The Compositional Nature of Tense, Mood and Aspect: Volume 167 (Cambridge Studies in Linguistics, Series Number 167) 1108839282, 9781108839280

Table of contents :
Cover
Half-title Page
Series Page
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Preface
1 Introductory Chapter
1.1 Roadblocks to Compositionality
1.2 Finding Our Way in Babylon: Terminological Problems
1.3 A Brief Inspection of the Chapters
2 How to Deal with the Long Tradition of Going Ternary?
2.0 Introduction
2.1 The Reichenbachian Matrix in Different Forms
2.1.0 Introduction
2.1.1 3 × 3 for Latin
2.1.2 Three Times 2 × 3 for Dutch
2.1.3 Reducing 3 × 3 to 7 for English
2.1.4 3 × 3 for Classical Greek
2.1.5 Two Times ((3 × 3)-2) for French
2.2 Ternary with Intervals
2.2.0 Introduction
2.2.1 The Present Perfect Puzzle
2.2.2 Topic Time as a Key for the Solution to the Present Perfect Puzzle
2.2.3 A Pragmatic Solution
2.3 Points and Intervals
2.3.0 Introduction
2.3.1 Point of Evaluation
2.3.2 A Point as a Landmark
2.3.3 The Fleeting Point n
2.4 Conclusion
3 Binary Tense Structure
3.0 Introduction
3.1 A Brief Survey of Te Winkel's Binary System
3.2 Binary Operators
3.2.0 Introduction
3.2.1 Dyadic Branching and Binary Tense
3.2.2 Preparing for the Semantics of Binary Operators
3.3 The Present Tense Domain
3.3.0 Introduction
3.3.1 Distinguishing between Present and the Fleeting point n
3.3.2 Simple Present
3.3.3 Present Perfect
3.3.4 Taking a Snapshot at n
3.3.5 Simple Future and Future Perfect in the Present
3.4 The Past Tense Domain
3.4.0 Introduction
3.4.1 Anteriority Seen as a Relation between Two Temporal Structures
3.4.2 Simple Past
3.4.3 Past Perfect
3.4.4 Simple Future and Future Perfect in the Past
3.5 A Compositional Account of Tense Structure
3.5.0 Introduction
3.5.1 Ontological Preliminaries: Events or Indices
3.5.2 The Semantics of the Operators pres and past
3.5.3 Negation
3.6 Conclusion
4 Naive Physics and Aspectual Composition
4.0 Introduction
4.1 What Did Aristotle Tell to Ryle, Vendler and Kenny?
4.1.0 Introduction
4.1.1 Formal Semantics and Aristotle
4.1.2 Tense Oppositions in Aristotle's Metaphysics
4.1.3 Translation Problems
4.1.4 At the Bottom of the Aristotelian Notion of Motion
4.2 On the Idiosyncrasy of Criteria for Aspectual Classification
4.2.0 Introduction
4.2.1 Ryle's Criterion for Allowing Achievements: Finis
4.2.2 A Binary Alternative to Ryle's Exchangeability Criterion: The Report Mode
4.2.3 Vendler's Criteria for a Quadripartition
4.2.4 Kenny's Criteria for a Tripartition
4.2.5 Monadicity as the Disturbing Factor
4.3 Features of Aspectual Composition
4.3.0 Introduction
4.3.1 Aspectual Features and Beyond
4.3.2 Doing Away with Features
4.4 Conclusion
5 Levels of Interaction between Aspect and Tense
5.0 Introduction
5.1 At the Bottom of a Predication
5.1.0 Introduction
5.1.2 Type and Token
5.1.1 Grounding a Verb Opposition
5.1.3 Function Format
5.2 Discretization and Bounding
5.2.0 Introduction
5.2.1 Intransitive Verbs Expressing Discretization
5.2.2 Discretization and Bounding by the Internal Argument of Transitive verbs
5.2.3 Wavering between d◦su and su
5.2.4 The Role of the External Argument
5.3 A Formal Account from Lexical Bottom to S[sub(0)]
5.3.0 Introduction
5.3.1 Syntax and Semantics of Noun Phrