, then, simply adds that the measure of Ann’s such E is greater δ, (354c).

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(354) a. J[Ann[θHo ] available] for 2 daysK = λsv .Ho(s)(a) & avail(s) & τ(s) = 2 days b. J(354a) sg plK ⇝ λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & τ(s) = 2 days)) c. J(354b) DegPK ⇝ λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & τ(s) = 2 days)) & μ(E) > δ The second of the target cases to be accounted for is repeated in (355a). Recall that the interpretive difference between this sentence and (349a) is that, here, we understand our attention to be confined to some two day period, during which we should find more occasions of Ann being available than of Bill being available. To derive this interpretation, I simply assume that the for-phrase occurs syntactically higher than the comparative complex, as illustrated in (355b). (355) a. Ann was available more than Bill was for two days. b.

for 2 days Ann available sg pl

moreμ thanP

This simple structural difference has as a semantic consequence that the for-phrase composes with a property of pluralities rather than with a property of states. The interpretation of the left branch of (355b), then, is as in (356a); a property of pluralities of events E, with each atomic part constituted by a state of Ann’s being available, such that the measure of E is greater than δ. Adding the interpretation of the for-phrase as in (356b) simply adds that the relevant Es took place over a period of two days. (356) a. J[Ann[θHo ] available sg pl] more thanPK = λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & e ⊳ s)) & μ(E) > δ b. J(356a) for 2 daysK ⇝ λE⟨v,t⟩ .∀e(E(e) → ∃s(Ho(s)(a) & avail(s) & e ⊳ s)) & μ(E) > δ & τ(E) = 2 days Compositionally, this analysis is quite simple, and it depends on structural assumptions that adhere well to the surface syntax of the target sentences. Their truthconditional differences depend on whether the for-phrase has combined directly with the adjectival complex, thereby specifying how long the relevant states hold, or whether it has combined after the comparative morphology, thereby specifying the period over which the relevant events took place. These ontological differences are important for

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how my theory fixes dimensionality in comparatives; what I have just shown is that assuming a rich interchange between grammar and ontology makes easy work of otherwise perplexing data. That is, the analysis is a lot less straightforward on an account that starts with the lexical theory. I will demonstrate this after first showing how the flexibility of my compositional theory extends to related cases in the adverbial domain.

6.3.3 Consequences for adverbs Semanticists working in the davidsonian tradition often start with the assumption that adverbial modifiers express simple properties of events. However, we can observe similar interactions between the syntactic position of an adverbial and the dimensional interpretation of a comparative as I have observed in the adjectival domain. My theory extends to these cases directly, if we assume that the adverbials have a richer internal semantics than that usually assumed. In particular, I will suggest that they, too, involve relations between states and events (cf. Higginbotham 2008). Consider (357) with the adverb quickly. (357a) and (357b) differ in whether more precedes or follows the adverbial, and this difference corresponds with a sharp distinction in meaning. (357a) expresses a comparison based on speed, and cannot be as a comparison of numbers of events. In contrast, (357b) cannot be read in terms of speed, but it can be read as a comparison by number, distance, or duration. I’ll focus on the number-based reading for a moment, as this helps to establish the desired parallel with the adjectival just discussed; the analysis I will sketch supports all three dimensional interpretations for (357b). (357) a. Al ran more quickly than Bill did. b. Al ran quickly more than Bill did.

speed, ∗ number ∗ speed, number

If we simply assumed the lexical theory’s approach to gradable adverbs, then the speed-based reading of (357a) would be attributed to the measure function expressed by that adverb, and the number-based reading of (357a) would be attributed to a covert much or many. But such data are initially challenging for my approach, where only much introduces degrees. That is, if I assumed that quickly and run express simple properties of the same sorts of entity, as in (358a)–(358c), then my theory would incorrectly predict (357a) and (357b) to be semantically equivalent. (358) a. JrunK = λev .run(e) b. JquicklyK = λev .quickly(e) c. Jrun quicklyK = λev .run(e) & quickly(e) More specifically, assuming (358) would lead my theory to assign both (357a) and (357b) the interpretation in (359).11 Measure functions, on my theory, are selected

11 Here and below, I continue to abbreviate A(μ) as μ, and the than-clause interpretation as the degree δ.

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based on the sort of entity provided as input to the measure variable, and the ordering (if any) on those entities. If run and quickly are true of one and the same entities, there should be no interesting differences in that selection attending the word order difference—both (357a) and (357b) would simple involve measurement of some (quick) running. (359) Jrun more quicklyK = Jrun quickly moreK = λev .run(e) & quickly(e) & μ(e) > δ I have some options for distinguishing (357a) and (357b), however, all of which involve positing (at least) a stative and eventive layer. In brief, this can be accomplished in one of three ways: (i) decompose quickly into two pieces, wherein (e.g.) quick expresses a stative property and -ly expresses a mapping from that stative property to an eventive one; (ii) assume that quickly is ‘born’ a property of states, which is mapped to a property of events by something like sg; or (iii) assume that quickly is stative, and becomes eventive via thematic marking. The third option is directly analogous to my analysis of hot coffee in Chapter 4 wherein hot introduces states and is mapped thematically to a property of individuals. I will thus assume (iii), and posit three relevant structures. Underlying (357a) is (360), in which the DegP combines directly with quickly prior to thematic interpretation. In contrast, (357b) involves combining quickly with the verb phrase headed by run directly, but is otherwise structurally ambiguous: in (361a), the DegP combines directly with that VP, and in (361b) it combines with that VP only after it has been further modified by sg and pl.12 (360)

VP run

AdvPθ quickly moreμ thanP

(361) a. run quicklyθ

moreμ thanP

b. pl sg

moreμ thanP

run quicklyθ And so: quickly is interpreted as the property in (362a). In a non-comparative sentence like Ann ran quickly, the adverbial is thematically interpreted as a property 12 I have assumed that the relevant second structure, (361b), interprets quickly lower than sg and pl. I make this assumption since it is not clear to me, for example, what quickly(E) would mean.

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of eventualities that instantiate some state of being quick, i.e., (362b). Combining this derived property with run, the result is as in (362c). (362) a. JquicklyK = λsv .quickly(s) b. Jquicklyθ K = λev .∃s(quickly(s) & θ(e)(s)) c. Jrun quicklyθ K = λev .run(e) & ∃s(quick(s) & θ(e)(s)) In the comparative context, interpreting (360) involves composing the interpretation of more with a property of states, and so the value of μ will be selected in accord with the measures of such states; the result of this composition is as in (363a). Interpreting the thematic marking on this complex adverbial delivers a property of eventualities, each of which instantiates a state of being quick that measures greater than δ, (363b). Finally, composition with the verb phrase headed by run goes as should be expected, (363c), and the net result for (357a) is the interpretation in (364). (363) a. JAdvPK = λsv .quick(s) & μ(s) > δ b. JAdvPθ K = λev .∃s(quick(s) & μ(s) > δ & θ(e)(s)) c. JVPK = λev .run(e) & ∃s(quick(s) & μ(s) > δ & θ(e)(s)) (364) JAnn ran more quickly than Bill didK = ∃e(Ag(e)(a) & run(e) & ∃s(quick(s) & θ(e)(s) & μ(s) > δ)) On my analysis, (361a) involves the measurement of running activity (which instantiates quickness etc.), where (361b) involves the measurement of pluralities of events (which bear certain relations to running activity, etc.). I should like to say that the interpretation of the subject is low, parallel to what I previously assumed for adjectival predications that are subsequently mapped to derived properties in the syntax. To keep things simple for now, I will compose the subject high, and interpret its referent as bearing the Agent relation to a plurality of events.13 The important pieces of the semantics I give for the parse of (357b) in (361a), then, are presented in (365)–(366). This structure is interpreted, then, as saying that some quick running by Ann out-measures that of Bill. Since running activity is measured, μ can resolve in this case to distance or duration—this is the right result. (365) a. Jrun quicklyθ K = λe.run(e) & ∃s(quick(s) & θ(e)(s)) b. J[run quicklyθ ] [more thanP]K = λe.run(e) & ∃s(quick(s) & θ(e)(s)) & μ(e) > δ (366) JAnn ran quickly more than Bill didK = ∃e(Ag(e)(a) & ∃e(run(e) & ∃s(quick(s) & θ(e)(s)) & μ(e) > δ)) 13 It seems likely that, if an individual x is the agent of a plurality of events E, then x is the agent of each atomic part of E. I suspect, though, that matters might get complicated once different types of subjects are considered. Nothing will go wrong by undoing the simplification in the text, and interpreting the subject closer to run.

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Meanwhile, the important semantic pieces of the parse represented by (361b) are given in (367)–(368). This structure expresses that Ann was Agent of a plurality of events, each atomic part of which is constituted by some quick running. As before, the measurement of pluralities will proceed comparison by number—this, too, is the right result. (367) a. J[run quicklyθ ] sgK = λe′v : Atom(e′ ). ∃e(run(e) & ∃s(quick(s) & θ(e)(s)) & e′ ⊳ e) b. J[run quicklyθ sg] plK = λE⟨v,t⟩ .∀e′ (E(e′ ) → ∃e(run(e) & ∃s(quick(s) & θ(e)(s)) & e′ ⊳ e) c. J[[run quicklyθ sg] pl] [more thanP]K = λE⟨v,t⟩ .∀e′ (E(e′ ) → ∃e(run(e) & ∃s(. . . θ(e)(s) . . .) & e′ ⊳ e) & μ(E) > δ (368) JAnn ran quickly (pl) more than Bill didK = ∃E(Ag(E)(a) & ∀e′ (E(e′ ) → ∃e(run(e) & ∃s(. . . θ(e)(s) . . .) & e′ ⊳ e) & μ(E) > δ)) This sketch makes assumptions that should, of course, be subject to further empirical scrutiny. To the extent that the sketch helps to illuminate the relevant semantic differences, though, and does so without positing more pieces than the theory had already made available, it helps to demonstrate the flexibility and extendability of my general approach. In exactly these respects, my theory fares quite well compared to the lexical theory; I turn to this comparison directly.

6.3.4 Comparison with the lexical theory Minimally, the data that I have focused on in this chapter requires at least one event argument, one whose temporal duration can be specified by a for-phrase. Yet extending the lexical theory so that it meets that minimal condition will still not be expressive enough, on its own, to capture the truth-conditional interactions between the ‘high’ comparative and differently-positioned for-phrases. To see this, suppose for the moment that gradable adjectives lexically express measure functions, but they involve mapping states to degrees rather than individuals to degrees.1⁴ Suppose further that gradable adjectives relate states to degrees as in (339), a modified version of the lexical axioms presented in Chapter 2. And suppose further that, outside of the comparative form, the covert morpheme abs relates eventualities 1⁴ My illustration presumes a simplified states-based lexical theory echoing Husband 2010 and Baglini 2015. One important difference in implementation is, for example, that Husband 2010 introduces the relevant states syntactically via a morpheme he calls posv , which also relates the type ⟨e, s⟩ adjectival interpretation to the contextual standard degree for that adjective. I don’t think that the differences between the specifics of this proposal and my simplified version matter for the present point, however.

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and the measure function to a standard degree, (369). (States are linked to their bearers in the usual way.) (369) JabsK(dstd ) = λg⟨v,d⟩ λαv .g(α) ≥ dstd Composing the interpretation of the basic cases is then straightforward. The absolute form in (370a) is interpreted as meaning that ‘Ann is in a state of availability s, the measure of which exceeds the standard for availability in the context, and s holds for two days’. The ‘low’ comparative form with a for-phrase in (370b) is interpreted as, ‘Ann is in a state of availability s which exceeds δ, and s is such that it holds for two days’. These results for the lexical theory, so far, are fine. (370) a. JAnn was pos available for two daysK = ∃s(Ho(s)(a) & available(s) ≥ dstd & τ(s) = 2-days) b. JAnn was more available for two days than Bill wasK = ∃s(Ho(s)(a) & available(s) > δ & τ(s) = 2-days) The trouble comes in with the ‘high’ comparatives. Suppose for the moment that the post-adjectival occurrences of more signal that DegP does not combine with the lexical adjective directly. Instead, in these cases, much introduces measure functions just as in the theory I developed in Chapter 3.1⁵ If so, much will apply to the states predicated of by the adjective. If we say nothing more, such an account incorrectly predicts the sentences in (371) to be synonymous. (371) a. Ann was [available for 2 days] more than Bill was. b. Ann was [available more than Bill was] for 2 days. The problem is that, regardless of whether it appears low, (371a), or high, (371b), the for-phrase will predicate of one and the same states. To see this, consider the property in (372), which is derived by combining the adjective with abs. (372) Jabs availableK = λs.available(s) ≥ dstd henceforth abbreviated: λs.available≥std (s) Now, where the for-phrase attaches will make no difference. Attaching it closer to the adjective than to the DegP derives the property in (373a), and attaching it higher than DegP delivers exactly the same property, (373b). (Plainly, there is no importance whatsoever attached to the different order of conjuncts in (373a) and (373b).) (373) a. J[[pos available] for two days] moreδ K = λs.available≥std (s) & τ(s) = 2-days & |s| > δ b. J[[pos available] moreδ ] for two days K = λs.available≥std (s) & |s| > δ & τ(s) = 2-days 1⁵ This assumption already leads to a worry. If stative predicates are, semantically, relevantly like substance mass predicates, it’s not obvious that they should lead to the comparisons by number characterizing the ‘high’ comparative. The issues I’m about to describe, though, will arise no matter what assumptions are made about the expression that introduces measure functions.

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Given only one eventuality, the ‘high’ comparative cannot support truthconditionally distinct interpretations. This is a bad result. At least, given a minimal and uncontroversial semantics for the for-phrase, we need one eventuality for its ‘low’ occurrences, and a different one when it appears structurally higher. Adding a second eventuality layer will, then, result in the same predictions for the lexical theory and the account that I have advanced. The only difference being, again, whether the GA itself lexicalizes a measure function. Unlike Chapter 4, then, there is no argument here against that core assumption of the lexical theory. However, there is an argument that, outside of that assumption, the lexical theory would have to assume pretty much exactly the analysis that I have offered in order to capture the data. Gradable adjectives will have to have an eventuality argument; my theory says that they need no more than this.

6.4 Conclusion I have suggested that there are good reasons to think that even simple adjectival predications can involve two layers of eventuality predication. At least this much was suggested by the interpretive results of different combinations of S-level adjectives, comparative morphology, and temporal for-phrases. ‘Low’ comparatives with S-level adjectives have their regular adjectival interpretations (i.e., they involve comparison of degrees that vary idiosyncratically, ultimately, with the adjective), whereas the ‘high’ comparatives are interpreted more like plural verbal comparatives (i.e., involving comparison by number). I have said that this difference is due to how comparatives determine dimensionality: what is measured determines, in large part, how it’s measured. The ‘low’ adjectival comparative involves measurement of states (Chapter 4), and the ‘high’ comparative involves measurement of pluralities (Chapter 5). The same is true, I have said, for related adverbial comparatives: combining more directly with the adverbial involves measurement of states, whereas combining it with the VP after it has been modified by the adverb (and potentially other covert elements) involves measurement of processes or pluralities. I derived the relevant plural properties in the same way as I did for process verbs like run in the previous chapter: like a property of processes, the adjectival stative property is mapped to a property of atomic events, which can then be mapped to a property of pluralities that have those events as atomic parts. The relation between the underlying states and events (i.e., temporal constitution), combined with plural modification implies that the relevant states can, in principle, hold ‘on occasion’— leading to a stage-level adjectival interpretation. This helps make sense of adjectives that prefer individual-level contexts: we can’t both understand the predicate to express a long-lasting, stable transitory, and a stable one. And so just as in the previous chapter, we see how grammatical elaboration can shift us towards talk of different thing; here, that elaboration is reflected in surface word order. I’ve argued that the relevant facts can be accounted for simply by assuming

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the small stock of independently motivated semantic units I posited previously. This analysis, though, raises to salience the question of whether there are any cases that require positing more than this. Thus, I turn next to a host of cases that have been classified as importantly different in the literature, and each usually accounted for in terms of an ambiguity of more. I will argue, instead, that such cases do not support moving away from the univocal semantics that I have offered. Instead, I take them to reflect further instances in which grammar impacts what is talked about and, concomitantly, the selection of particular measure functions.

7 Measuring accuracy

When discussing adjectival comparatives, I have primarily been concerned with characterizing the semantics of sentences like (374). I have discussed ‘subcomparatives’ like (375) in some cases in order to probe the interpretive consequences of comparing with pairs of adjectives that intuitively share a dimension, as in (375a), versus with pairs that don’t, as in (375b). The fact that (375b) is marked in some way is usually taken as evidence that the comparative morphology presupposes comparison of degrees drawn from a common scale. (374) Al is taller than Bill is. (375) a. Al is taller than Bill is wide. b. ?Al is taller than the wall is purple. Often, subcomparatives feature pairs of adjectives that don’t obviously relate to a common scale, yet do not give rise to any sense of anomaly; some naturally-occurring examples are given in (376). To compare the degree to which some x is time-consuming and the degree to which x is difficult, i.e., to imagine these as lying on a common scale, we would minimally expect that these degrees are at least correlated in their extent. Yet something can be time-consuming even if it’s easy; and something’s being more addictive definitely doesn’t imply that it’s more fun, (376b). Why, then, are sentences like these acceptable, where examples like (375b) seem odd? (376) a. This badge is more time-consuming than it is difficult.1 b. Frankly, I think Farmville is more addictive than it is fun.2 Much of the literature would likely label the sentences in (376) as instances of ‘metalinguistic’ comparatives. But I should like to remain neutral, for now, on this classification; there are a variety of cases that the literature assigns different labels, and I should not like to prejudge whether those cases are distinct enough to deserve such differentiation. Furthermore, I should not like to imply that all of the cases are meaningfully understood as ‘metalinguistic’. Minimally, it seems to me, the sentences in (376) express that a thing is better characterized as an instance of one category over another; hence, I will adopt the neutral descriptive label, ‘categorizing comparatives’, to refer to sentences like these.

1 kongregate.com/games/Vitaly/feudalism 2 gamasutra.com/ . . . /Farmville_Social_Gaming_and_Addiction.php The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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In brief, here are some specific examples that have been discussed: we have ‘comparisons of deviation’ like (377a) (see especially Bartsch & Vennemann 1972 and Kennedy 1999), ‘indirect comparisons’ like (377b) (this term comes from Bale 2006, 2008), and ‘metalinguistic’ comparatives like (377c) (see e.g. Bartsch & Vennemann 1972, McCawley 1988, Morzycki 2011, and Giannakidou & Yoon 2011). For now, I will include all of these examples under the ‘categorizing’ label, and probe whether and how we should make a bipartite distinction between ‘regular’ and ‘categorizing’ comparatives, through consideration of such examples. (377) a. Team A is more legitimate than Team B is fraudulent. b. Esme is more intelligent than Einstein is clever. c. Your problems are more financial than legal. In the end, I’ll suggest that there are two descriptive classes: regular and categorizing comparatives. These classes are not delimited by different comparative morphology, but in whether they involve a silent trigger of clausal abstraction (categorizing comparatives) and in whether the degrees compared are based directly on the lexical category targeted on the surface (regular comparatives).3 I posit that categorizing comparatives are interpreted much like the example in (378), or to their Japanese correspondents (see Sawada 2007; cited by Morzycki 2011): (379) is interpreted the same as its English gloss, but features an overt morpheme iu meaning ‘to say’ affixed to the head of the dependent clause, yori. (378) It’s more accurate to say Farmville is addictive than to say Farmville is fun. (379) Taroo-wa sensei-to iu-yori gakusya-da. Taroo-top teacher-as say-than scholar-pred ‘Taroo is more a scholar than a teacher.’ Beginning with the distribution and interpretation of these two classes, I will consider the extent to which the data support making even finer class distinctions, and which analytic distinctions are minimally required in order to capture their semantic differences.⁴ I ground the important semantic distinctions that I find in syntactic differences: the abstract syntax of categorizing comparatives features an instance of a covert morpheme, κ (see Embick 2007), which I interpret as introducing states of being accurate; correspondingly, the categorizing comparative compares degrees representing the accuracy of two statements. I begin by probing the descriptive differences between regular and categorizing comparatives, and determine that there are just these two varieties, if anything. What

3 My analysis of categorizing comparatives, then, is similar to some analyses of the so-called ‘metalinguistic’ comparative. Mine differs, though, in positing no ambiguity in the comparative morphology (Morzycki 2011 and Giannakidou & Yoon 2011; cf. Bale 2006, 2008), and in its characterization of the degrees compared. ⁴ I mainly focus on -er/more comparatives throughout this chapter, but the characteristically ‘categorizing’ reading can be detected at least in equatives as well; e.g., as in this overheard example, Your plan is as foolhardy as it is desperate.

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interests me, though, is the possibility of accounting for the descriptive differences without modifying the univocal comparative semantics that I have advocated up to this point. In conjunction with my reimagining of the semantics of adjectival and adverbial comparatives, the major takeaway from this chapter is that we have little support, in any grammatical context, that expressions like more are ambiguous.

7.1 Two varieties I focused on the interpretation of ‘regular’ adjectival comparatives alone in Chapters 2 and 4, concluding that they are interpreted as comparisons between measures of states which are introduced by lexical adjectives. Minimally, there appears to be a second sort—those I call ‘categorizing’ comparatives, for now—which can be distinguished from regular comparatives in the adjectival domain, but which are in fact found across categories. Considering the differences in distribution and interpretation between these two varieties, I ultimately conclude that we need not hypothesize more than these two types, and that the differences existing between them are not due to the comparative morphology. Instead, while categorizing comparatives involve the measurement and comparison of states, much like regular adjectival comparatives, those states are not introduced by a lexical item, but instead are derived compositionally via an abstraction operation. I call these states of accuracy, for reasons that will become clear below. I suggest that my analysis will cover many of the core cases usually labeled ‘metalinguistic’, and is thereby offered as an alternative to extant proposals for their syntactic and semantic analysis.

7.1.1 Regular vs categorizing A simple form of the regular comparative involves comparison between the extents of one or two objects along a single dimension. For instance, (380) expresses that Box A’s vertical extent is greater than Box B’s; (381a) expresses that Box A’s vertical extent is greater than its horizontal extent; and (381b) says, now, that Box A’s vertical extent is greater than Box B’s horizontal extent. Each of these three sentences are intuitively true in the scenario depicted in Figure 7.1, with just Boxes A and B present. A

B ha = 2hb wa = 1/hb

Figure 7.1 Boxes A and B.

wb = hb

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(380) Box A is taller than Box B is. (381) a. Box A is taller than it is wide. b. Box A is taller than Box B is wide. ‘Regular’ comparatives are those that, on their most natural interpretation, require attending only to the entities mentioned in the sentence for their evaluation. That is, the three sentences just discussed all remain true against the scenario in Figure 7.2, which keeps Box A and B the same as in Figure 7.1, but adds additional boxes to the context. Categorizing comparatives are different in this respect: intuitively, the evaluation of more X on its categorizing reading depends on where the entities mentioned in the sentence fare with respect to their extent of X, as compared to their contextual competitors. To demonstrate this semantic difference, I will capitalize on the fact that adjectives that normally take the -er form (i.e., those adjectives that invoke the morphophonological rule of comparative formation) are most naturally interpreted in the usual mode, but interpreted in the categorizing mode when they occur with more.⁵ I’ll thus illustrate the categorizing variety using more, and mark the adjective or other lexical target using small caps to indicate prosodic emphasis. Later, I will say a bit about why this emphasis helps to support the availability of the categorizing reading. Thus, I treat the comparatives in (382)–(383) as categorizing comparatives. Used as descriptions of Figure 7.1, any of these strike me as bizarre; if anything, they invite the question of why one didn’t just use one of (380)–(381). As descriptions of Figure 7.2, though, such usages seem fine. Moreover, here, (382) invites us to think that Box A is a better exemplar of the category ‘tall’ than B is, although it isn’t obvious that either Box A or Box B are in fact positive instances of the category. (383b) is read similarly, except it conveys that A’s fit to the category ‘tall’ is better than B’s to ‘wide’. Since A is taller than only two others, while B is wider than at least three others, (383b) strikes me as false here. (382) Box A is more tall than Box B is. (383) a. Box A is more tall than it is wide. b. Box A is more tall than Box B is wide.

A

B

Figure 7.2 Boxes A and B in context. ⁵ There is some question about whether the distinction between synthetic -er and analytic more for a given adjective tracks, once and for all, the regular versus categorizing readings. Bartsch & Vennemann 1972 and Kennedy 1999 are tentative on this point. I will talk mainly as if the correlation is absolute. If it isn’t—i.e., if the categorizing reading is always available in principle—then almost any semantic proposal for the regular comparative form will have to be revised (cp. Bale 2006).

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The intuitive aptness of talking about category fit invites my label ‘categorizing’. It should be clear how, despite this difference, such readings can involve comparison of degrees on a common scale—i.e., one representing something like extent of fit to a category or categories. Such talk invites thinking about whether the categorizing variety should be thought of as ‘evaluative’ in Rett’s (2015) sense. However, I hesitate to pursue this line, since categorizing comparatives don’t support the basic inferences that comparatives targeting evaluative adjectives do.⁶

7.1.2 Distributional differences Regular comparatives involve comparing measures along dimensions that vary along with a targeted lexical item or phrase; categorizing comparatives, instead, involve comparing measures of the extent to which, say, entities fit into the category or concept introduced by that lexical item or phrase. Fixing on these glosses as diagnostic, we can see that a lot of evidence suggests these two readings come along with distinctions in syntactic construction. My study will be geared towards locating the structural sources and semantic consequences of these distinctions.⁷ We have already seen that regular and categorizing comparatives differ in the extent to which they depend on features of the surrounding context: a regular comparative stated between A and B involves evaluating relative to A and B, simpliciter, while a categorizing comparative involves first evaluating A and B relative to their respective categories, which in turn invites the relevance of contextual comparison classes. A second difference is that regular comparatives require more than a bare adjective in the than-clause; cp. (384a)–(384b).⁸ We see the same restriction in the equative, (385a), unless much appears in its matrix clause, (385b). (384) a. ?Box A is taller than wide. b. Box A is more tall than wide. (385) a. ?Box A is as tall as wide. b. Box A is as much tall as wide. In contrast, only the regular comparative is compatible with a lone measure phrase like 6 feet in the standard phrase, cp. (386a)–(386b).⁹ The simple thought expressed by (386a)—that John’s height is greater than 6 feet—cannot be expressed by (386b); in fact, (386b) simply sounds bizarre. It’s not clear to me whether the oddity here points to a

⁶ That is, A is shorter seems to imply that A is in fact short, where A is taller doesn’t imply that A is tall; and so short is considered evaluative to the exclusion of tall. However, categorizing comparatives don’t require that their adjectival properties positively hold of their subjects, as I noted above. ⁷ Many of the pieces of evidence that I introduce directly were originally intended to distinguish regular from ‘metalinguistic’ comparatives. I continue to avoid such labels in order to avoid prejudging how the typology should ultimately be characterized. ⁸ Such patterns are observed in di Sciullo & Williams 1987; see also Embick 2007 and Morzycki 2011. ⁹ This pattern was observed by Giannakidou & Yoon 2008.

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difference in grammaticality, or whether the semantic implications of the categorizing comparative clash with the meaning of measure phrases. (386) a. John is taller than 6 feet. b. ?John is more tall than 6 feet. Regular adjectival comparatives require that their adjectives introduce states that can be measured along the same dimension; as this is not intuitively available for tall and smart, the oddity of (387a) makes sense. However, (387b) invites thinking that it is more apt to categorize Sue as tall than it is to categorize Al as smart. In the latter case, at issue is the aptness of categorizing the individuals with respect to different properties; thus it also makes sense that the categories needn’t share a dimension. (387) a. ?Sue is taller than Al is smart. b. Sue is more tall than Al is smart. Examples with putative antonyms are similar. Regular comparatives are sensitive to adjectival polarity: (388a) cannot express a direct comparison of Sue’s and Al’s heights. On one prominent account, examples like (388a) are ruled out semantically because they can never evaluate to true or false: tall supports measurement by positive degrees, while short supports measurement by negative degrees; these, by hypothesis, are not orderable with respect to one another (see Kennedy 1997, Büring 2007, Heim 2006, 2008). Yet (388b) seems fine, suggesting again that one categorization is more apt than another. (388) a. ?Sue is taller than Al is short. b. Sue is more tall than Al is short. Finally, there are almost no restrictions on the syntactic category of expression that the categorizing variety can combine with; many of those in (389) and (390) shouldn’t even meet the semantic requirements of regular uses of more. (The examples in (389a)– (389b) are from Morzycki 2011, (389c) is from Embick 2007, and (389d) is from Lin 2009.) All of these examples are naturally read as categorizing comparatives; none seem to have a paraphrase which invokes direct measures on a common, lexically-associated dimension. (389) a. b. c. d.

He is more beneath contempt than beyond help. Al is more incredibly dumb than really crazy. Al is more Las Vegas than Monte Carlo. Al cried more because Julie lied than because she stole.

PP DegP PrN CP

(390) a. b. c. d. e. f.

Bill is more a boss than the boss. That bird is more a rooster than a duck. Al is more seven feet tall than six and a half feet tall. Al more likes Bill than loves him. Al swam more excitedly than skillfully. The world is more to be admired and enjoyed than used.

DP DP MP VP AdvP TP

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7.1.3 Patterns of implication We have seen a number of distributional and semantic differences between the two varieties already. They also differ in their implicational profiles. In previous literature, a variety of classes are attributed different patterns of entailment, presupposition, and implicature. I find, studying the reported patterns that the only implication which distinguishes the regular and categorizing comparatives is that the latter licenses a certain conditional inference (Bale 2006, 2008), as we will see. First, as is well-known, regular comparatives do not entail the attribution of the positive form of its adjective to its subject, in either of its matrix or than-clauses. Consider Figure 7.3 in this light. Intuitively, in this scenario A is neither tall nor short; it is, however, taller than at least two other boxes—B, and the squat middle box. Box B, in contrast, is the shortest box, and it is wider only than A. In my judgment, none of the sentences in (391) accurately describe this scenario; i.e., neither A nor B meet the conditions for positive attribution of the adjectives in this context. Yet, both of the sentences in (392b) can be true here. (391) a. b. c. d.

Box A is tall. Box A is wide. Box B is tall. Box B is wide.

(392) a. Box A is taller than Box B is. b. Box A is more tall than Box B is. It has occasionally been reported that sentences like (392b) do imply such positive attributions, but this is more than likely due to conversational implicature (Embick 2007, Morzycki 2011; cf. Rett 2015): given that the default comparative form for wide is wider, yet the marked form more wide is used, one infers that the intention was to convey something more than what the regular comparative form conveys. Whatever its nature, (393b) minimally shows that the inference is cancelable. (393) a. The alley is wider than it is long, but of course it’s still pretty narrow and short. b. The alley is more wide than it is long, but of course it’s still pretty narrow and short. Categorizing comparatives do license a related but weaker inference, which isn’t usually licensed by the regular comparative (cf. Bale 2006). That is, the regular com-

A

Figure 7.3 Boxes again.

B

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parative in (394a) fails to entail either variant of the follow-up conditional sentence, whereas the categorizing comparative in (394b) licenses both. This pattern is sensible if the categorizing comparative establishes that a is a better fit to category P than b is to Q; if b is a (very) good instance of Q, a must be at least as good an instance of P. (394) a. Box A is taller than Box B is wide. So if Box B is (very) wide, then Box A is (very) tall.

invalid

b. Box A is more tall than Box B is wide. So if Box B is (very) wide, then Box A is (very) tall.

valid

What doesn’t appear to have been noticed is that categorizing comparatives prefer (presuppose?) that the entity said to be a better fit isn’t the superlative exemplar of the relevant category: it seems odd to say, for example, of the tallest person in the world a that they are more tall than anyone else, while it’s fine to say that a is taller. This makes sense if categorizing comparatives are about fit to a category, as invoking a notion of ‘better’ fit for a would seem to imply that there was a question about whether a fits the category in the first place. This discussion suggests that, in fact, the categorizing comparative should be infelicitous in any case where there is simply no question, about whether an entity fits the relevant category. In this light, consider the scenario in Figure 7.4, in which B is clearly tall. Saying that, it is fine to add that, nonetheless, A is taller, (395a). But use of the categorizing comparative here is awkward: (395b), in particular, seems to relitigate the question of whether B is tall. (395) Wow! Box B is tall, isn’t it! a. Yes; but Box A is taller. b. ?Yes; but Box A is more tall. The variant dialogues in (396) can be used to make the same point, and it is one that can be reproduced with the negative adjective short substituting talk of Boxes A and B with talk of C and D. (396) Box A and Box B are both definitely tall. a. Yet Box A is taller than Box B. b. ?Yet Box B is more tall than Box A is.

A

B

C

Figure 7.4 More boxes.

D

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7.1.4 Comparison with accuracy reports I would now like to suggest that categorizing comparatives are interpreted very much like regular comparatives targeting the adjective accurate, along with its oft-needed infinitival complement to say (cf. Sawada’s 2007 data from Japanese). The overall similarity in distribution provides some evidence for a parallel semantics, i.e., as involving the comparison of degrees representing how accurately a predication characterizes a certain state of affairs.1⁰ Consider (397). These sentences express that the truth of A is tall is more or at least as accurate as that of A is wide. If so, this would seem to minimally imply that A is a better fit to the category ‘tall’ than ‘wide’. Moreover, it seems to me that neither sentence in (397) entails that A positively fits either category. In parallel with these interpretive similarities, the most natural prosodic realization of (397), with focal stress on the matrix and embedded predicates, is also parallel.11 (397) a. It’s more accurate to say A is tall than (to say) A is wide. b. It’s as accurate to say A is tall as (to say) A is wide. Moreover, comparative accuracy reports have a similar distribution to categorizing comparatives. For example, they are odd with than-clauses containing only a measure phrase, (398). They are insensitive to whether the properties expressed by their gradable adjectives are otherwise incommensurable, (399a), and they are insensitive to whether they have opposite polarity, (399b). Moreover, any category in the embedded clauses of an accuracy report can be focused, e.g., (400), with interpretive consequences that again parallel what we’ve seen for categorizing comparatives. (398)

?It’s more accurate to say that A is tall than 5 feet.

(399) a. It’s more accurate to say A is tall than to say Bill is smart. b. It’s more accurate to say A is tall than to say Bill is short. (400)

It’s more accurate to say she’s a boss than to say she’s the boss.

As near as I can tell, the implications that hold for particular categorizing comparatives (but not for regular comparatives) hold for comparative accuracy reports as well. Recall that while (401a) fails to guarantee the positive attribution of either adjective to A, it does seem to guarantee the weaker conditional inference in (401b) (cf. Bale 2006, 2008). The same appears to be true of the inference from (402a) to (402b), where the conditional is contained inside the complement of accurate.

1⁰ In Wellwood 2014, I offered an alternative diagnosis of these data, suggesting that categorizing comparatives correspond to implicit confidence reports. However, J. Hawthorne (p.c.) points out that, if that were right, a sentence like Ann wonders whether Bill is more tall than wide should be read as a report of Ann’s wondering about her own confidence levels, and this seems wrong. I’ll return to this kind of consideration when I compare my current proposal with others that are on offer. 11 I think similar meanings can be expressed by a non-comparative sentence using say, e.g., I’d say that A is tall before (I’d say that) A is wide.

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(401) a. A is more tall than she is wide. b. So if A is (definitely) wide, then she’s (definitely) tall. (402) a. It’s more accurate to say that Ann is tall than that to say she’s wide. b. So if it’s accurate to say that Ann is wide, then it is/will be accurate to say that she’s tall. Finally, the constructions have similar felicity conditions. Recall Figure 7.4. In such a context, claiming that it’s more accurate to say that the tallest box is tall than to say that the second tallest box is tall sounds just as odd as claiming that A is more tall than B. Why don’t such claims just ring true? I suggest that this is so because both raise the question of whether A or B is in fact tall, a question answered by simply apprehending the context. Such assertions, then, would to requests for unnecessary and unhelpful relitigation of a matter that is simply not at issue. I will suggest that categorizing comparatives involve the measurement and comparison of accuracy states. This is how I would analyze the explicit accuracy reports, based on the template established in Chapter 4. Even if one isn’t yet on board with my states-based analysis for adjectival comparatives, though, the semantic equivalence between the adjectival accuracy reports and their nominal correspondents in (403) is suggestive. Absent a competing theory of nominal data like this, they tell us that much can introduce degrees representing accuracy. (403) a. There’s more accuracy in saying A is tall than in saying she’s wide. b. There’s as much accuracy in saying A is tall as in saying she’s wide.

7.2 κ comparatives And so: is there one type of comparative, or two? There are certainly differences between regular comparatives and categorizing comparatives: where the former involve comparison between degrees on a scale that is closely linked to the adjectival, nominal, or verbal target of the comparative morphology (i.e., scales that represent the ordering relations on that target’s domain), categorizing comparatives ignore various facts about the apparent lexical target and instead quantify in relation to their embedded sentences. What supports the latter profile? Outside of accounting for the interpretive differences, I see no obvious grammatical motivation to impose any ambiguity on the comparative morphology. Yet certain features of the categorizing comparatives (i.e., the utility of prosodic emphasis in grasping the categorizing reading, restrictions on the surface structure of than-clauses, etc.) suggest there are important differences. I’ll suggest that, indeed, categorizing comparatives involve different syntactic structures than regular comparatives, a consequence of which is a shift in what the comparative measures and compares. Thus, there is just one type of comparative. As in other cases, I attribute shifts in dimensional interpretation to differences in grammatical context and concomitant differences in ontological commitment.

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7.2.1 The proposal I build on the morphological analysis of Embick (2007), who posits a silent morpheme κ to account for the apparent optionality of the comparative formation rule that derives the -er form for a number of adjectives in English. I build on prior semantic analyses in positing covert sentence-level modification of the comparative (cf. Giannakidou & Yoon 2011; but see §7.3.3). My analysis, in a nutshell, is that κ maps sentence-level interpretations to properties of states ordered by increasing accuracy.12 I won’t give anything like a complete morphosyntactic analysis here, but merely state my assumptions. Embick’s (2007) morphological account concerns the patterning in data like (405) within a framework that disallows optionality in the application of morphological rules. First, (404) shows that adjectives like smart accept the -er form, while those like intelligent disallow it. This suggests there is a morphological rule, applicable only to a subset of adjectives, which should apply whenever its structural conditions are met. Thus, without saying more, the fact that (405a) is acceptable (even if somewhat less so than (405b)) is problematic. (404) a. Al is smarter than Bill is. b. ∗ Al is intelligenter than Bill is. (405) a. Al is more smart than Bill is. b. Al is more intelligent than Bill is. Embick thus assumes that some morpheme can combine with the adjectival complex which, when present, blocks the regular derivation of smarter by changing the structural conditions such that the comparative formation rule doesn’t apply. He gives this morpheme the label κ, and assigns it the syntactic position represented in (406). On a structural approach like this, the supportive prosodic prominence in categorizing comparatives could be understood as a marker of some interaction between κ and a focus-licensing element, or simply as a type of surface realization for that morpheme. (406)

AP AP tall

κP DegP

thanP than κ wide

κ

moreμ 12 I could imagine breaking this down further by taking the correspondences between explicit and implicit accuracy reports a little further: the former require to say given adjectival accurate and in saying given nominal accuracy; thus, one could additionally posit a covert counterpart of say and in to achieve what I will bundle up into κ alone.

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My analysis will demand a sentence-level interpretation for the categorizing comparative, however, and so I can’t simply assume (406).13 Instead, I posit that the complex of more and κ are raised from their base position in a structure like (406), which has the semantic effect of a lambda abstraction over worlds; the resulting proposition (if that’s what it is) specifies the content of the states that κ introduces.1⁴ There are many ways one could ground this analysis structurally; for simplicity’s sake, I will assume that the interpreted structure looks as in (407).1⁵ (407) moreμ thanP

κ Ann is tall

A κ-comparative like this will express that the degree to which it is accurate to say that Ann is tall exceeds δ (e.g., the degree to which it is accurate to say that she is wide). Evaluating whether such talk merely equivocates with talk of comparing degrees of belief (cf. Villalta 2008, Anand & Hacquard 2013) or of likelihood (cf. Davis et al. 2008, Swanson 2011) is beyond the scope of my present project. All I shall wish to say for now is that comparing degrees of accuracy involves the measurement of states that have propositions as their contents, and which are ordered by the accuracy of those contents.1⁶ Such an analysis dovetails with the distributional and interpretive demands of the categorizing comparative. For example, it will have little trouble supporting an account of why they are more permissive in the types of syntactic and semantic categories that they appear to target. If their semantics requires sentence-level modification, then any restrictions on their interpretation should be borne out at that level; the inner workings of the modified sentences should be, for the most part, free to vary.

7.2.2 Mapping to degrees I first demonstrate the formal details I assume for explicit accuracy reports, and then leverage that analysis to specify the semantics of the structural elements underlying categorizing comparatives.

13 One could, of course, attempt to give a local interpretation of expressions that are usually thought to entail sentence-level modification; e.g., Schein 2017, Nouwen 2011, or Bogal-Allbritten 2013b. Morzycki’s 2011 account of metalinguistic comparatives is local in this sense. 1⁴ Hacquard 2006 (see also Kratzer 2006), combining the traditions of Hintikka 1962, Lewis 1983, and Stalnaker 1984 with that following Davidson 1967, makes a similar proposal for attitude verbs. Their semantics involves a relation between davidsonian attitude states and their propositional contents. 1⁵ (407) has κ combining with the sentence where (406) has it combining with the adjective. I suspect that raising the lower AP from (406) to the sentence level would accord better with independent assumptions about syntactic movement, however, that analysis complicates the semantic details enough that I prefer the formulation in (407) for present purposes. 1⁶ Cariani et al. under review offer a similar analysis of comparative reports with confident and likely; I refer the reader to their work for comparison with the present proposal.

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In the neodavidsonian framework I assume, extended as in Chapter 4, accurate expresses a property of states; see (408). The only differences between an adjective like accurate and one like tall pertains to the nature of the thematic roles they license: accurate licenses no thematic role for a contentful subject, while tall does; accurate licenses a thematic role for its propositional complement,1⁷ while tall does not. I assume, following previous works, that the thematic role linking accuracy states and their contents is the Content relation. (408) JaccurateK = λs.accuracy(s)

type ⟨v, t⟩

I assume an ordering on accuracy states according to how much accuracy they instantiate. Put differently, this amounts to the claim that accuracy states s are ordered according to the likelihood that their contents, i.e., Content(s), are true. Every distinct sentence-level interpretation will have its own associated accuracy state, and all are ordered with respect to one another by, call it, ≼acc .1⁸ Given the semantic requirements of much and -er, these ordering relations will be preserved in the mapping to a scale representing increasing accuracy. I have advanced the claim that categorizing comparatives are covert comparative accuracy reports. The simplest semantic hypothesis, then, is that the quiet morpheme that occurs in the categorizing comparative, κ, has the same semantics as the gradable adjective in (408); hence, (409). Given this hypothesis, everything I have said so far about accuracy reports should also obtain for the categorizing comparative. (409) JκK = JaccurateK The two constructions differ in that accurate is related to its thematic clause locally, by syntactic merger (e.g., accurate (to say) that it’s raining), while κ is related to its thematic clause only following syntactic movement.

7.2.3 Composition: categorizing comparatives I will demonstrate the parallels I assume for the compositional derivation of both the explicit accuracy report and the categorizing comparative, using the sentences in (410) as illustration. (410) a. It’s more accurate to say A is tall than to say she’s wide. b. A is more tall than (she is) wide. Whether dealing with a comparative involving accurate or κ, we want the accuracy states to be related to a sentence-level interpretation in each of the matrix and than-clauses. I set the details of the than-clauses aside for now. A sentence-level 1⁷ This of course ignores any contribution of to say. 1⁸ It may be that ‘accuracy measures’ bear non-trivial similarities to credence measures (see e.g. Davis et al. 2008, Swanson 2011) or confidence measures (Cariani et al. under review); however, the present semantics hardcodes no requirement for as much structure as required for probabilistic accounts.

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interpretation is provided in the complement position of accurate on the surface in the explicit report, (411a), and covertly following syntactic movement in the implicit report, (411b). (411) a. It’s

moreμ thanP

accurate (to say) A is tall

b. moreμ thanP

κ A is tall

So far, my semantics would interpret the relevant sentential complements as in (412a), prior to thematic interpretation. However, I will now suppose that those complements are interpreted as propositions, and that propositions are functions from worlds to truth values. This can be made explicit while making little additional modifications as follows: making the domain restriction Dv on the existential quantifier in (412a) explicit, we can simply add the needed property of worlds by indexing that domain to worlds w, i.e., Dwv , and abstracting over that variable as in (412b). (412) JA is tallK = a. ∃s ∈ Dv (Ho(s)(a) & tall(s)) b. λw.∃s ∈ Dwv (Ho(s)(a) & tall(w)(s))

abbr. λw.a-tall(w)

Interpreted as in (412b), the sentential complement is linked to the states introduced by accurate/κ by thematic interpretation; the relation linking states with their contents is Content (here and below abbreviated Co). The result of thematic interpretation, then, is a property of states which has the proposition expressed by A is tall as its content, (413a). Combining this with accurate or κ adds the further specification that accuracy states with these content are at issue, (413b). (413) a. J[A is tall][θCo ] K = λsv .Co(s)(λw.a-tall(w)) b. Jκ/accurate [A is tall][θCo ] K = λsv .accuracy(s) & Co(s)(λw.a-tall(w)) From here, the usual compositional process will deliver the interpretation in (414) for the sentences in (410), abbreviating the than-clause interpretation as δ and A(μ) as μ. On this analysis, both the explicit accuracy report and the categorizing comparative in (410) are understood to say: ‘there is a state of accuracy that has as its content the proposition expressed by Ann is tall, which is such that it measures greater than δ.’1⁹ 1⁹ Here, δ = max(λd.∃s(accuracy(s) & Co(s)(λw.a-wide(w)) & μ(s) ≥ d)).

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(414) ∃s(accuracy(s) & Co(s)(λw.a-tall(w)) & μ(s) > δ) In normal contexts, an utterance of an explicit comparative accuracy report or a κ comparative indicates that the speaker, at least, judges that the truth of Ann is tall is more likely than the truth of Ann is wide. However, since the relative accuracies aren’t tied to any judge, we expect that either sort of claim should be open to disagreement, and they are: it is perfectly felicitous to follow up either of (410) with “That’s not true! Ann is more wide than she is tall”, etc. Ultimately, in my view what is at issue in such disagreements is the specifics of an accuracy ordering. This analysis maintains a uniform interpretation of more etc., in the face of what appears to be a quite different category of interpretation. Independently motivated morphosyntactic analysis (Embick 2007), a gesture towards independently motivated semantic-pragmatic analyses (e.g., Swanson 2007, Davis et al. 2008, Cariani et al. under review), and a little covert syntax appears to do the trick. This shows, at least, that there is no need in principle to posit ambiguity in the comparative morphology.

7.3 Alternatives On my account, comparative expressions like more are unambiguous: they always contribute a mapping to degrees, and a relation between degrees. Depending on what is input to much, the part of expressions like more that introduces measure functions, that mapping varies. Similar to how more coffee involves measures that are unavailable to more coffees and vice versa, taller involves measures that are unavailable to more κ tall and vice versa. In the last case, I have supposed that states of accuracy are measured. In this respect and in its avoidance of ambiguity in the comparative morphology, my proposal differs from any relevant alternative. In what follows, I first take on the question of whether we should delimit more subclasses of comparatives than just those I have labeled ‘regular’ or ‘categorizing’. Finding that this distinction is enough, I consider two recent proposals for ‘metalinguistic’ comparatives (Morzycki 2011, Giannakidou & Yoon 2011) that could reasonably be applied to the categorizing comparatives, and sketch the major differences between our proposals. Each account is attractive in its own right; nonetheless, both posit that expressions like more are ambiguous, which I would like to revisit.

7.3.1 More varieties? Many authors have discussed comparatives of different sorts, using different class labels than the two I have considered throughout this chapter. The examples I gave at the outset are repeated in (415), with (415c) a sample of what has been called a ‘deviation’ comparative, (415b) an ‘indirect’ comparative, and (415a) a ‘metalinguistic’ comparative.

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(415) a. Your problems are more financial than legal. b. Esme is more intelligent than Einstein is clever. c. Team A is more legitimate than Team B is fraudulent. Ultimately, the differences between these purported classes usually comes down to the sorts of degrees they are thought to compare. For example, (415a) is said to involve degrees of appropriateness (McCawley 1988) or precision (Morzycki 2011), while (415c) involves degrees representing deviation from a standard (e.g., the subtraction of the contextual standard for legitimacy from Team A’s degree of legitimacy etc; Bartsch & Vennemann 1972, Kennedy 1999), and (415b) involves universal, or dimensionless, degrees (Bale 2006, 2008). Most of the authors just cited discuss, in greater or lesser detail, the metalinguistic comparative variety (MCs; the example in (415a) comes from McCawley 1988). In their analysis of MCs, Bartsch & Venneman (Bartsch & Vennemann 1972) distinguish the class on the basis of their judgment that it presupposes the positive attribution of at least the matrix clause adjective to its subject. In other words, the truth of (416) should, minimally, guarantee the truth of Your problems are financial. (416) Your problems are more financial than legal. This charge of presupposition is leveraged by Bale (2006) to distinguish MCs from his ‘indirect’ comparatives like his (415b). He shows that such sentences do not, in fact, presuppose the truth of the relevant positive attribution: witness that any implication to Esme is intelligent, for example, fails to project in negative, question, and conditional environments, (417). Rather, Bale contends, such an implication seems to be a mere implicature of (415b), a conclusion supported by the fact that it is cancelable, (418). (417) a. Esme isn’t more beautiful than Einstein is clever. b. Is Esme more beautiful than Einstein is clever? c. If Esme is more beautiful than Einstein is clever, I’ll invite her out on a second date. (418) Esme is more beautiful than Einstein is clever, which isn’t saying much since he was actually an idiot. Morzycki (2011), for his part, draws the same conclusion about MCs: any implication to the positive attribution for MCs cannot be characterized as a presupposition, since the relevant examples show the same patterns as Bale showed for his target cases. Thus, it can’t be that a difference in presupposition or implicature differentiate sentences like (415a) and (415b). (I leave it to the reader to verify that the tests exemplified in (417) and (418) lead to this conclusion for McCawley’s original example.) The last class—which Kennedy (2001a) terms ‘comparisons of deviation’—fares similarly. Kennedy analyzes sentences like (415c) as comparing the degree of difference, or deviation, between Team A’s degree of legitimacy and the standard for legitimacy in the context, with the result of the same sorts of calculation for Team B and fraudulence in the than-clause (cf. Bierwisch 1989). Kennedy’s implementation of this idea predicts

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that such sentences have the entailment to the positive form of the predications in both the matrix and than-clauses. Yet, even for these examples, that implication is at best an implicature (consider following (415b) with and this is hilarious because Team B isn’t remotely fraudulent or the like). Bale furthermore distinguishes his indirect comparatives from regular comparatives via the conditional inference licensed by the indirect but not regular comparatives. That is, (415b) entails (as opposed to presupposing, or implicating) (419). While it does appear that this implication distinguishes regular comparatives from what I have called categorizing comparatives, it can also be readily verified that this inference pattern holds for the other classes purportedly exemplified in (415). And so licensing Bale’s conditional entailment doesn’t distinguish those classes either. (419)

If Einstein was very clever, then Esme is (at least) very beautiful.

At first it seems as though this inference might not go through for our sample MC in (415a); consider (420). However, this could be due to the oddity of very legal or very financial in the first place, perhaps suggesting that these items are not lexically gradable. Another possibility is that (415a) can be read as distinguishing the likelihood that the same things instantiate what are otherwise two mutually exclusive, absolute properties, and this clash is brought to the fore with (420).2⁰ (420) ?If your problems are very legal, then they are (at least) very financial. Indeed, the conditional inference seems to fail in more obvious cases of mutual exclusivity, as when the two adjectives are antonymous and predicated of the same individual. Consider the minimal variants of Bale’s (415b) in (421). Where (421a) compares Esme’s beauty with Einstein’s ugliness, the conditional inference follows straightforwardly. But this is not so comparing Esme’s beauty with her ugliness, (421b). These patterns suggest that the conditional inference may not be diagnosing what Bale understands it to diagnose, namely a category of comparatives distinct from any other. (421) a. Esme is more beautiful than Einstein was ugly. So if Einstein was very ugly, then Esme is very beautiful. b. ?Esme is more beautiful than (she is) ugly. So if Esme is very ugly, then she is very beautiful. Here is the issue, then, in a nutshell. The literature has provided little consistent evidence on which to base a multiplicity of categorical distinctions between comparative structures, and the consequent ambiguity-based analyses of expressions like more. It simply doesn’t seem that we can distinguish MCs, indirect comparisons, or comparisons of deviation from each other on the basis of any stable entailments, 2⁰ It could be that we need a more explicit algorithm for generating the conditional inference. That is, (415a) reads to me like it could express a different thought—one amounting to saying that you have more financial problems than legal problems. The inference from that sentence to If some of your problems are legal, then some are financial, which also gets rid of the independent issue with very, doesn’t seem bad. However, see the next point.

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presuppositions, or implicatures. In their analyses, researchers have tended to localize the differences in the degrees compared, as I noted above; but as should be clear by now, these differences can be characterized in other ways. In my view, the purported variety discussed in this section reduces to the class of comparatives that I have called ‘categorizing’. This means that (415b), for example, claims that there is more accuracy in saying Esme is beautiful than in saying Einstein was clever. Given that Einstein is often taken to be an exemplar of cleverness, using (415b) will likely be taken as an endorsement of Esme as a superlative examplar of beauty. And so on. Understood in this way, we expect none of these sentences to entail or presuppose attribution of the positive form from the matrix or than-clause predications, though this may occasionally arise by implicature. Given this characterization, my analysis should be most closely compared with extant proposals for MCs, as these explicitly invite something like the kind of contextsensitivity that I have said differentiates categorizing from regular comparatives.21 I consider two accounts: that of Morzycki (2011) and Giannakidou & Yoon (2011). They suggest that MCs express comparisons between the degree of desirability or precision in the use of a given sentence or property. I briefly review these accounts directly, and say why the present analysis is to be preferred.

7.3.2 Morzycki 2011 At the broadest level, my analysis looks a lot like Morzycki’s.22 Where I would interpret a sentence like Morzycki’s (422) as expressing a comparison between degrees of accuracy, Morzycki interprets it as a comparison between degrees of precision. In implementation, the two are very different: Morzycki indexes the interpretation function with a precision parameter d, such that metalinguistic more can compare the sizes of the focal adjectives’ alternative sets at d. (422) Bill is more dumb than crazy. Morzycki’s implementation thus utilizes pragmatic halos (Lasersohn 1999) and an alternatives-based semantics (e.g., Hamblin 1973, Rooth 1985, Kratzer & Shimoyama 2002, and Shimoyama 2006). To illustrate the basic framework, Jσ Kd maps expression σ of type τ at precision level d to a set of alternatives of type τ, i.e., σ’s halo; any alternative in that set must be at least d-similar to the ordinary semantic value of σ, i.e., Jσ K. For example, given Jσ K1 , i.e., the interpretation of σ at precision level 1 (the maximum),

21 Evaluating a categorizing comparative ultimately involves knowing how things stack up with respect to a given category, in order to determine how accurate it is to say that a named entity fits into that category. While Bale’s (2006, 2008) universal scale-based analysis could potentially also be leveraged in this respect, that account would require substantial reimagining before it could be used to capture the distinction, as I’ve characterized it, between regular and categorizing comparatives. 22 I present his proposal using the language of ‘metalinguistic’ rather than ‘categorizing’ comparatives, in order to stay closer to his own presentation.

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the halo contains just Jσ K; at precision level 0 (the minimum), it contains everything of type τ; etc. I present some of the compositional details directly. As a word of caution, however, there are two aspects of Morzycki’s analysis that I leave intact here, but which are not relevant for comparing our two accounts: first, Morzycki assumes the lexical theory of GA semantics (Chapter 2), and second, he assumes that comparative morphology leads to an ‘A-not-A’, existentially-quantified interpretation (see Schwarzschild 2008 for overview and references), rather than one couched in terms of a greater-than relation. In brief, he would interpret a sentence like A is taller than B along these lines: ‘there is a degree d such that A is d tall, but B is not d tall.’ (423a) presents Morzycki’s take on the ordinary semantic value of a regular comparative, unrelativized to degrees of precision, namely, a proposition. Relativized to a degree of precision, as in (423b), the result is instead a set of propositions. An assumption of this framework is that the successful assertion of a sentence S requires, minimally, that one of the propositions in S’s pragmatic halo is true. At precision level 1, this means that the proposition in (423a) must be true; at lower levels of precision d, that proposition needn’t be true, so long as one of its alternatives at d is true. (423) a. JBill is dumber than AnnK = λw.∃d(dumb(a)(d)(w) & ¬dumb(b)(d)(w))

[A-not-A]

b. JBill is dumber than AnnKd ′

[Morzycki] ′

′

λw.∃d [dumb(d )(b)(w) ∧ ¬dumb(d )(a)(w)], ⎧ ′ ′ ′ ⎪ ⎪ λw.∃d [dumb(d )(b)(w) ∧ ¬foolish(d )(a)(w)], ′ ′ = λw.∃d [foolish(d )(b)(w) ∧ ¬dumb(d′ )(a)(w)], ⎨ λw.∃d′ [foolish(d′ )(b)(w) ∧ ¬foolish(d′ )(a)(w)], ⎪ ⎪ ⎩ ...

⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

The quantification over degrees in the regular comparative is established before the sentence-level interpretation, or its halo, is derived. MCs, in contrast, involve quantification over the precision parameter. For example, the MC in (424) is interpreted at precision level d roughly as follows: there is a level of precision d′ at which an alternative to dumb at d′ holds of George, but no alternative to crazy at d′ does. (424) JBill is more dumb than crazy.Kd = ′

= { λw.∃d′ [

∃f [ f ∈ JdumbKd ∧ f(b)(w)]∧ ] } ′ ¬∃g[g ∈ JcrazyKd ∧ g(b)(w)]

The difference between regular comparatives and MCs, on this account, arises from a lexical ambiguity of more: the former involves (425a), the latter (425b). Both moreR and moreM take the interpretations of the matrix adjective, than-clause, and matrix subject as arguments. They differ in where they invite the calculation of alternatives: external

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to any argument-taking required by moreR , versus internal to those calculations for moreM . (425) a. JmoreR Kd = {λg⟨s,⟨e,⟨ω,t⟩⟩⟩ λf⟨s,⟨ω,t⟩⟩ λxe λw.∃d′ (g(d′ )(x)(w) & ¬f(d′ )(w))} b. JmoreM Kd = λh⟨s,⟨e,⟨ω,t⟩⟩⟩ λi⟨s,⟨ω,t⟩⟩ { λxλw∃d′ [

h(d′ )(x)(w) & ] } ¬i(d′ )(x)(w)

There is overlap in the interpretations of the two mores, inviting the question of whether their differences couldn’t be derived by means other than lexical ambiguity. One consequence of keeping things as so far presented is that this ambiguity must be reproduced across any of the comparative forms that show MC-type interpretations in English (Morzycki notes this for at least more, less, and as; Morzycki 2011, p. 70), as well as across languages.23 We’d like to avoid positing systematic ambiguity whenever possible, of course. Until it is shown that lexical ambiguity is necessary for Morzycki’s account, I leave worry as an analytic challenge rather than any deep objection to the account.

7.3.3 Giannakidou & Yoon 2011 Giannakidou and Yoon (2011; updating Giannakidou & Yoon 2008 and building on Giannakidou & Stavrou 2009) also posit lexical ambiguity, but offer an account that differs considerably from Morzycki’s. In motivating their account, they take issue with his local, property-relative analysis, and suggest that an appropriate characterization of MC meaning requires sentence-level interpretation.2⁴ They analyze MCs as expressing an attitude-holder’s preference ordering between two sentences (i.e., linguistic objects), which makes it the most explicitly metalinguistic of the three proposals. I gloss over this aspect of their proposal, and talk simply of sentence-level interpretations, or propositions.2⁵ In demonstrating their account, I make some assumptions about the derivational details, as not all of them are entirely clear to me from the paper (see also Morzycki 2011, p. 74). Sufficient details are provided that I can isolate the major components of the analysis, however. Note first that where Giannakidou & Yoon assume the degree relation version of the lexical theory (i.e., gradable adjectives are interpreted in type ⟨s, ⟨e, t⟩⟩), I have simplified this to the measure function version (type ⟨e, s⟩). 23 Giannakidou & Yoon suggest that regular and metalinguistic more take different forms in Greek, which seems a welcome result. However, the Greek forms they consider might actually correspond to more and rather. 2⁴ Morzycki 2011, for his part, suggests that the essentials of his account can be modified to accommodate these concerns, as needed. In particular, their contention that MCs relate sentences/utterances rather than meanings is explored in his §6; as he notes, the evidence for such an analysis is surprisingly sparse. 2⁵ In particular, this glosses over their discussion of the “accuracy assessment” MC (see especially Giannakidou & Yoon 2011, p. 639). This is given as moreM3 below, where u, u′ range over quotations of sentences in the sense of Potts 2007, and α is the individual anchor in the sense of Farkas 1992 and Giannakidou 1998, 1999. Here and below I omit reference to the context c. JmoreM3 Kg = λuλu′ .u ≻des(α) u′ .

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Thus, I would characterize their interpretation of the regular comparative in (426) as expressing the proposition that Bill’s degree of dumbness exceeds Ann’s.2⁶ (426) JBill is dumber than Ann.KA = λw.dumb(b)(w) > dumb(a)(w) MCs, in contrast, involve comparing the degrees of desirability of two propositions, according to the speaker.2⁷ In (427) and below, I use want to reflect Giannakidou and Yoon’s suggestion that MCs express comparative desirability, and to make transparent that their semantics is meant to mirror, in part, that given by Villalta (2008) for desire reports.2⁸ Thus (427) expresses that the speaker, A(s), desires the proposition expressed by Bill is dumb more than that expressed by Bill is crazy. (427) JBill is more dumb than crazy.KA ≈ λw.wantA(s) (b-dumb)(w) > wantA(s) (b-crazy)(w) If this is right, then Giannakidou and Yoon’s two mores can be understood as follows. Regular more receives the same analysis that I have assumed since Chapter 2, modulo the layer of abstraction over worlds, (428a). That appearing in MCs, moreM2 , includes the attitude predicate, and relates two propositional arguments to a comparative relation between degrees. The claim that moreM2 has propositional arguments dovetails, of course, with the suggestion that the abstract syntax of MCs involves sentence-level modification of the comparative morphology. (428) a. JmoreR2 KA = λdλgλw.λx.g(x)(w) > d b. JmoreM2 KA = λqλpλw.wantA(s) (p)(w) > wantA(s) (q)(w) Both this account and mine posit sentence-level interpretation, and both invite thinking that MCs involve the expression of an attitude. The differences that matter, though, are (i) the idea that the comparative morphology is ambiguous, and (ii) their contention that MCs involve expression of comparative preference. As I said in relation to Morzycki’s account, plainly I reject (i), but I don’t see this as a strong argument against accounts that accept it. However, it is nonetheless possible to find issue with (ii). First, the account would seem to predict that sentences like (429) report wondering about one’s own preferences, which doesn’t seem right. (429) Ann wonders whether Bill is more dumb than crazy. Second, the examples that they give in support of a preference-based semantics (p. 623) all involve an instance of the comparative form kalitera, which they gloss

2⁶ On the degree relation version of the lexical theory, the interpretation would, equivalently, look like max(λd.dumb(b) ≥ d) > max(λd.dumb(a) ≥ d). 2⁷ Actually the ‘individual anchor’, which is the speaker in matrix MCs. 2⁸ The analysis implied in their paper would paraphrase the interpretation of (427) in English as: ‘The speaker wants Bill to be dumb more than they want Bill to be crazy.’ I won’t push on whether this interpretation is adequate to its task here, though.

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as ‘better’.2⁹ It seems to me that perissotero (‘more’) and kalitera (‘better’) could be importantly different in this respect; however, Giannakidou & Yoon treat them as instances of the same metalinguistic operator. To see the issue, consider one of their examples, (430). Constructing an example in English that conveys the same meaning without using better or rather is exceedingly difficult; my best efforts deliver the unnatural-sounding I’d be poor and healthy more than rich and sick. (430) kalitera ftoxos ke ijiis para plusios ke arostos! better poor and healthy than rich and sick ‘I would rather be poor and healthy than rich and sick!’ One final thought. Giannakidou & Yoon cite as evidence for (i) data from Greek (also Korean, not shown here). This language has two standard markers, para and apoti. When para appears with perissotero (‘more’), (431), there is only an MC-type reading of the sentence; its correspondent with apoti has only the ‘regular’ interpretation. Given that this distinction is marked on the head of the standard clause, however, it doesn’t yet support an analysis in which more itself is ambiguous. (431) o Pavlos ine perissotero filologhos para/apoti the Paul is-3sg more philologist than ‘Paul is more a philologist than a linguist.’

glossologhos. linguist

7.4 Conclusion We have seen evidence for a robust distinction between two classes of comparative sentences: those which have been the topic of most of this book (‘regular’ comparatives), and those I have called ‘categorizing’. The former mainly tracks the -er comparative form and the latter the more form, for those adjectives that can surface either way. I grounded this semantic difference primarily in a syntactic ambiguity, wherein the categorizing comparative involves the morpheme, κ (cf. Embick 2007), and additionally signals sentence-level interpretation of the comparative morphology (cf. Giannakidou & Yoon 2011). At that level, the comparative expresses a comparison between measures of how accurate two propositions are. I defended my bipartite classification against charges of yet greater variety in the comparative typology—including metalinguistic, deviation, and indirect—which in many cases has been taken to suggest that expressions like more are ambiguous, potentially many times over. Finding little systematic differences between these varieties, whether syntactic or semantic, I suggested, then, that the balance of evidence favors a univocal analysis, and offered my own version of such an approach. I can say with confidence that the sketch I’ve offered raises many questions; however, I view it as a proof of concept that can be built up or modified in future research. 2⁹ The one exception is their example glossed, ‘He is goofing off rather than studying’. However, the relevance of preference/dispreference may be attributable to negative valence associated with (the Greek equivalent of) ‘goofing off ’.

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Briefly considering extant, non-univocal proposals for the semantics of ‘metalinguistic’ comparatives, I found some reasons for disfavor and some for doubt. Morzycki’s (2011) approach is similar to mine in its emphasis on degrees of precision, while dramatically different in the implementational details; it’s not obvious to me yet quite where our accounts might make different predictions, except in relation to Morzycki’s charge of ambiguity in the comparative morphology. Giannakidou & Yoon (2011) share with me an emphasis on sentence-level interpretation, but I found their account wanting in its insistence that the relevant interpretations involve a semantics based on preference. The idea that categorizing comparatives are instances of covert accuracy reports raises interesting questions on its own. For one, we have seen that comparatives like (432a) pattern interpretively and distributionally like comparatives with overt accurate in (432b). The analysis I have given provides a template for this correspondence with little difficulty. Yet (432b) seems in turn to be very similar in meaning to (432c) with likely. This suggests avenues for exploration that link up the study of metalinguistic comparatives with that of the semantics of expressions like likely.3⁰ (432) a. Ann is more tall than Bill is wide. b. It’s more accurate to say Ann is tall than to say Bill is wide. c. It’s more likely that Ann is tall than that Bill is wide. With this chapter, I have reduced the number of variant mores from at least four or so to one. At root, there is only one kind of comparative in English, and it is constructed out of two pieces, much and -er, each univocal across their various occurrences. Just as I eliminated many-er in Chapter 5, this chapter shows how the unique semantic properties of a class of comparatives can be supported by the same comparative morphology that supports the others, given other independentlymotivated morphosyntactic assumptions. Differences in dimensionality arise due to what is measured, not which expression introduces the measure. I’ll have more to say about the predictions of my univocal account outside of semantic analysis in Chapter 9. To ensure the broadest semantic coverage for my theory, though, I would like to first consider a few peripheral cases where lexical items have been assigned the semantics of degree, for example nouns like idiot and verbs like want. I argued against lexical degree introduction for gradable adjectives as a class in Chapter 4, assigning that job instead to much. If more is indeed univocal and decompositional, as I have argued, then it should not occur as it does with any lexical item that itself incorporates degree introduction. I consider a few of these cases in Chapter 8, and provide sketches of proposals for their semantics under the auspices of my formal theory. With that, there will be little more that I can say about the semantics of comparatives; and so in the conclusion of the book, I will shift my focus to the relationship between my formal theory and what is known about how comparative constructions are understood and acquired. 3⁰ For a start, see Cariani et al. under review and references therein.

8 The limiting theory

In this chapter, I turn my attention to survey a variety of empirical domains in which a degree-theoretic semantics has been proposed for lexical items other than gradable adjectives. Among these are attitude verbs like want, degree achievement verbs like lengthen, and count nouns like fool (see esp. Bolinger 1972). In general, it appears to me that what have been characterized as diagnoses of scalar structure in such cases can be understood, rather, as diagnostic of order-theoretic structure on the relevant domains of predication. I suggest, thereby, that these cases can be explicated within my general framework, and provide small sketches of how such analyses might look. This work thus amounts to a demonstration of how my theory can be used as a general recipe for analysis, where usually this role has been played by the lexical theory. In my view, the kinds of data that quickly lead researchers to posit lexical measure functions should be seen, rather, as inviting investigation into the order-theoretic properties of the relevant expressions, and how elements of these orderings are mapped to scales. Far from providing evidence for lexical degrees, the behavior of predicates P in comparatives evidences the ontological implications of P. This is so if, as I’ve maintained since Chapter 3, differences in dimensionality reveal differences in the nature and structure of the measured domain. I focus in on cases involving attitude verbs like want (as opposed to know), verbs like lengthen which show variable telicity, and gradable nouns like idiot which are fine in comparatives if embedded in the partitive frame (cp. more of an idiot, ?more idiot). For each case, I will suggest that the availability of a ‘degree reading’ involves accessing a property of states, while the other detectable readings involve prior, quiet mappings to properties of other things. What I won’t do is check whether all of the work usually attributed to lexically-associated scales can instead be done appealing only to the (possibly weaker) orderings so provided. This general recipe raises theoretical questions: when is a degree semantic treatment of a given lexical item appropriate? Is it the case that any non-functional item lexicalizes such a semantics? If not, why not? And if my analytic sketches are on the right track, then what should we expect to see in comparatives as we look across languages? My preferred answers to these questions, of course, are that no lexical item natively incorporates a degree semantics, since this role is uniquely played by (a morpheme like) my much. Among other consequences, this means that languages which show

The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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the comparative constructions proper should not be distinguished from those which don’t by their adjectival lexicon (cf. Bochnak 2010). I will not offer anything like a complete account of the relevant phenomena. My goal is simply to show how they can be profitably approached within the parameters of my theory, in contrast with alternatives.

8.1 Gradable attitudes 8.1.1 Data Some attitude verbs are fully compatible in the comparative, others aren’t. A canonical case of the former class is want, whether in construction with a nominal object, as in (433a), or with a clausal object, as in (433b). The most natural interpretation of these sentences are comparisons between the degrees of Ann’s desire directed at different entities (cupcakes, rice pudding) or states of affairs (her getting coffee, tea). (433) a. Ann wanted a cupcake more than (she wanted) rice pudding. b. Ann wanted to get coffee more than (she wanted) to get tea. Other attitude verbs do not show the same distribution. A canonical attitude verb that is notably awkward when targeted in the comparative is know. Consider that, if Ann knows Bill’s name and his address, it’s not at all obvious what could literally be meant by saying that her knowledge of his name is greater than her knowledge of his address, (434a), and the same for saying one knows, of two people who were right about something, that one knows this more for one individual than for another, (434b). (434) a. ?Ann knew Bill’s name more than (she knew) his address. b. ?Ann knew Sue was right more than (she knew) Bill was. What has not been noticed is that there are ways of sidestepping the natural, ‘intensity’-based reading of comparatives with want, and ways of making comparatives with know felicitous. To see this, consider first the pairs in (435). Targeting a single occasion—e.g., Friday’s lunch—naturally suggests a reading in terms of the intensity of the desire, (435a). Targeting a plurality of occasions—i.e., those that include all lunches from last week—it is more natural to compare numbers of occasions of desiring, (435b).1 (435) a. Each day, students choose between cupcakes and strawberries. Friday lunch, Ann wanted a cupcake more than Bill did. b. In the past days, Ann chose cupcakes three times, Bill only once. Last week, Ann wanted a cupcake more than Bill did. 1 Getting these interpretations for (435) requires you to be generous and entertain that choosing a cupcake requires first wanting one.

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The examples in (434) were well-chosen to illustrate the oddity of know in the comparative, but it is possible to construct contexts in which know is fine here. For example, targeting a single question in a series, it is odd to compare Ann’s knowing the answer to Bill’s knowing the same.2 Considering performance across a series of questions, though, it seems fine to use the same sentence to convey that the number of occasions on which Ann knew the answer exceeded that of Bill, (436b). (436) a. Ann and Bill are competing in a quiz with ten questions. For question 4, ?Ann knew the answer more than Bill did. b. In the end, Ann got 6 questions right, and Bill only got 4. In the quiz, Ann knew the answer more than Bill did. Before diving into the implications of these data, it is important to note that several previous analyses have taken data like that in (433) to suggest the viability of a lexical measure function approach for want. Yet, unlike in the case of gradable adjectives, there is no morphosyntactic evidence supporting such a hypothesis (cf. Rett 2013; cp. Lassiter 2011a, pp. 136–7). For example, in all of the comparative forms outside of those with more, an overt much surfaces, (437). Any advocate of extending the lexical theory to these cases should expect direct composition of the verb and the comparative morphology. (437) a. b. c. d.

Ann wanted a cupcake as much as she wanted an ice cream. Ann wanted a cupcake so much that she couldn’t sleep. Ann wanted a cupcake too much to say ‘no’. Ann wanted a cupcake very much.

And given data like that in (435), it would be nice if we could accommodate degreelike readings alongside what looks like a verbal comparative reading (cf. Chapter 3). I think we can. The literature is rife with much discussion of various of want’s distributional properties; of pertinent interest here, though, is the fact that we can use the deverbal nominal form of want to refer to something, (438a), which can be the antecedent to an anaphor, (438b), and which can be quantified, (438c). The data in (437) and (438) minimally suggest that want introduces something that can be measured. (438) a. The opioid antagonists seem to work in part by affecting the liking of food, as opposed to the wanting of food.3 b. The wanting of food killed him. It came on suddenly, and had disastrous effects. c. With every wanting of food, he dosed himself with glucomannan.⁴ 2 It seems to me that it is possible to interpret (436a) as fine, and true, if Ann knew the answer but Bill didn’t. If so, I don’t have a ready-to-hand explanation for this. 3 Based on an example from The Gravity of Weight, books.google.com ⁴ Glucommanan is a product derived from the fibrous root vegetable konjac which is often used as an appetite suppressant.

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8.1.2 A sketch of a proposal I assume, with others, that attitude verb semantics involves a davidsonian argument (e.g., Kratzer 2006, Villalta 2008, Hacquard 2006, 2008, 2010). This assumption directly supports the introduction of something that can be measured by much, and, as I will show, supports an explanation for why we see this form overtly on the surface of attitude comparatives. What needs to be accounted for, though, are: (i) comparative sentences with want support comparisons both of intensity and number of occasions; (ii) comparative sentences with know, when conditions are right, support only comparisons of numbers of occasions. My account directly supplies a structural ambiguity account for (i); see (439). Assuming that want is ‘born’ expressing a property of states s, which are related to their contents by the Content relation, (440), targeting this property delivers the intensitybased reading, (440a).⁵ (Of course, this assumes that the relevant states are ordered according to how much desire they instantiate.⁶) Otherwise, the verbal singular and plural morphemes from Chapters 5 and 6 can be used to map the stative property a property of pluralities of events, each atomic part of which is temporally constituted by a state of desire, (440b), which delivers the occasions-based reading. (439) a. want

ϕ[θCo ]

moreμ

b. pl want

ϕ[θCo ]

moreμ

sg

(440) Jwant ϕ[θCo ] K = λsv .want(s) & Co(s)(p) a. J[want ϕ[θCo ] ] moreK = λsv .want(s) & Co(s)(p) & μ(s) > δ b. J[want ϕ[θCo ] ] sg pl moreK = λE.∀e(E(e) → ∃s(want(s) & Co(s)(p) & e ⊳ s)) & μ(E) > δ Approaching (ii), it is important to highlight the two-fold contrast between the relevant want and know sentences. First, they differ in whether they intuitively support gradation in extent: while it is plainly possible to want things to different extents, it seems that we either know something or we don’t. This difference can be accounted for by positing that the states predicated of by know, unlike want, are unordered—i.e., the extension of this verb lacks non-trivial structure. Second, they differ in the extent to which one can be in a state of desire or of knowledge transitorily: one can want

⁵ Here and below, I assume p is the interpretation of ϕ, and I abbreviate A(μ) as μ and the contribution of the than-clause as δ. ⁶ A complete account will relativize this ordering to the states’ Holders.

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something at some times and not others, whereas typically once one knows something, that knowledge persists. Depending on how we individuate ‘occasions’, however, it will be possible to quantify over occasions of knowing. For example, in the case of the quiz show, Ann’s knowing the answer more than Bill amounts to Ann demonstrating her knowledge of the relevant answer on six occasions, while Bill only demonstrated his knowledge on four occasions. This could suggest a certain sort of coercive effect in the mapping from states of knowledge to occasions of knowing, perhaps on a par with the effect of pluralizing certain sorts of mass nouns (e.g., my three anxieties are . . .). Thus, an account for (ii) will distinguish the flat stative structure associated with the lexical verb, from a derived plural predicate that will be measured for its number. Such an account suggests an analysis of attitude verbs that disassociates the gradable/non-gradable from the S-/I-level predicates just as it does in the adjectival domain (cf. Pasternak 2017). The two verbs that I have considered—want and know— would instantiate cells on the diagonal of this dissociation: want is gradable, and S-level readings are natural; know is non-gradable, and generally persistent but can be coerced. Filling out such a table has proved, in my initial attempts, to be tricky. Perhaps prefer is gradable and can be naturally S-level, while intend or believe are non-gradable but I-level.

8.1.3 Comparison with previous work As a point of comparison, I will consider Villalta’s (2008) analysis (cf. Stalnaker 1968, Heim 1992; cf. Katz et al. 2012), and Lassiter’s (2011a, 2011b; cf. Levinson 2003). Both capture the gradability of verbs like want by lexically encoding a measure function. Lassiter, though, presupposes that the relevant measure function relates simply to an antecedent degree scale, whereas Villalta derives the scale based on an antecedent ordering between propositions.⁷ My sketch is similar to both: I assume antecedent orderings on states (with propositional contents), and on degrees representing the quantitative relationships holding between the states. Villalta’s (2008) innovation is the addition of a degree-theoretic layer to what is otherwise a fairly standard treatment of attitude verbs: want, on her account, expresses a relation between a wanter, a state of affairs, and degrees representing the extent to which the wanter desires that state of affairs. In brief, the lexical entry she settles on to encode these features (ibid., p.515) is as in (441), where ℱ(R) symbolizes the field of relation R. (441) JwantV K = λdλpλxλw.want(x)(p)(w) > d, where d ∈ ℱ(>desx,w )

⁷ Villalta implements her analysis using a type-theoretically degree-relation starting point, whereas Lassiter starts with measure functions (see Chapter 2). The text eliminates this point of contrast for ease of comparison.

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She derives a degree ordering from, first, a base ordering of the (appropriately relativized) desirability of worlds. The base ordering is defined as in (442a), and an ordering on propositions derived from that base is in (442b); this says that the relation ‘p is more desirable than q’ holds so long as at least one p-world is better than every q-world, and no q-world that is better than every p-world. The correspondence between these two orderings is defined as in (443), making use of the equivalence relation stated in (444). (442) Definition of >desx,w [Villalta 2008, p. 479] a. For any w, w′ , w″ ∈ W, w′ >x,w w″ iff w′ is more desirable to x in w than w″ . b. For any p, q ⊆ W, p >desx,w q iff ∀w′ ∈ q, ∃w″ ∈ p such that: i. w″ >x,w w′ , and ii. ¬(∀w′ ∈ p, ∃w″ ∈ q such that w″ >x,w w′ ). (443) d ∈ ℱ(>desx,w ) iff: ∃p ∈ ℱ(> desx,w ) : d = {z : z ≈ p}

[Villalta 2008, p. 515]

(444) p ≈ q iff: [Villalta 2008, p. 515] ∀r((p >desx,w r iff q >desx,w r) & (r >desx,w p iff r >desx,w q)) Any complete implementation of the proposal I sketched in the previous section will differ from Villalta’s in its starting place—an ordering on states of desire, call it ≼want —and can recover any needed ordering on propositions via the thematic Content function. For example, a bridge between these frameworks might take the form in (445), given attitude holder x and world w. (The two will also differ in that much of the compositional heavy lifting done by Vilallta’s lexical entry for want will be distributed amongst pieces of the functional morphology in my approach.) (445) For all s, s′ ∈ Dom(≺want ), s ≺want s′ iff Co(s) ≺desx,w Co(s′ ). Lassiter, though, charges that while Villalta’s orderings support only ordinal comparisons, the data suggest that more is needed.⁸ He suggests instead that the needed ordering relationships are provided by a full probabilistic structure (see his Lassiter 2011a,b for details and argumentation). On his account, then, a sentence of the form x wants to do A etc. involves recruiting an expected utility function/probability-weighted preference function, 𝔼, via the lexical entry for want; see (446). (446) JwantL K = λpλx.𝔼(x)(p), where 𝔼(x)(p) is calculated w.r.t. x’s beliefs and preferences. In turn, he relates this to a basic ordering on worlds, and in turn to an ordering on propositions. In his (447a), the world ordering is defined with the structure of an ⁸ For example, to capture sentences like I want ϕ much more than ψ.

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interval scale; ≽want2 is read, ‘w1 is more desirable than w2 by more than w3 is than w4 ’. From this the ordering ‘w1 is more desirable than w2 ’ is obtained by the equivalence in (447b), and finally “relates the degree of [. . .] desirability of a proposition to the degree of [. . .] desirability of its component worlds”—i.e., (447c) defines a probabilityweighted preference function.⁹ (447) a. A bouletic preference order 𝒮W want2 is a structure ⟨W, Y, ≽want2 ⟩, where: [Lassiter 2011a, pp.151–2] i. Y ⊆ W × W; ii. ≽want2 is a weak order on Y; and, iii. 𝒮W want2 obeys the usual interval scale axioms.1⁰ b. w1 ≽W want2 w2 iff ∃we ∈ W, (w1 , w3 ) ≽want2 (w2 , w3 ). c. μPwant2 (ϕ) = ∑ (μW want2 × prob(w|ϕ))

[Lassiter 2011a, p.158]

w∈ϕ

Thus, Latter’s want ϕ involves calculating the expected utility of ϕ. The comparative form, then, expresses a comparison between expected utilities. To relate this proposal with my sketch, one first severs the measure function from the interpretation of want, and then checks whether the states-based ordering introduced by that verb can be seen to have the ordering properties that Lassiter wants. I see no barrier to this at present. For example, suppose that, for any attitude holder x, there is an ordering on states s that instantiate x’s subjective preference towards Co(s). If all goes well, a measure of these states will represent expected utility.

8.2 Degree achievements 8.2.1 Data Degree achievement verbs (DAs; Dowty 1979) include lengthen and shorten, (448a), and closely related are verbs like ascend and descend, (448b), among others.11 For simplicity, I refer to both types as DAs, and I focus only on a distinctive semantic property that they share: the implication that an entity in state s at time t is now in state s′ at time t′ , t ≺ t′ . Both show the full panoply of comparative forms; see (449) for example. (448) a. The tailor lengthened the dress. b. The balloon ascended. (449) a. The tailor lengthened the red dress more than the blue dress. b. The red balloon ascended more than the blue balloon. ⁹ As near as I can tell, (447c) helps to elaborate (446), modulo relativization to attitude holder x. 1⁰ See Lassiter 2011a, ch. 3, §2.1.2.3. 11 Rappaport Hovav 2008 calls these ‘property scale’ and ‘path scale’ verbs, respectively. Also related are ‘extent scale’ verbs like eat, also known as ‘incremental theme’ verbs. See also Hay et al. 1999, Caudal & Nicolas 2005, Piñón 2008, Bochnak 2010, and Henderson 2012; Kennedy & Levin 2008 gives a more complete reference list.

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DAs show variable telicity profiles. That is, (448a) is perfectly compatible both with for-phrases (marking atelicity; (450a)), and in-phrases (marking telicity; (450b)). Depending, though, the implications about the dress or the balloon differ: with (450a), it is possible that the tailor has not yet completed the intended lengthening, whereas (450b) implies that she has; the pattern is similar for verbs like ascend, (450a)–(450b), except that (450b) implies initiation of the expected ascent, rather than termination.12 (450) a. b. a. b.

The tailor lengthened the dress for an hour. The tailor lengthened the dress in an hour. The balloon ascended for an hour. The balloon ascended in an hour.

The difference with in-phrases reappears in other grammatical contexts. For example, modified by almost, (451) with lengthen is ambiguous between a reading in which the lengthening almost reached completion, (451a), and one in which it wasn’t initiated, (451b). In contrast, (452) implies no ascending at all; it has no ‘shy of the maximum’ reading, (452a). Also, lengthen fails to license the completion inference from the progressive to the simple past, (453a), while ascend does, (453b). (451) The tailor almost lengthened the dress. a. ‘The dress was lengthened shy of its maximal extent.’ b. ‘The tailor didn’t start lengthening the dress.’ (452) The balloon almost ascended. a. ‘The balloon ascended shy of its maximal extent.’ b. ‘The balloon didn’t start ascending.’ (453) a. If the tailor is lengthening the dress, then it has lengthened. b. If the balloon is ascending, then it has ascended.

[unavailable!] [not valid]

What hasn’t been observed, to my knowledge, is that both verbs have multiple readings in the comparative form. Consider a tailor who is lengthening a red and blue dress. If she has accomplished enough to render the (a) and (b) sentences in (454) true, the inference to (454c) is secured as a comparison by length. The same is true for the inference from (a) and (b) in (455) to (455c), as a comparison by duration. (The reader can check that the same patterns obtain with ascend, mutatis mutandis.) (454) a. The tailor lengthened Red by 3 inches. b. She lengthened Blue by 2 inches. c. Therefore, Red was lengthened more than Blue was. (455) a. The tailor lengthened Red for an hour. b. She lengthened Blue for 45 minutes. c. Therefore, Red was lengthened more than Blue was.

12 In this respect, still, a verb like ascend isn’t importantly different from other DAs like widen, which similarly have an initiative meaning with temporal in-phrases; see Hay 1998, Hay et al. 1999.

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As in the previous case, these data directly suggest my analytic strategy: DA predications first involve a property of states, and second a property of (something like) processes or pluralities of events. The extant alternative—assigning lexical measure functions to DAs—will need more in order to capture data like (454) and (455), and to explain why these verbs require mediation by much in the equative form, e.g., (456). An analysis based on stative predication receives further support from the usual sorts of data involving reference and quantification, e.g., (457c). (456) The tailor lengthened Red as much as Blue. (457) a. Fires in the area affect the lengthening of the road. b. The lengthening of the road was nearly complete. It had been delayed several times. c. With every lengthening of a dress, the tailor grew more despondent.

8.2.2 Sketch of a proposal I consider an analysis which starts by decomposing DAs, or (more generally) change of state verbs. Bobaljik (2012) describes a broad generalization whereby, if a comparative adjective is suppletive, its corresponding change of state verb shows the same suppletion pattern; this can be seen for English and German in (458). He proposes, thereby, that such verbs are constructed out of three pieces: an adjectival root, the comparative morpheme, and one that we may simply refer to as ‘-en’. (458) Comparative suppletion preserved in verbs of change (Bobaljik) good bett-er (to) bett-er English gut bess-er ver-bess-er-n German hyvä pare-mpi para-ntaa Finnish I will show how these pieces may be composed so as to deliver the relevant semantic properties, illustrating using (459). First, the adjectival root is simplex and stative, (460a). Skipping over many issues, the comparative morpheme cmp (this label follows Bobaljik) expresses an inclusion relation between states, (460b).13 (460c) supposes that -en is just like ev in mapping stative to eventive properties, but without imposing the requirement that the es are atoms (cp. Chapters 5 and 6). (459) The pie cooled more than the soup did. (460) a. JcoolA K = λs.cool(s) b. JcmpK = λPλs′ .∃s(P(s) & s′ ⊐ s) c. J-enK = λPλe.∃s′ (P(s′ ) & e ⊳ s′ ) Positing inclusion relations between states requires more structure to these entities than I have so far assumed, such that: if a is in a state of coolness s′ measuring d, then a is 13 My hope is that further analysis will unify such an entry with that otherwise assumed for -er, which is based on greater-than relations between degrees.

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also in many other coolness states s measuring d′ , d′ ≤ d; in other words, a is in many ss such that s ⊒ s′ . Adding cmp to the adjectival interpretation forms a property of these s′ s, (460c). Now the idea is that adding -en existentially quantifies s′ and introduces an event e temporally constituted by s′ , (461b). (461) a. Jcool cmpK = λs′ .∃s(cool(s) & s′ ⊐ s) b. J[cool cmp] -enK = λe.∃s′ (∃s(cool(s) & s′ ⊐ s & e ⊳ s′ ))

[i.e., cooledV ]

If the subject combines with cooledV , then we should say that the pie is the theme of a cooling event, but the interpretation would not tell us how the pie relates to the state of being cool. Preferably, we can say something about the state(s) of the pie, and other things about the events temporally constituted by such states. If the subject combines with the adjectival root prior to cmp, though, the pie would instantiate the initial state of coolness but not its expansions, at least not without saying more. Yet we should like to say that we’re talking about states of the pie in both cases. One way of doing this is to suppose that the subject combines with Adj+cmp prior to -en. Thus. we have a structure like (462b) for (462a) which, applying the normal interpretive rules, derives (463). Here, the pie holds the state s′ which expands s; necessarily, then, the pie holds the state s, as well, and there is no issue with thematic interpretation. (462) a. The pie cooled. b. -en DP[θHo ] the pie

cool coolA

cmp

(463) J(462a)K = ∃e, s′ , s(cool(s) & s′ ⊐ s & Ho(s′ )(p) & e ⊳ s′ ) Under what conditions would such an interpretation be true, though? Suppose that the pie starts out in coolness state s, and at no time enters into a coolness state that includes s. So (462a) is false. But then so is (463): while we have the relevant s, there is no s′ ⊐ s, and without that s′ we have none of the needed es. Now suppose that the pie changed its state a little bit, enough so that (462a) is true; then we have s′ such that s′ ⊐ s, so (463) will be true, too. By design, such a proposal can support the difference between comparisons of degree of cooling and duration of the cooling process. As in previous cases, I take these two readings to suggest a structural ambiguity that supports measurement of the expansion state s′ or the process temporally constituted by s′ , respectively. Structurally, this corresponds to attachment of DegP Adj-cmp prior to -en, or the other way around; see (464). Assuming that DegP is interpreted as in (465), as usual,1⁴ we have the simplified (466a) for (464a) and (466b) for (464b). 1⁴ I suppress reference to the assignment A, and abbreviate the than-clause degree as δ.

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(464) a. -en DegP DP[θHo ] coolV b. DegP -en DP[θHo ] coolV (465) JDegPK = λα.μ(α) > δ (466) a. ∃e, s′ , s(cool(s) & s′ ⊐ s & Ho(s′ )(p) & μ(s′ ) > δ & s′ ⊳ e) b. ∃e, s′ , s(cool(s) & s′ ⊐ s & Ho(s′ )(p) & s′ ⊳ e & μ(e) > δ) Such a proposal would share with Filip (1993, 1999) the idea that DAs involve relating structure in the (embedded) adjectival domain to structure in the (derived) verbal domain. For her, this corresponds to a homomorphic map between a scale and a mereology on events. The present sketch can incorporate this idea via the constitution relation; minimally, this means ⊳ should guarantee at least a homomorphic mapping between states and their expansions (via ⊐), and the temporal structure of the (derived) processes.

8.2.3 Comparison with previous work The predominant degree-theoretic treatment of DAs is given by Hay (1998), Hay et al. (1999), and Kennedy & Levin (2008) (see the last for detailed discussion of previous approaches). Focusing on Kennedy & Levin (2008), the basic idea is that DA interpretation is sensitive to and derives in part from the semantics of their source adjectives (cf. Dowty 1979, Abusch 1986). An obvious correspondence between the two is in their dimension—e.g., both straight and straighten clearly have something to do with the property of being straight. Less obvious is their shared sensitivity to maxima: if a rod is straight, this usually implies it is totally straight, as does saying that it has been straightened. First, they assume that GAs express measure functions (see Chapter 2) from individuals and times to degrees, i.e., type ⟨e, ⟨i, d⟩⟩ in (467), with i the type of times. With a few other pieces, they define a measure of change function. For example, given the measure function md , (468) defines a difference function m↑d , and (469) a measure of change m∆ . This last takes an object x and event e and returns the degree representing the difference in m-degree of x from the beginning to end of e.1⁵ (467) JcoolK = λxλt.cool(x)(t) 1⁵ More needs to be said here, in particular about the relationship between the measures and the events; cf. Kennedy & Levin 2008, fn.15, p.174.

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(468) Difference function [Kennedy & Levin 2008, p.172] For any measure function m from objects and times to degrees on a scale S, and for any d ∈ S, m↑d is a function just like m except that: a. its range is {d′ ∈ S | d′ ≽ d}; and, b. for any x, t ∈ Dom(m), if d ≽ m(x)(t) then d = m↑d (x)(t) (469) Measure of change [Kennedy & Levin 2008, p.173] ↑ For any measure function m, m∆ = λx.λe.mm(x)(init(e) (x)(fin(e)). Given these pieces, the DA associated with (467) is interpreted as in (470); i.e., a measure of change along the coolness dimension. As these authors suggest, the use of the difference function ensures that a minimum point is available for reference (supporting atelic uses of the DA), and any adjective lexically associated with scalar maxima (e.g., straight) will pass along that maximum point to the DA (supporting telic uses of the DA). (470) JcooledK = λxλe.cool∆ (x)(e), ↑ equivalent to: λxλe.coolcool(x)(init(e)) (x)(fin(e)) The interpretation this account would assign to my earlier example, then, is given in (471).1⁶ With e is the cooling of the pie and e′ the cooling of the soup, (471) says that the difference in the pie’s coolness from the start to finish of e is greater than the same calculation for the soup in e′ . This seems exactly right, if the comparative is read as comparing differences in lengths. So far, though, this is the only reading the account will derive. (471) JThe pie cooled more than the soup.K = ∃e, e′ (cool∆ (p)(e) > cool∆ (s)(e′ )) Extending their account so that it allows for both readings isn’t likely to be technically difficult. For example, one might offer the interpretation just given for one parse of the sentence, and alternate this with that of a different parse that involves measuring the duration between the initial and terminative points of the relevant events (e.g., via the temporal trace function τ), instead of those events’ participants. If so, Kennedy and Levin’s account would be structurally similar to the one that I’ve sketched, though they would still differ in where and how they package the semantic work. I leave any extended comparison for the future.

8.3 Gradable nouns 8.3.1 Data I have so far said little about count nouns in comparatives, since their simple combination is odd (e.g., ?more traffic cone). Bolinger (1972), however, observes an important 1⁶ Kennedy and Levin don’t actually treat the comparative cases, but nothing goes obviously amiss with (471).

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contrast within the class of count nouns, dividing fool and person, for example ((472); cf. Tovena 2001, Francez & Koontz-Garboden 2017). While it’s true that anyone who is a fool is also a person, such a fool implies something about how foolish the person is, (472a), while such a person implies something about the type of person they are, (472b). Nouns like fool are ‘intensive’, nouns like person aren’t. (472) a. Such a fool as that will never get ahead in life! b. Such a person as that will never get ahead in life! Morzycki (2005) in particular details how nouns like fool and idiot interact semantically with adjectives like big, e.g., (473). We may observe what appears to be a lack of such an interaction with person, (474).1⁷ That is, big idiot can be used to talk about Bill’s physical size or the magnitude of his idiocy, while big person appears to only be usable to talk about physical extent. The availability of the ‘big in significance’ reading is usually taken to indicate a degree-based reading. (473) Bill is a big idiot. a. ‘Bill is an idiot who is big’ b. ‘Bill has great idiocy’

[big in size] [big in significance]

(474) Bill is a big person. a. ‘Bill is a person who is big’ b. ‘Bill has great personhood’

[big in size] [?big in significance]

Focusing on Morzycki’s discussion, the fact that big appears able to access a ‘degree of N’ interpretation when it composes with nouns like fool and idiot is surprising. By our usual tests, neither noun is gradable, (475); if felicitous combination with comparative morphology minimally diagnoses ordering relations associated with an expression, then the usual tests turn up no evidence for such structure here. The pattern is different with of a: (476a) is fine and seems to mean roughly what more foolish means, while (476b) is odd in the same way that, I suppose, more person-like would be. This asymmetry dovetails with the pattern witnessed in (473)–(474). (475) a. ?Bill is more fool than Ann is. b. ?Bill is more idiot than Ann is. (476) a. Bill is more of a fool than Al is. b. ?Bill is more of a person than Al is. Morzycki (2005) points out that the possibility for the variant readings of a combination like big idiot disappears when that phrase occurs in predicative position: i.e., there is no ‘big idiocy’ reading of (477). Relatedly, languages that allow for adnominal adjectives to alternate syntactically between a prenominal and postnominal position only permit the variant readings in the former (e.g., (478); Morzycki 2005, p.118). 1⁷ I hedge a bit because related constructions in a language like French have two interpretations, and I suspect that the English (474) can be read in two clear ways, e.g.: un grand homme (‘a man big in size’ or ‘a man of importance’ vs un homme grand (only ‘a man of importance’). The correspondence is easier to hear with a noun like man.

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(477) That idiot is big. only: ‘that person is an idiot who is big’ (478) a. Pedro es un idiota grande. Pedro is a idiot great only ‘Pedro is an idiot who is big’ b. Pedro es un gran idiota. Pedro is a great idiot ‘Pedro’s has great idiocy’ or ‘Pedro is an idiot who is big’ Furthermore, both readings are available when big occurs as an attributive adjectival comparative (Morzycki 2005). That is, all of the forms in (479) can be read as comments on the size of the men or the magnitude of their idiocy. Interestingly, we may observe that the equative and degree question forms show evidence of the sort of of a embedding as above, (480) and (479c), yet various imaginable surface forms realizing such elements are impossible: within the comparative, e.g., (480a)–(480c). (479) a. b. c. (480) a. b. c.

Bill is a bigger idiot than Pedro. Bill is as much (of) an idiot as Pedro. How big (of) an idiot is Pedro? ∗

Bill is bigger (of) an idiot than Pedro. Bill is a as much big (of) idiot as Pedro. ∗ How big is Pedro (of) an idiot? ∗

Indeed, there are important differences between nouns like idiot and nouns like person, revealed in cases where the NPs they head occur with intensive modifiers, comparative morphology (with something like of a), and/or gradable adjectives like big. Ultimately, one hopes that any explanation of these differences will link the syntactic and semantic facts. The sketch I offer next attempts to do just this.

8.3.2 Sketch of a proposal Distilling the data just presented, the facts to be explained are: (i) nouns like idiot do not combine directly with comparative morphology; but (ii) of an idiot does; (iii) sentences with big idiot have two readings; and, (iv) so do sentences with bigger idiot. Moreover, only (i) is plainly true of nouns like person. Thus, I contend, the explanation for (i), both for idiot and person, is that their extensions lack non-trivial structure; like other count nouns, they denote flat sets consisting only of atomic individuals. More than this (and as pointed out by Morzycki 2012), idiot raises to salience what it means to be an idiot, whereas person doesn’t do this; Moreover, what it means to be an idiot is, really, just to instantiate some non-zero amount of idiocy—i.e., to be in a certain sort of state. Discussion like this suggests the interpretation in (481) which is a

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property of individuals in some idiocy state; by restricting the function to atoms x, it is plain why idiot doesn’t combine directly with more. (481) JidiotK = λxe : Atom(x).∃s(idiocy(s) & Ho(s)(x)) To capture (ii), though, I need of an idiot to mean more or less what the adjective idiocy means (cp. the rough intuitive equivalence between A has more idiocy than B and A is more of an idiot than B). Applying the usual recipe, this means that the domain of the function expressed by that phrase should be ordered. But this ordering cannot be over the individuals who instantiate some idiocy state, on pain of contradiction; rather, I should want to say that of an idiot orders states of idiocy, not their holders; i.e., an ordering on the domain of a function like that in (482). (482) Jof an idiotK = λsv .∃x(idiocy(s) & Ho(s)(x)) The difference between (481) and (482) is, of course, in which variable is ‘open’ for further modification—x or s. Details aside, the possibility of abstracting over one or the other can support an account of the multiple readings of that noun when it combines with an adjective like big: e.g., big idiot can pronounce either structure in (483). When this phrase occurs in attributive position (as in my analysis of hot coffee in Chapter 2), big is subservient to the noun, which means that it is θ-marked and the composite function is true of individuals, not states. (483) big idiot spells out either: a. bigθ idiot b. bigθ

of an idiot

The structure in (483a), then, supports the ‘big in size’ reading: the states themselves introduced by big will be thematically related to the individuals who instantiate some idiocy, (484a). In contrast, the structure in (483b) supports the ‘big in idiocy’ reading, since now the bigness states will be instantiated, themselves, by states of idiocy, rather than by idiots, (484b). Here’s one way of understanding this: the idiocy states which instantiate bigness are substantially higher in the base ordering on idiocy states than others (cf. Francez & Koontz-Garboden 2017, ch. 6). (484) a. J(483a)K = λx.∃s(bigness(s) & θ(s)(x)) & ∃s(idiocy(s) & Ho(s)(x)) b. J(483b)K = λs′ .∃s(bigness(s) & θ(s)(s′ )) & ∃x(idiocy(s′ ) & Ho(s′ )(x)) These assumptions suggest an approach to (iv), the fact that comparative forms give rise to ‘big in idiocy’-type readings, while also appearing with variant realizations of the of a N structure. At least, I take the patterns in (480) and (479c) to suggest an underlying morphosyntax like (485), and thus inviting the measure of states of bigness that are instantiated by states of idiocy. Here again, then, we should expect that the bigness is about the idiocy, rather than the idiots.

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(485) bigger idiot spells out:

big DegP

of an idiot

This sketch supports a view on the core cases, but does it help explain the Bolinger observation we started with (cf. Francez & Koontz-Garboden 2017, ch. 6)? That is, such an idiot and such a person feel like they are read differently, with the former indicating a high degree of idiocy and the latter a certain type of person. However, if it turns out that such an idiot can also be read as indicating something about a certain type of idiot, then the present account can be extended, wherein such pertains either to the individuals or the states. The sketch presupposes, of course, that person is different from idiot in that it contains no such stative layer; hence it is odd even with of a in the comparative, and is unambiguous when it occurs with big, such, etc.

8.3.3 Comparison with previous work On Morzycki’s (2005) account, nouns like idiot are interpreted very much like gradable adjectives on the lexical theory (cf. Rodríguez Ramalle 2001, Baker 2003, Matushansky & Spector 2005, Schwarzschild 2008). For example, both (486a) and (486b) express properties of individuals which, when mapped to a degree by an embedded measure function, exceed a certain contextual standard, s+dim (i.e., the standard degree for dimension dim); these standards are interpreted as free variables unless revealed by (486c). (486) a. Jidiotd,s+idiocy K = λx.dim+idiocy (x) = d & d > s+idiocy b. Jbigs+size K = λx.dim+size (x) > s+size c. Jdeg-sizeK = λN⟨s,⟨,et⟩⟩ λA⟨e,t⟩ λx.A(ιd(N(d)(x))) On this account, the ambiguity evinced by big idiot tracks whether or not degsize applies to the function in (486a) prior to combination with big. Thus, as near as I can tell, the two readings depend on whether the underlying structure of the phrase delivers the property in (487a), one true of individuals whose degree of (individual) size and degree of idiocy exceed their respective standards, or that in (487b), one true of individuals whose degree of idiocy exceeds the standard for (degree) size. (487) a. Jbig idiotd,s K = λx.dim+size (x) > s+size & dim+idiocy (x) +idiocy = d & d > s+idiocy b. Jbig [ deg-sized idiotd,s+idiocy ] K = λx.dim+size (ιd[dim+idiocy (x) = d & d > s+idiocy ]) > s+size The analysis I’ve sketched attempts to do just what Morzycki’s does, but without appealing to lexicalized measure functions. Additionally, Morzycki’s analysis appears to entertain a certain polymorphic flavor for the interpretation of big, in that his dim+size must apply both to individuals and degrees. In contrast, the stative

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interpretation I give to big applies uniformly to states, and the ambiguity depends on whether that state is instantiated by an individual or some other state. Depending on what that means, exactly, so far it is possible to view the analyses as essentially notational variants. Here, as with the previous case, the question of which is to be preferred awaits future research.

8.4 A general framework 8.4.1 Diagnosing scales, or something else? The sketches I’ve provided suggest a general analytic prescription, given the temptation to posit a degree-theoretic lexical entry for a given expression σ: posit, instead, some minimal ordering on the domain of σ, and check whether more is needed. If nothing else can be taken from this book, it should be that any test suggesting σ is gradable can, at least at first, only be taken as an indication that some order-theoretic properties are important for σ’s interpretation. I hope to have shown that we can get pretty far interpreting a gradable adjective like tall, for example, just as a property of ordered states. If some functional morphology prefers to manipulate degrees, those can be introduced on the basis of lexically-specified orderings by much. This raises the question, of course, whether we need to or should posit any degree-theoretic interpretations outside of the comparative paradigm. To begin to answer this question, it is worth revisiting the path we’ve traveled up to this point. Standard degree semantics interprets gradable adjectives as lexicalizing measure functions, and it is often cited in support of this move that adjectives are a special syntactic category. More recently, though, there has been an explosion in the type and range of extensions of the lexical degree-based analysis across the lexicon. I have attempted to take a step back, re-focusing our attention on how the semantics of comparatives interacts with those lexical items not generally subject to degreetheoretic analyses, and then take another look at the core cases and see whether they should really be treated so differently. What ended up being crucial was that those nouns, verbs, etc. that are acceptable and interpretable in comparatives are independently thought to have non-trivial structure on their domains, for example the way that the semantics of coffee and traffic cone are differentiated in the literature on the mass/count distinction. Appeal to such structures supported a simple formulation of the distribution of lexical items in comparatives, and in how dimensions are fixed in their interpretation. There is, of course, no necessary implication from detecting that an expression is gradable, to a type-theoretic distinction. This implication seems to be widely assumed, however, and is the reason I initially introduced the distinction, instead, between ‘measurable’ and ‘non-measurable’ predicates. Measurable predicates introduce nontrivial structure on their domains, and the measures selected for their comparative occurrences must strongly preserve those ordering relations. Non-measurable

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predicates do not provide such structures, and hence do not natively enter into measure function selection. No degrees need enter the picture, then, until one of these lexical items is targeted by comparative morphology. The program is to see how far we can get with non-degree orderings, and to discover the properties of these orderings based on independent evidence (i.e., drawn from outside of the comparative paradigm). In the case of NPs and VPs, such evidence comes from judgments of cumulativity, divisiveness, atomicity, etc. In the case of APs, so far it has seemed harder to come by. A promising avenue, though, may involve returning our attention to a division between the comparatives proper—constructions with more, as, too, etc.—from so-called degree modifiers—e.g., a lot of, extremely, etc. It would be interesting to develop a theory on which comparative morphology requires degrees, but these others don’t.1⁸ I would like it if, in the end, only one expression introduces the semantics of degree: much. No noun, adjective, verb, or adverb does. An arena in which this theory could be differentiated further from the lexical theory, then, is in language variation. For example, if we find languages wholly lacking in comparative morphology (in the privileged sense), but nevertheless expressions that function like a lot of, extremely, etc., then we may find it easier or harder to explain such gaps depending on the theory. Given mine, we can say such languages lack expression of much. In contrast, the lexical theory would have to say that large swathes of the lexicon are different.

8.4.2 Prospects for language variation Why might a language have just one morpheme that introduces degrees? Why not reproduce its semantics across the lexicon? Eventually, one hopes that this will follow from the nature of language design. For example, lexical meanings might generally instantiate simpler types than is usually assumed, which could aid language acquisition and processing (e.g., Pietroski 2018). Or, it might be that language abhors overlap in meaning, just as much as it abhors synonymy (e.g., the No Containment Condition on grammars proposed by Dunbar & Wellwood 2016). Whatever the cause, if this pattern is not accidental, then it suggests some predictions for the cross-linguistic picture. First, if much does what I’ve said it does, and if this functionality is restricted as it is in English for good reason, then we might not expect to see any language that lexicalizes a degree semantics in the open-class vocabulary. In the limit, this prediction will be difficult, if not impossible to test. It would require a complete description of every putatively distinct language, and then some kind of proof for each of those languages that not one of its lexical items requires a degree-theoretic interpretation. Finding evidence for or against the theory I advocate thus cannot turn on this sort of prediction; at best, it suggests that when we look at a particular language and are tempted to apply 1⁸ That is, most if not all of the adjectival ‘intensifiers’ show all of the vagueness and uncrispness properties that bare APs do, while comparatives are crisp; cf. Fults 2006.

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the degree analysis to a given item, it is worth taking another look to see if we couldn’t, instead, appeal to order-theoretic relations between more basic entities. Second, much scaffolds the enterprise of degree-theoretic manipulation by comparative morphemes, regardless of the lexical category targeted. If this sort of dependency is necessary—that is, if the job of introducing degrees must be taken up separately from the morphemes that introduce the degree relations—then we should expect to see languages like English, with cross-categorial comparatives, and the opposite, languages that show none. We definitely should not find languages which have comparative constructions (say) that target nouns but not adjectives.1⁹ In other words, we should find languages with much, and which consequently show the range of cross-categorial comparatives, or we should find languages without much, and which thus fail to show any of the range of comparatives. This view, in sum, undermines the thought that the category ‘gradable adjective’ is particularly robust. And indeed, there is little cross-linguistic evidence to support it; some languages fail to instantiate the syntactic category ‘adjective’ at all (cf. Dixon 1982, Thompson 1989).2⁰ If interpretation as a degree predicate were restricted to a subset of adjectives, it is unclear exactly what we should predict for adjective-less languages (cf. Francez & Koontz-Garboden 2017). Should they fail to have comparatives? Should they lack words that express concepts like those underlying English tall or intelligent? There do seem to be languages which lack comparatives altogether (see especially Beck et al. 2010; cf. Shimoyama 2012). Bochnak (2013), addressing this sort of puzzle in Washo, suggests that the gap presented by this language is rooted in lexical differences. Instead of expressing a degree predicate, Washo adjectives express (vague) properties: that is, where English tall was interpreted as ‘the measure function that maps individuals of type e to their measure of tallness’, Washo’s equivalent would express something like ‘the property that is true of individuals of type e just if they count as a positive instance of tallness in context c’. In other words, Washo adjectives express what tall plus pos/abs expresses in English on the lexical theory. An alternative diagnosis is, of course, that Washo lacks an expression with the semantics of much. If it is unavailable, then so should any operator that operates on degrees be unavailable. Some caution is warranted here, however. Bochnak (2015) considers this type of explanation for Washo, and points out that Washo’s closest equivalent to the comparative form (e.g., ‘Bill is tall, Ann is not tall’) is equally possible with tall as with their correspondent of English much. However, these constructions show the hallmark properties of vagueness, uncrispness, etc. that morphological comparatives with -er/more lack. For Bochnak, positing that the lexical semantics of the adjectives is

1⁹ Of course, evaluating this prediction depends on whether we should expect languages to differ with respect to whether a given morpheme expresses a function that is neutral with respect to a variety of primitive input types. But given that the correspondents of English more appear similarly univocal across an array of languages, I suspect that languages may not vary much in this way. 2⁰ A summary discussion of such languages appeared on the Linguist List, 4.442, Wed. June 9, 2013, “Sum: Languages without adjectives”.

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different in these languages suffices to explain this pattern, while my conjecture, so he supposes, misses a generalization. To my mind, this matter requires further investigation. For example, does the fact that Washo has a form that patterns like an adjective with respect to its ‘A-not-A’ construction mean that Washo has a translational equivalent of much? It’s not obvious that this is so. Bare occurrences of much in English show the same properties of vagueness, uncrispness, etc. as its overt occurrences. Perhaps all this suggests is that the morpheme I’m describing is covert, only sometimes taking the shape much (cf. Corver 1990). I’m not sure. But I should not like to suggest that Washo isn’t a counterexample to the strong prediction of my theory before this investigation, since it dodges the question of what would count as a real counter-example in the first place.

8.5 In conclusion I explored three distinct domains in which the degree analysis has been extended beyond the adjectival domain, and suggested initial ways of seeing how my theory— which eliminates degrees from the semantics of the contentful vocabulary, wholesale— could profitably be applied to the relevant data. The general recipe I suggested is that, rather than holding fast to the implication that gradability implies a degree-theoretic semantics, we first posit a neodavidsonian entry with order-theoretic properties on its domain. Given evidence of additional structural complexity, whether morphological or syntactic, we can see how those additional structures shift whether an ordering is manipulated, or which ordering is manipulated. With this discussion, I have completed the characterization of my compositional theory of comparatives that I intended to offer, based just on the sorts of evidence that usually motivate analyses in formal semantics: judgments of truth and falsity in context, systematic entailment patterns between classes of sentences, lack of homophony, etc. I defended my theory based on this evidence, and it can thus be seen as no more or less than a theory of how the truth conditions of comparative sentences in English are composed out of a stock of primitive units. In that sense, my work here is done; little more is required in order to have given a semantics for a certain fragment of a natural language. Yet I can say more, and I will. In particular, I should like to say a little about what more means, i.e., how it is understood by speakers, and how it is acquired by children. Moreover, thinking about meaning proper, rather than mere truth conditions, will allow me to zoom out and ask what it is we mean to do when we do semantics, and more importantly, what sorts of data count as evidence for that theory. If the kinds of non-traditional evidence I consider next should weigh in the balance, then we will see evidence for it abounds. Thus in the final Chapter 9, I go ‘beyond the formal’, tackling the question of just what it is we can be said to know, when we say that we know what more means.

9 Beyond semantics

A major claim of this book is that ontology plays a big role in determining how we quantify in comparatives. When more targets a given nominal, verbal, or adjectival phrase, etc., both the sorts of entities in the extension of the phrase, and the structural relationships holding between those entities, restrict the accessible dimensions for comparison: any structural relations must be strongly preserved in the mapping to degrees (i.e., the Monotonicity and Invariance conditions); if the targeted phrase fails to make such relations accessible, then that phrase is indemnified from participating in the comparison construction. Semantic explanations like this raise to the fore: what do we mean by ‘ontology’? Until we get clear on this, it isn’t obvious how we would be able to decide between theories which show this dependence over others. Semanticists tend to cluster along one of two lines in this respect. Either our ontology—the things we take referring expressions to refer to, and quantificational expressions to quantify over—is that of the metaphysician, or it is somehow that of the psychologist. Broadly speaking, these two positions are distinguished by whether they commit to a mind-independent or mind-dependent ontology. This chapter suggests that the present theory, at least, is best understood in cognitive terms. Somehow, the meanings of words must be related to the kinds of (mental) concepts and categories that speakers use to represent and reason about the world. Given appropriate linking hypotheses, it might be possible to explore these connections using the formal semanticist’s toolkit. If so, then it should be possible to use non-traditional sources of evidence to distinguish between fine-grained theoretical proposals. I will focus on two distinctive aspects of my theory—lack of ambiguity, and ontologydependent dimensional selection—and explore how explicating the relevant linking hypotheses can render this theory predictive of observations about how comparative sentences are acquired and understood. To preview some of the relevant facts, young acquirers of English (i) leverage independent properties of conceptualization to determine dimensionality for novel nouns in the comparative (e.g., more fem), and (ii) they easily dispense with such determinations when the grammatical context changes (e.g., more fems). Various studies suggest that this concept- and grammar-sensitive understanding of more is in place early on. Such data thus invite exploration of our semantic theory as specifying an interface between linguistic structure and nonlinguistic conceptualization; to the

The Meaning of More. First edition. Alexis Wellwood. © Alexis Wellwood 2019. First published in 2019 by Oxford University Press.

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extent that this conceptualization is independent of purely worldly contingencies, it is unhelpful to view the theory under its metaphysical interpretation. Perhaps more interestingly, as research in cognitive psychology grows increasingly abstract in its characterization of the relevant conceptual knowledge, tantalizing similarities with our ontologically-rich semantic theories emerge. For example, we often assume that atomic reference jointly distinguishes object- from substance-referring terms, and event- from process-referring terms. On the face of it, a similar distinction is at play in research attempting to explain why, for example, prelinguistic infants are able detect differences in number between two sets of solid objects, but not in the number of piles of sand. If such correspondences are robust, this too suggests the potential fruitfulness of linking semantics with psychological explanation. Meanwhile, degree semantics presupposes the existence of ‘scales’, and psychophysical research is developing explicit models of a variety of systems that humans and other species use to estimate and compare magnitudes. These systems share a common format—all obey Weber’s law, for example—but they have their own individual-specific, content-specific acuity (e.g., one may be better than average at line length estimation, but worse than average at number estimation). One debate in this arena thus concerns whether there is a single, domain-general system for magnitude representation (a ‘universal scale’?), or whether there is a plurality of such systems, individuated by their representational content (e.g., Feigenson et al. 2004, Odic 2017). On a cognitive view of semantics, this debate will interact with how we ultimately think about the meaning of expressions like more. On a non-cognitivist view, it is unclear whether the theory relates to such independent lines of inquiry at all. That is, if the meaning of an expression σ is just a relationship between (the parts of) σ and worldy entities of various sorts, however abstract, then any alignment between our ideas about how our domain entities are structured and the categories that cognitive psychology uncovers should be viewed as suspicious coincidences, at best. A purely non-cognitive, referential semanticist can, of course, happily embrace such a state of affairs; semantics is simply not about psychology (e.g., Lewis 1970; cf. Katz & Fodor 1963). But if facts about how magnitude estimation works end up being important for explaining why comparatives mean what they do, then such an anti-cognitivist project must be regarded as independent of the scientific investigation of linguistic meaning. It should be clear where this goes: an explicitly cognitivist perspective can support greater progress towards explanatorily adequate linguistic theories (Chomsky 1965), and which depends in important ways on the contributions of formal semantics. More narrowly, consideration of a broader set of the semantic properties of any given expression can support the discovery of new generalizations that our traditional models cannot yet account for, thus spurring the development of new models that illuminate a territory long thought impervious to such study. Armed with appropriate demonstrations of the fruitfulness of this framework-level perspective, semantic theory could become a rich source of sophisticated hypotheses about mental representation and the special role of language in human cognition.

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I’ll attempt to make such a case in what follows, stepping through each of these points in more detail.

9.1 Understanding more Comparative expressions are univocal: more is a composite of much plus -er. Semantically, much introduces a context-sensitive measure function μ, and -er a strictly greater-than ordering on the degrees in the range of μ. A theory like this predicts, ultimately, that demonstrating knowledge of the semantics of more σ, where σ is related to one conceptual domain, will immediately pair with such a demonstration for more σ ′ , σ ′ related to a different conceptual domain. That is, competence with more minimally requires understanding how the selection of values for μ is constrained by its measuranda. So long as one has sufficiently adequate prior knowledge of the semantics of the relevant σ, σ ′ , the rest should follow. I developed this theory based on mature (i.e., adult) intuitions about the distribution and interpretation of comparative sentences. Testing any strong prediction it makes, though, requires getting serious about what is meant by ‘the semantics of σ’. Recent research in cognitive psychology can be leveraged in this respect. To the extent that such an exploration supports substantial generalizations about how comparative sentences are understood, it suggests the profitability viewing semantic theory as a relation between linguistic and nonlinguistic representation, rather than as a relation between linguistic representation and worldly entities.

9.1.1 Language acquisition My theory makes two major predictions for acquisition. First, all else being equal, a univocal meaning for more predicts all-or-nothing acquisition: we shouldn’t detect gaps wherein children understand more when it targets adjectives, for example, but not when it targets nouns. Moreover, this understanding should consist in children’s choosing only from among the relevant structure-preserving dimensions for comparison, and a sensitivity to how subtle changes in the morphosyntactic context (such as adding the plural morpheme) shifts the available dimensions. Second, in light of my claim that many is a morphological variant of much, we should expect that any error patterns in children’s acquisition of these forms to be characteristic of morphological rather than semantic acquisition. Children demonstrate comprehension of the meaning of adjectival comparatives by at least three (see Carey 1978 for early discussion and references). In production, they make a variety of errors which appear to reveal developing morphophonological rather than semantic competence. For example, children produce forms like (i) more dirtier (presumably instead of dirtier), (ii) prettiest than (instead of prettiest of ), and (iii)

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orange than (instead of orange as or orange like; see references in Syrett 2016). Errors like (i) could reflect incomplete application of the morphological rules that produce the exceptional -er form, assumed at least since Bresnan (1973). Errors like (ii) could reflect the fact that superlatives are constructed out of comparatives, as conjectured by Bobaljik (2012) in his cross-linguistic survey of comparative and superlative suppletion patterns (e.g., prettier is underlyingly pretty er est). Errors like (iii) could reflect the failure to distinguish one of than or as as exceptional; in many languages, a single form is used here (see e.g. Larson & Wellwood 2015). The best available evidence suggests that children acquire the ability to competently use more targeting nominals within the same developmental time window (e.g., Odic 2017). A couple of differences are observed between children and adults here, however. First, children generally prefer number-based quantification whenever discrete perceptual units are available (cf. Barner & Snedeker 2004); for example, 3- and 4-year-olds counted individual pieces of broken forks when asked ‘how many forks?’ (Shipley & Shepperson 1990). Such a perceptual preference has not been observed in the verbal domain, so far; while we know that even young infants are able to track differing numbers of events (Wynn 1996, Wood & Spelke 2005), they are not likely to count events based on temporal pauses that occur along the way to a goal, at least when the count is requested using telic language (Wagner & Carey 2003; cf. Wagner 2010). Moreover, we have solid evidence that children’s earliest understanding is sensitive to ontology and grammar in the expected ways. Barner & Snedeker (2004) leveraged independent research into the conceptualization of objects and substances to present adults and preschoolers with items varying in the degree to which they intuitively suggested these categories, and both populations answered a more question by number when introduced to the items with count syntax (e.g., Who has more fems?). With mass syntax (e.g., Who has more fem?), adults’ choice of number varied along with the shape complexity of the items, while children (mean: 3 years 3 months) generally answered based on number of discrete units. Relatedly, Odic et al. (2013) found that children as young as this preferred to evaluate by area when presented with a question containing more goo, but by number when given more blobs. This pattern obtains even when the nominal stem is identical (and novel), and children are presented with identical perceptually ambiguous displays (Barner & Snedeker 2005). Finally, the univocal account assigns no special semantic status to the much/many distinction in English. And there is evidence that children’ don’t, either. One of the primary findings of the developmental study by Gathercole (1985) is that children extended much to plural nouns as late as 7 years 6 months, yet never extended many to bare nouns. This error pattern again suggests time taken to acquire a morphological exception. Such a hypothesis could be tested directly by using materials like those in Barner & Snedeker (2006), and varying whether 3-and-a-half-year-olds are asked how much fem or how many fems there are. If they have no semantic difficulties with these forms, they should quantify by number whenever given how many, and be more flexible given how much.

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9.1.2 Psycholinguistics My theory similarly makes predictions for psycholinguistics. First, comprehension by naive adults should show the ontology-dependence of cross-categorial comparatives as specified in my theory. This pattern is so far borne out both in informal judgments and in formal experimental studies. Second, I’d like to claim that variability in dimensional selection for plural comparatives follows as a prediction of my theory. My semantics for comparatives targeting pluralized phrases (whether nominal or verbal) holds only that any measure is permissible so long as it is Invariant with respect to the measured domain; prior accounts, in contrast, hardwire a cardinality function into the compositional semantics of such sentences directly. Thus, if multiple such distinct, Invariant measures are recruited, this is evidence for my theory. First, only one study that I know of attempts to mediate between different proposals about the truth-conditions of adjectival comparatives, and that is Solt & Gotzner (2012). They attempt to distinguish between measure function-based approaches like that assumed in this book, and the rank-ordering based approach of Bale (2006, 2008). On the latter, the default interpretation of a comparative like Ann is taller than Bill is wide is a comparison of the degrees to which Ann and Bill, respectively, count as tall in the context. Instead, the oft-cited intuition that such sentences express measurementbased comparisons reflects a derivative interpretation. Solt and Gotzner’s studies probed this by asking how people evaluated the positive attribution of an adjective to a subject, and found that responses tracked measurement-based statistics rather than rank ordering information. More studies have focused on what we might call ‘sub-truth-conditional’ aspects of the meaning of comparatives, focusing primarily on sentences with most. Here, the motivating idea is that a given description of a function can be understood in two ways: as a format-neutral specification of which input/output pairs define the function, or as a specification of the information used to compute the function (i.e., Church’s 1941 distinction between functions-in-extension and functions-in-intension; cf. Marr 1982, Peacocke 1986). In such an approach, the symbolic outputs of J⋅K can be cast as psychological hypotheses about representational format. In this vein, Hackl (2009) suggested that most sentences do not specify the same computations as more than half sentences, and a variety of studies have furthermore suggested that plural occurrences of most minimally call for numerical information (Pietroski et al. 2009), and different sets when occurring as a determiner or an adjective (Lidz et al. 2011, Tomaszewicz 2011). Importantly, children’s earliest demonstration of competency with most is independent of their knowledge of precise cardinality (Halberda et al. 2008). Just like adults under speeded conditions, children instead use representations from their approximate number system (ANS) to evaluate comparatives with plural nouns. Such data raise the promised questions and potential challenges for accounts that hardcode a semantics based on exact cardinality here. On my theory, however, both

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approximate number and exact number can be possible values for μ with plural XPs, just in case both of these ‘measures’ meet the structure-preservation conditions imposed on that valuation. And indeed, despite the fact that we model exact numbers as points and ANS representations as Gaussian distributions, these two ‘scales’ are isomorphic (e.g., Gallistel & Gelman 1992). Thus, if one satisfies Invariance, so will the other. Such considerations raise the possibility of deep connections between the grammar of comparatives and the cognition deployed for magnitude estimation and comparison. This possibility is suggested by Fox & Hackl (2006). Arguing that all degree scales invoked by natural language are dense (as we would antecedently expect for scales representing height or volume, but not number), Fox and Hackl claim the ability to resolve a grab bag of grammatical puzzles related to exhaustivity, scalar implicature, question semantics, and definite descriptions. They note that, as a consequence, “when we say that John has 3 kids or that he has more kids than Mary, the presupposed scale [. . .] is not the ordered set of natural numbers or anything like it. Instead, it is the same domain of measurements that is needed to capture our intuitions of space and time, something closer to the rational or real numbers” (538)—in other words, just the sorts of structures posited for magnitude estimation systems. This interconnectedness goes deep. Odic & Halberda (2015) presented adult speakers with displays of ‘blobby dots’ (i.e., differently-colored, spatially non-overlapping regions with irregular perimeters), and varied whether they were asked about whether more of the blobs or more of the blob was blue. Their materials, meanwhile, correlated and anti-correlated whether the correct answer was “yes” by surface area or by number. They found that, asked the plural question, participants’ behavioral responses were compatible with approximate number estimation, and implicit measures revealed greater time spent looking at the display with a greater number of individual units and many more short saccades and switches between these units. Asked the mass question, responses were compatible with estimation by area, and participants’ eyes lingered longer on the target with a greater area, with eye movements displaying fewer, longer saccades. Much less is known about how language and cognition interact in the evaluation of verbal comparatives. What evidence exists is suggestive, however. In a questionnairebased study, adult participants judged the relevant dimension for do more V-ing (mass syntax) depending on whether V named an event or activity category (kickV lead to number comparison, danceV to temporal comparison), whereas do more V-s (count syntax) uniformly lead participants to compare by number (Barner et al. 2008). Moreover, Barner et al found that adults understood more kicks (count), more kicking (mass), and more dances in terms of number of discrete events, but more dancing in terms of time. Wellwood & Farkas (under review b) replicates this sort of result using dynamic displays rather than text-based questionnaires, and using verbal (rather than deverbal) language (i.e., eventive jump more vs process move more).

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9.2 The ontological zoo Many linguists consider semantic theory to be a part of cognitive science. Yet there is a tension here between the internalist commitments we inherit from the Chomskian tradition and the externalist commitments of the Lewisian tradition. I would now like to take a high-level perspective on this matter, focusing on how we can view semantic theory such that it vindicates claims to predictive power like those I’ve just made. I will continue to suppose that the theory describes an interpretation function, J⋅K, with morphosyntactic objects as inputs, but at issue is whether its outputs are (i) worldly objects (possible or actual individuals, sets of individuals, etc.), or (ii) mental representations. When explicit, semanticists tend to assume (i), because this helps to maintain a tight connection between the theory and its primary source of data— judgments of sentence truth and falsity. On this view, semantics properly interfaces with (at least) independent theories of metaphysics (Bach 1986b, Bach & Chao 2012). Yet adopting “the ‘correct’ theory of the world” would make doing semantics very hard; in practice, we simply “assume a theory of the world that is isomorphic to the way we talk about it” (Hobbs (1985); pp.19–20). Going far enough, “[o]ne abandons all ontological scruples” (ibid., p.5), and our “ontological zoo” (Bach, 1986b) can contain almost anything we like: individuals, substances, pluralities and kinds of individuals; events, processes, pluralities of events; states, times, worlds, degrees, and facts; incomplete objects, negative events; and on and on. Such profligacy is necessary, of course, if we want to say that v’s being an entity of one sort means that v cannot be an entity of another sort, on pain of contradiction (cf. the ring and the gold; e.g., Parsons 1979). And the demands increase along with the need to posit structural relationships that hold within and between the relevant entities (e.g., at least pluralities, times, and degrees need to be ordered in particular ways). A commonly-accepted position in semantics is to stake out neutral ground between (i) and (ii), citing that “it would be unethical for us as logician or linguist to take a stand” on the matter (Bach & Chao 2012:192, echoing Montague 1973), even “immoral” (Bach 1986b:592); Pelletier (2011), sympathetically, calls this view ‘Semanticism’. With few exceptions (see e.g. Asher 1993, Dölling 1993, Moltmann 2017), we tend to shy away from saying much more about it than this. Agnosticism, though, is not scientifically tenable, since it would render us unable to disprove any semantic theory which depends on properties of the ontology for its explanations. Put differently, semantic theorizing is bounded on the left by independent theories of morphosyntax, with their own conventions for discovery and self-evaluation. Rarely would a semanticist insist on a compositional interpretation that is plainly incompatible with structural assumptions that a syntactician would accept. But what about on the right? Assuming with Hobbs that mapping expressions into physical theory is off the table (this would entail, among other things, that we say how the meaning of chair relates to something like quantum theory), we have two options. Either we find some suitable

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alternative theory that can provide an independent check on the entities and structures that we posit in formulating semantic explanations (i.e., a metaphysics that provides ‘bigger’ entities for (i), or an understanding of cognition that can support (ii)). Or we continue in the agnostic mode, and decline to specify which, if any, independent theory constrains the range of our interpretation function. I think we should reject agnosticism. For one thing, it is supposed to allow us to continue in our casual talk of semantics as relating expressions to ‘the world’, and ‘as if ’ we can use language to express our thoughts about the world. How’s that now? The relative dearth of defendants of (ii) could be due to some wariness about what would constitute a suitably predictive cognitive theory. But the past decades have revealed a lot more about the cognitive systems that plausibly interact with linguistic cognition than the previous, setting the stage for new interdisciplinary collaboration (cf. Spelke’s 2003 review). Perhaps worse, the semanticist might wonder if relating expressions to mind-internal things prevents seeing “how mutual understanding can ever be guaranteed or even achieved”, or “how any truth-conditional account [of meaning] could be involved” in semantics (Pelletier 2011, p.33). But the ‘coordination’ problem in semantics can be reduced to that arising already for perception and conception independently of language. Our perception of a common experience reflects a species-level and species-specific construction, with little transparent relationship to whatever is actually ‘out there’ (cf. Jackendoff 1994, Hoffman 2009). Reference is a problem even when not giving a semantics for natural language. It’s also possible that an approach along the lines of (ii) hasn’t seemed so useful to pursue because the relevant cognitive science hasn’t been couched in the right sort of vocabulary, such that we could see how to connect it up with our disciplinary foundations. (For reasons of time and space, I won’t point to some of the attempts that have been made but which have failed to take hold in mainstream formal semantics.) If so, this could simply highlight the need for a greater degree of interdisciplinary engagement. For his part, Pelletier (2011) expresses some skepticism of relevant work in the direction of (ii) (i.e., Wisniewski 2009). But I think the present question is serious enough that we should look more closely at the generalizations that do exist. And indeed, this sort of survey quickly reveals robust evidence for a host of conceptual categories, there ‘from the get go’ (e.g., Spelke 2003, Hespos & vanMarle 2012), many of which invite quick analogy to the animals that inhabit our semantic zoo. To some extent, experimental results informing how adults and children implicitly understand language to line up with their conception and perception is irrelevant from the perspective of the traditional view in (i). Why not just understand semantic theory as purely computational in the sense of Marr’s (1982) Level 1, as providing statements of certain input/output relations, and leave it at that? In other words, perhaps only theorists motivated to leverage such a theory with algorithmic implementation should pay attention to these results. However, if this amounts to deliberately holding the relevant psychology at arm’s length, then we will be unable to develop explanatorilyadequate theories (cf. Chomsky 1965). For the semanticist, contributing to explanatory adequacy will mean saying how children come to know the meanings of words and

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sentences. Minimally, this will entail accepting a characterization of semantic theory as involving mental representations even at Level 1, and should attend support for investigations into sub-Level 1 semantic properties. I should like to pursue a theory that accepts (ii), which explicitly builds on the descriptive successes of truth-conditional semantics. Recent work at the language– cognition interface provides an initial starting point in its investigations into sub-truthconditional aspects of meaning, getting us closer to Marr’s (1982) Level 2. For example, Lidz et al. (2011) offer an ‘Interface Transparency Thesis’, whereby truth-conditionally equivalent formalizations of a meaning—call it Jσ K, for expression σ—are understood as variant hypotheses about the kinds of information recruited for understanding σ; i.e., Jσ K is a function-in-intension in Church’s (1941) sense. A strong hypothesis invited by this idea is that each symbol in a formal presentation of σ’s interpretation delimits a class of representations or operations that can be invoked during language understanding. Such an exploration opens up new questions that have and will mutually benefit research in formal semantics, cognitive science, and the philosophies of language and of mind. Far from remaining neutral on the question of what sort of stuff occurs ‘on the right hand side’, semantic theory can be seen as, in fact, busily offering testable hypotheses about the representations and operations that linguistic representations call for in the maze of nonlinguistic cognition. And that’s more than okay. At least, if it’s true, semanticists will be well-placed to shine in the relevant interdisciplinary engagements; there are so many things that we theorize to exist or happen, most of which other cognitive scientists haven’t even heard of. And more than just supposing we’re modeling talk ‘as if ’, serious probing into how people represent those things could prove fundamental to understanding our common linguistic and cognitive inheritance. Now cast in the spirit of (ii), the theory I have proposed in this book predicts that how we conceptualize the world, rather than however the world happens to be, should determine dimensional selection in comparatives. We have seen some evidence that such a prediction is likely to be borne out, in the previous sections. What I should really like to see, though, is a test of the very strong prediction that conceptualization predicts semantics in any case when there is no non-conceptual (i.e., “worldly”) reason why dimensional selection should differ. Moreover, such effects should be visible from the very onset of acquisition. In order to ultimately test this prediction for cross-categorial comparatives, we need to have a very good grasp on how such conceptualizations work. I’ll review some of what is known about this in section 9.3, reviewing some relevant studies directed at the semantics–cognition interface, but with a heavier emphasis on results in cognitive psychology proper than I’ve so far attempted.

9.3 Looking inside The mass–count literature often seeks to characterize that distinction based on interactions between grammar and ontology. For example, concrete mass NPs differ from

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singular count NPs in displaying cumulative reference, which suggests that the latter are true of atoms, while mass NPs aren’t (though mass NPs like those headed by furniture may have atomic minimal parts). The telicity literature often characterizes telicity distinctions in VPs similarly (Taylor 1977b, Bach 1986a): atelic VPs are cumulative but telic VPs are not, because the latter are true of atoms etc. This property— reference to atoms—is a precursor for plural reference and numerical quantification, and it has parallel effects on the interpretation of nominal and verbal comparatives. This ontological feature is thus of particular interest for my present purposes. Ideally, we could understand properties like atomicity, cumulativity, divisiveness, etc. in representational terms. Which categories of representation are likely to satisfy atomicity? Which not? Already, such questions have been explored in the literature on object versus substance representation, and they have begun to be explored in studies on event versus process representation. Presently, research in cognitive psychology suggests broad continuity both for object and event representation from infancy through adulthood. This research reveals that objects and events are conceived in particular as the sorts of things that count as ‘one’—i.e., as relevantly atomic. And so we might ask, what factors influence categorization in these terms, such that a given portion of experience is better labeled using a count NP or telic VP as opposed to some other expression? I have asserted that semantic theories which depend on features of the ontology can be fruitfully tested only once this ontology is recast in cognitive terms. And so what we need to do, first, is get a handle on what people think there is, how they come to think there are those things, and how those thoughts or ideas are related to their understanding of the relevant sentences. I’ll discuss some of what is currently known, or will plausibly soon be known, addressing these points.

9.3.1 ‘Oneness’ and atomicity First, let us consider the atomicity property in the nominal domain. Semantically, mass nouns like water, count nouns like cup, and plural noun phrases like cups are distinguished by demonstrating different combinations of cumulative, divisive, atomic, or plural reference (for early discussion, see Quine 1960, Cheng 1973, Cartwright 1975, Massey 1976, Burge 1977, Bunt 1979, 1985, Link 1983, Krifka 1989). And intuitively, nouns that refer like water does apply to substances, cup applies to objects, and cups to pluralities of those very same objects (Parsons 1979, Link 1983, Champollion 2010, 2012, 2017). Formally, then, we might say that object representation is atomic—object categorization frames a portion of experience in such a way as makes sense to say that they is ‘one’ thing, and this in turn licenses talk using singular and plural language. Linking atomicity with object representation suggests hypotheses from semantics to categorization, such that it must include at least ordinary objects (a car), (some of) their parts (a carburetor), and collections thereof (a fleet). But what, independently of language, determines what an object is? Various formal proposals exist: objects strike

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us as having some ‘integrity’ (Moltmann 1998), ‘non-arbitrary structure’ (Prasada et al. 2002), or, as meeting a principle of ‘unity and organization’ (Rips & Hespos 2015) that entities of other categories lack.1 Indeed, they are just the things that meet appropriate conditions for ‘isolation’ and ‘non-arbitrary division’, such that it makes sense to count them (i.e., Frege’s criteria; see Koslicki 1997). It is sensible to count how many cups are on the table, for example, but not how many milks are in the cups. Prasada et al. (2002) argue that we should understand these as conceptual rather than perceptual distinctions. Their experiments studied how people preferred to label one and the same portion of (novel) stuff in object as opposed to non-object terms. Presented with regularly-shaped as opposed to irregularly-shaped stuff (think of clay molded into the shape of a cube as opposed to a splatter), participants preferred to label the former using mass syntax but the latter using count syntax (e.g., a blick vs some blick). Presenting the irregularly-shaped piece alongside others with the same shape, this preference flipped. However, that shift in preference wasn’t merely due to the presence of a multiplicity of pieces: when each was presented with a different shape, participants again preferred the mass description. Thus, their participants appeared to respond to evidence about whether the entity had a non-accidental, perhaps constitutive shape. Wellwood et al. (2018b) replicated Prasada et al.’s result with different materials, and extended it to the event versus process distinction. Based on the semantic analogy discussed at length in this book, we reasoned that the connection between atomicity and non-arbitrary spatial shape should extend to non-arbitrary temporal shape. Thus, we manipulated how, when, and how many times a simple object paused during its traversal of an invisible path. Of primary interest was whether n periodic pauses would lead people to see the movement pattern as non-arbitrary, and thus preferentially labeled in ‘event’ terms, compared to n random pauses. We found that people preferred deverbal plural descriptions for the former (e.g., doing some blicks; Barner et al. 2008) as opposed to deverbal mass descriptions (e.g., doing some blicking), which supports the link between satisfaction of the atomicity property and temporal structure. Importantly, still images corresponding to the dynamic scenes (i.e., pieces of line drawing broken at regular versus arbitrary points) showed the same pattern. Wellwood et al. (2018a) took this result further, asking whether the forced-choice linguistic nature of the task could have influenced these results. In our Experiment 2, we tested the same stimuli as before using a similarity judgment task, presenting pairs of static or dynamic scenes that differed in the regularity of their spatial or temporal shaping, and in the number of spatial or temporal divisions. We reasoned that people should rank pairs of scenes with regularly shaped entities as more similar than displays with irregularly-shaped entities, and that numerical differences between the scenes should be more salient just when the entities have a regular shape. And this is what we found, suggesting that non-arbitrarily divided scenes prompt the choice of count 1 A recent crop of work has investigated context-sensitivity in determining atoms; see e.g. Rothstein 2010, Sutton & Filip 2016.

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over mass descriptions; recognizing non-arbitrariness of form distinctively suggests the appropriateness, and hence the salience, of number.

9.3.2 Substance and process Mass nouns like mud apply anti-atomically. Assuming it is used in a grammatical context that places no further restrictions on its reference (e.g., mass noun occurrences), it reveals the properties of cumulativity and arbitrary divisiveness: the sum of two portions of stuff that are mud is also mud, and for any x that is mud, it is also the case that any arbitrary subparts of x are mud. These properties render N unsuitable for use in counting, since without some indication of what bounds may be imposed nonarbitrarily on what N applies to, any count up to n or m, n ≠ m, will be equally arbitrary. Supposing a cognitive interpretation of the semantic principles, such considerations lead us to expect people to represent and reason about the satisfiers of expressions like mud—intuitively: substances—importantly differently than they do the objects satisfying count NPs. The same formal characterization can be given for the application of atelic VPs like sleep (cf. Taylor 1977b, Ter Meulen 1984, Bach 1986a, Krifka 1989, Jackendoff 1991, Rothstein 2004). Atelic descriptions do not support non-arbitrary counts: Ann slept describes a happening of which it makes no sense to ask how many sleeps were in it, and we can make sense of Ann slept three times last week only by counting something like the minimal occasions which include her falling asleep and waking up again. Such a move marks a conceptual shift analogous to the sorts of maneuvers we make when confronted with expressions like muds. Here too we have the sense that understanding a properly atelic description involves deploying a cumulative and divisive concept of processes distinct from the events satisfying telic descriptions. Meanwhile, evidence is mounting that substance representation indeed is importantly different from object representation, based on asymmetries in tracking ability and quantity estimation. A long-standing result in cognitive psychology is the finding that adults can track up to four moving objects in an array (Pylyshyn & Storm 1988, Pylyshyn 2001). More recently, we have learned that this ability is substantially degraded if the tracked entities appear to ‘pour’ from one location to another (vanMarle & Scholl 2003), i.e., if they move more like substances than like objects. Similarly, 8-month-old infants are surprised when two rigid, cohesive objects made of sand are replaced with one, but they fail to detect two poured piles of sand being replaced with one (Huntley-Fenner et al. 2002). In contrast, infants do detect when a single pile of sand quadruples in size (Hespos et al. 2012; see the review in Hespos & vanMarle 2012). Results like this are taken to suggest the existence of dedicated perceptual-cognitive processes for objects but not substances and vice versa. We know less about whether adults or infants have dedicated mechanisms for reasoning about processes as distinct from events. Certainly, even very young infants represent different kinds of events as distinct (e.g., events of occlusion, containment,

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and support; see Hespos & Baillargeon 2001b,a, Casasola et al. 2003, McDonough et al. 2003). And they are able to extract discrete events from a sequence of continuous activity (Hespos et al. 2009). The experiments reported by Wellwood et al. (2018a,b) have established that similar factors influence whether people categorize a static scene in terms of objects as for dynamic scenes and events. In follow-up work, though, we are testing for the same distinctions with prelinguistic infants. We expect, parallel to the results described in the previous paragraph, that infants will detect differences in the number of temporal breaks in a scene just in case those breaks plausibly support event as opposed to process categorization. If these results bear out, they will present clear instances in which formal semantics was uniquely positioned to generate fine-grained predictions about core cognitive capacities. Without our operative linking hypothesis, data like this would otherwise be left unexplained or even mysterious.

9.3.3 Pluralities Continuing in the same thread, the cognitive interpretation of the theory makes a number of predictions for any case in which we have independent reason to believe that speakers will parse a scene into atomic entities (e.g., those which cannot be arbitrarily divided, and still count as instances of the same type of entity). First, they should be happy to treat multiple instances of the same sort of entity as a coherent group—i.e., a plurality. Second, they should immediately understand that any noun, for example, used to singularly describe one of these entities can be used plurally to describe that plurality. And finally, they should just as immediately understand that the bare form of the noun is anomalous with more, and that only number-based comparisons are possible when the target noun is plural. These predictions appear to be borne out for nominal more (see especially Barner & Snedeker 2004). Given a certain strand of literature in event semantics, we should make identical predictions for pluralities of dynamic entities, novel verbs, and verbal comparatives. These have not yet been tested. First, a number of researchers have discussed explicit and implicit pluralization in the verbal domain (see for example Cusic 1981, Ferreira 2005, Wood 2007, Henderson 2012, Wellwood 2016). Pluralization here imposes the same semantic commitments as in the nominal domain: the base predication must support atomic reference, such that the pluralized property applies to sums of those atoms. As in the cognitive psychology literature on nominal more, what we should like to see here is that the independent likelihood of parsing a scene into a plurality of events (as opposed to merely interrupted process) predicts quantification gleebed more, for novel verb gleeb. Some evidence suggests that these predictions will bear fruit. For one thing, the cognitive infrastructure for representing and reasoning about pluralities of events appears to be in place early on, and to persist into adulthood. For instance, we know that adults’ Approximate Number System—the cognitive faculty responsible for

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generating ‘numerosity’ percepts—is crossmodal, in the sense that it can apply equally well to static and dynamic entities (e.g., a set of dots, a set of beeping sounds). We also know that infants can detect numerical differences between sets of jumping events, even when differences along other continuous dimensions are controlled (Wynn 1996; Sharon & Wynn 1998; cf. Wood & Spelke 2005), and this ability shows much of the same developmental trajectory as comparing sets of objects (cf. Feigenson et al. 2004). Some of the preliminary steps towards a test involving verbal comparatives are currently underway. In Wellwood & Farkas (under review a, b), the base evaluation of verbal and adverbial comparatives were tested. For example, exposed to displays involving two objects moving up and down (the jump condition) or moving from side to side (the walk condition), adults chose number for jump more but equivocated between number and height for walk more, in line with the predictions of the semantic theory.2 This result extends that of Barner et al. (2008), who used a similar design but with text-based descriptions. We were interested in knowing what children might do, and found that 4-year-olds patterned differently than adults: while they were adultlike (if noisier) in their evaluation of adverbial comparatives, they did not differentiate the dimension for comparison with bare more based on the verb. We suspect that this reflects problems with lexical understanding, which we are testing using a novel verb in ongoing work (cf. Carey 1978). We are also working on the cognitive psychology side in order to find scenes that quite directly support the plural versus process interpretation of a dynamic scene, based on minimal variations in the patterns of movement (cf. Zacks 2004), and the presence/absence of regular/irregular temporal pauses. After determining that we’ve got a good grip on the preferrred lens on these stimuli, independently of language, we can see whether labeling a given scene using a novel verb has concomitant, immediate effects on how sentences with gleeb more are understood. If successful, this test will provide an exact parallel in the dynamic domain as that provided by Barner & Snedeker (2004) in the static domain.

9.4 The meaning of more And so there are interesting generalizations about how semantic theory and conceptualization might connect, as revealed by adults’ and children’s understanding of comparatives. I have claimed that a good semantic theory will be able to explain some of these generalizations in terms of how it links morphosyntactic representations with representations and operations in extralinguistic cognition. Focusing on more, can we say something more concretely about how this ‘translation’ might look?

2 This was so, even while (i) the height/distance, number of crossings, and total duration were counterbalanced, (ii) the movement patterns (modulo the difference between horizontal and vertical movement) were identical, and (iii) participants’ dimensional selections were not at all influenced by the verb when they evaluated sentences with higher/farther, more times, or longer.

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9.4.1 Indeterminacy I have maintained the decompositional analysis of expressions like more in which both it and its synthetic variant -er pronounce much plus -er. I was inspired in this by Bresnan (1973), and since Chapter 3 I have modified little about its interpretation apart from specifying the conditions on the selection of appropriate measure functions. much shows meaning underspecification in the sense that it doesn’t necessarily express any measure function in particular (even given a particular measurand), but rather one among a selection that meets certain conditions. Formally, I represented this underspecification in the interpretation of much in the same way that pronoun interpretation is formalized, by assigning the expression an index, typed a certain way, which receives its value from the assignment function. We saw in Chapter 3 that the evidence for an index-based formalization like this is mixed. Minimally, we should expect to see that dimensional resolution with more patterns with the resolution of lexical ambiguity, since this is the way other indexed expressions pattern (see discussion and citations to prior literature in Gillon 2004). I briefly considered an alternative implementation which I called ‘polysemy-based’, which predicts the opposite patterns with respect to the relevant tests.3 The results of those tests were mixed; this, and given that the index-based approach is both easier to implement and less controversial, I chose and maintained this analysis. But, so far, this sheds no light on how we might connect the theory with psychology; to say that a variable receives a value in a context, subject to certain constraints, isn’t yet to say very much. This raises the question of whether the alternative approach, in which much introduces a variable in the metalanguage—i.e., a metavariable—would do better. There are some reasons to think it might. However, such a move would involve theoretical changes that require some care. Given the index-based theory, J⋅K can be seen to exhaustively specify the truth-conditional content of an expression (relative to an assignment function, a context, etc.). Call this the ‘direct’ analysis. Given the metavariable-based theory, we can’t understand J⋅K in this way. While the theory may assign some expressions (those that are not polysemous, for example) their complete truth-conditional contents, polysemous expressions will be assigned contents with a variable awaiting a value. Call this the ‘indirect’ analysis. On the direct analysis, we needn’t expect any principled connection between the functions that can value μ in a given context (except that they are typed in a certain way, and meet the structure-preservation conditions); just so, there need be no principled connection between the different senses of bank, or between the individuals that her can be used to refer to. This fails to dovetail with the fact that quite a lot is shared between how cognition represents and manipulates magnitudes. First, those representations are approximate rather than exact; the spread of guesses around the 3 The two implementations also support different ways of thinking about how conditions like Monotonicity and Invariance are checked. See below.

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actual magnitude increases along with its absolute size; and, the discriminability of two magnitudes depends on their ratio (see e.g. Gallistel 2011). Does this suggest that there might be some principled connection between potential values for μ, i.e., some generalization which the direct analysis fails to capture? The indirect analysis can potentially do it, since it will assign a single interpretation to much; meanwhile its specific interpretation is assigned in conceptual space. Of course, there is a third possibility. There is a debate in cognitive psychology as to whether there exists one general-purpose magnitude system, or whether there are multiple (Odic 2017 outlines the relevant discussion and debate in the context specifically of the meaning of more). If it turns out that there is a single magnitude system, then perhaps we may understand much to contribute just a ‘pointer’ to that system, with its specific content being filled in by details of that system’s internal workings. If there are multiple such systems, a polysemy-based approach seems like it could be promising. The point, for present purposes, is that different ways of formalizing underspecification in the semantics can make it more or less easy to see how language and mind might connect. Finally, the two analyses support different ways of thinking about the conditions on much, namely Monotonicity and Invariance. On the direct analysis, these conditions must be enforced by something like presuppositions on the values that the assignment function assigns in a context (as I’ve assumed). Again, such constraints needn’t tell us anything interesting about those values. Yet given evidence to support the idea that there are interesting principled connections between those values—independently of language—then alternative ways of thinking about the semantics which capitalize on those connections may be preferable. On the indirect analysis, these conditions might be seen not as constraints on the selection of measure functions per se, but as descriptions of the measurement-theoretic properties of the class of operations it is related to.

9.4.2 Magnitude systems and counting Thus, we are invited to consider how the semantics relates to reasoning about magnitudes. There is an enormous literature on the computational properties of such reasoning (see e.g. Dehaene 1997, Feigenson et al. 2004, Halberda & Feigenson 2008, and Gallistel 2011). As noted above, there have been a few occasions on which researchers have conjectured that people understand expressions like more and most to make direct contact with these systems (Fox & Hackl 2006, Pietroski et al. 2009, Lidz et al. 2011, among others). Attempts at making the connections formally precise, whether within a system of two-stage interpretation or not (i.e., the one-stage direct analysis, or the two-stage indirect analysis), have not yet surfaced, however. I take the case of plural comparisons to be informative here. While the vast majority of the literature on quantification in semantics has presupposed that expressions like

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more and most hard-code reference to cardinalities, in concert with certain literature at the morphology-semantics interface (Chapter 5), challenges this assumption. This is important for how we might think about the relationships between these expressions and mental magnitude systems, since the precise counts required for use of the term ‘cardinality’ are not representable by these systems. Thus, the question of whether more is defined in these terms rather than the more general, measurement-theoretic terms I have laid out, dovetails with discussion in cognitive psychology and cognitive development of how exact and approximate number are related. In this respect, a couple of points are worth noting. The approximate number system (ANS) generates percepts of ‘numerosity’ that are isomorphic to the ordering on the natural numbers (Gallistel & Gelman 1992; cf. Odic et al. 2015). It is innate, demonstrably in place within the earliest time window in which it is possible to test (see especially Dehaene 1997), and not only in humans but also in many other species. The ANS supports the evaluation of a host of arithmetic relations and operations over those estimates, including addition and subtraction, etc. In contrast, demonstrating facility with natural number requires an exceedingly lengthy, explicit learning process, which is striking in light of how quickly it appears that almost any other category of word is acquired. (As Gallistel & Gelman 1992 discuss in detail, a child’s ability to explicitly demonstrate natural number understanding could be due to the difficulty in establishing the isomorphism between the structure and meaning of the count list, and representations in their antecedently and easily available ANS.) Second, children’s acquisition of an expression like most in its plural determiner occurrences (e.g., most of the animals are foxes) appears to be independent of their acquisition of the proper meaning of words for natural number: Halberda et al. (2008) observed that children that were fully adult-like in their evaluation of most sentences, up to the limit of their still-developing ANS acuity; a substantial subset of these children failed to demonstrate mastery of the cardinality basics, and another substantial subset did demonstrate such mastery but treated the most sentence as if exact number had nothing to do with it. Thus, there appear to be at least some reasons to suspect that there is a basic or primary connection between comparative interpretation and the extralinguistic systems involved in magnitude representation; any connection with precise number develops later, if at all (cf. Pica et al. 2004).

9.4.3 One to one, or one to many? One way of thinking about the relationship between morphosyntactic and extralinguistic units is that it is one to one. Then it would simply be a matter of discovery which pieces of morphosyntax are related to which dedicated representations or operations in nonlinguistic cognition. Such an approach can certainly be methodologically useful (see e.g. recent discussion and references in Tucker et al. 2017, forthcoming). However, the kinds of considerations I just raised suggest that discovering whether it is true will depend on very many factors, both properly linguistic and nonlinguistic, and there may

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already be reasons to suppose that we get a high degree of alignment in some cases but not others. Glanzberg (2014), for example, supposes that the semantics of some expressions involves (whether wholly or partially) pointers to concepts properly outside of the language system.⁴ These pointers fill in the truth conditional contributions of the expressions that bear them, and their distribution is restricted just to those cases where, otherwise, semantic theory has very little of explanatory value to offer. According to Glanzberg, this is so for most (but not all) lexical items, while the pieces of functional vocabulary—the grammatical ‘glue’ holding sentences together—gets its meaning properly within the language system. But if it turned out, for example, that there was a domain-general concept of measurement, why not suppose that a functional item like more could simply point to it? These considerations raise a number of issues, none of which can be treated here in any detail. But there are reasons to think that a one-to-one mapping is too stringent a requirement for our theorizing, and reasons as well to think that out-sourcing meaning to nonlinguistic cognition in the general case will not be satisfying. For the first, a oneto-one relationship makes it difficult to see how we might distinguish lexical ambiguity from polysemy. For the second, one might think that one of the very special properties of human language is the generality that it affords to human thought (cf. Spelke 2003). If all we supposed was that linguistic meanings link pieces of syntax with concepts that, in many cases, are domain-specific and isolated from other ones, it would be difficult to see how that kind of generality could ever emerge. Thinking about how a human language could support transcending the modular limitations of a cognitive architecture will involve thinking seriously about what meanings are, and semanticists can play this game only by taking the cognitive interpretation seriously. What’s more, it may be that progress can’t be made on such a question until semanticists get involved in finding their answer. Our pursuit is geared almost entirely towards explicating the semantic properties of the functional vocabulary which, unlike lexical items like coffee and run, have endlessly fascinating syntactic and semantic stories. Figuring out what words like more mean, then, is likely to have a transformative effect on cognitive science that shouldn’t be underestimated.

9.5 Conclusion The semantics of more invokes the concept of measurement. Figuring out whether a sentence with more is true often involves checking in with cognitive systems that represent and compute magnitudes. In this chapter, I’ve suggested that a complete theory of the meaning of such an expression will link these ideas—the formal and the cognitive—which in turn can deliver new avenues for inquiry into the nature ⁴ Glanzberg is careful to say that we needn’t construe this theory internalistically, though I will here.

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of language and mind. The cognitive science of the future, in my view, will draw on formal semantic description as a means of developing novel and sophisticated hypotheses about mental representation. The linguistics of the future will say how the functional and contentful vocabularies of language interact with mental representation in the ways that they distinctively do. Hopefully, it will also say why they interact in those ways. The semantic theory I offered assigns little heavy lifting to any element of the openclass vocabulary, and very little to any particular element of the closed-class. Instead, morphemes like much and -er, appropriately generalized, each have a job to do, and they do their job wherever they occur. Meanings get fancier as the number of functional morphemes increase, and combine in just the way that they do. This sort of theory raises to the fore questions about the set of possible (functional) morphemes, and restrictions on that set such that we should expect to see decomposition like this all over the place. I’ve barely scratched the surface of these questions here, instead preferring to focus my attention in this chapter on connections between formal semantics and neighboring disciplines. Drawing and elaborating these disciplinary connections will deliver new sources of evidence that can be leveraged in evaluating our semantic theories, whether narrowly descriptive or broadly theoretical. There is much that we can say about these connections already, but, as always, we have far more yet to do.

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Index accuracy reports 142 adjectives antonyms 19 attributive occurrences of 29, 51, 77 nominalizations 67, 85 non-gradable 13, 15, 25, 36, 114 positive occurrences of 15, 20, 28 semantics arguments for states 67, 121 compositional theory of 73, 75 lexical theory of 22, 25, 26, 30, 130 vagueness of 17, 85, 175 with very 82 adverbs bieventive analysis 128 non-gradable 16, 32 semantics compositional theory of 73, 75, 79 lexical theory of 31, 32 aspect imperfective 42 perfective 33, 41 cognition 177, 178 magnitude systems 178 mental magnitudes 182, 191, 192 modularity 188 comparatives attitudes 160 comparison of deviation 19, 148 composition more of an idiot 170 adjectival 28, 78, 120 adverbial 32, 33, 79 attributive adjectival 78 nominal 52, 104 post-adjectival 124 verbal 53, 106 with κ 147 crispness 17, 85 degree achievements 165 dependent clauses 26, 27 differentials 57 indirect comparison 148 metalinguistic 135, 148, 151 morphemes 25, 31 typology of 14, 15, 38, 40, 174 cross-linguistic 18, 71 regular vs categorizing 135 subcomparatives 18, 66, 79, 134

covert morphemes degree-based abs 29, 31, 56, 84, 130 many 90 much 35, 37, 38, 41, 80 pos 29 Meas 58 Quantity 58 non-degree-based κ 135 sg 95, 105, 107, 123 little-e 29–30, 57 little-v 24 verbal plural 91 degree pluralities 51 degree semantics much 48 indeterminacy 54, 64 framework 17, 22 compositional recipe 157, 173 dispensing with degrees 80 motivation for degrees 18 intervals 19, 20, 58 positive vs negative degrees 19 scales 13, 19, 20 antecedent vs constructed 20 contextual selection 35, 37, 48, 64, 74, 105, 107, 114, 125, 148, 158, 160, 164, 180, 182, 187, 189 density 182 formal properties 20 operations 51, 76 delineation semantics 17, 18 discourse 122 domain restriction 48, 86 evaluativity 138 explanatory adequacy 185 formal semantics comparatives 52 direct objects 29, 30 framework 23 conventions 25 foundational questions 184 rules 23 types 23, 29, 31 with events 24

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formal semantics (cont.) existential closure 25 thematic binding 24, 32, 124, 129 incommensurability 18, 65, 79 language acquisition 177, 179, 180 number 181, 193 languages other than English Bangla 99 Breton 95 Bulgarian 41, 42, 91 Classical Arabic 95 Czech 72 Fox 95 German 123 Greek 71, 155 Hebrew 95 Italian 72, 99 Macedonian 72, 99 Mandarin 99 Ojibwe 95 Russian 95 Serbo-Croatian 71 Spanish 91, 99 measurability 36, 49, 62, 73, 88, 89, 98, 173 measurement in semantics 13, 192 compositional theory 35, 38, 48, 75 lexical theory 34 monotonicity 35, 38, 40, 42, 49, 50, 100, 102 permutation invariance 103, 182 intensive vs extensive 62 practical vs conceptual 14, 34, 38 theory 34 mereological semantics 38, 40, 42, 43 anti-atomicity 47 atomicity 43, 44, 47, 94, 96, 105, 186 constitution material 96, 100 temporal 97, 107, 123 grammar mass and count 43, 95 plurality 94 telicity 44 part-of structures 45, 50 plural 98, 100, 101 reference 186 cumulativity 43, 94, 101 divisiveness 43, 95, 101 homogeneity 43 state structures 74, 104, 146 modality 145, 147, 153, 158, 161 morphology 193 κ 144 many 99, 101 much 99

as many 99 cross-linguistically 71 deletion 70 distribution 37, 69 insertion 70 with very 82 comparative adjectival 13, 15 analytic vs synthetic 137 nominal 15, 36, 37, 39 verbal 16, 36, 37, 41 comparative morphemes adjectival 69 plural 95, 108 singular 95 suppletion 165 nouns fool vs person 169 plural occurrences of 39, 89 positive occurrences of 15, 29 singular count 36, 39, 40, 43, 89 ontology 177, 183 events 188 objects 186 processes 188 substances 188 talk ‘as if ’ 185 plurality 94, 97, 109, 124, 158 pragmatics 85, 140, 143, 148, 149, 151 psycholinguistics 181 eye movements 182 forced choice task 187 functions-in-intension 181 similarity judgments 187 syntax classical vs non-classical DegP 27 comparative clauses ‘high’ adjectival 125 adjectival 120 adverbial 32, 128 attitude VPs 160 attributive adjectival 31 degree achievements 166 post-adjectival 124 with κ 144, 147 dependent clauses 26, 27 direct objects 30 regular vs categorizing 138 transitive clauses 30 thought 194 verb phrases arguments for states 159 atelic 40, 92 telic 41, 42, 91, 92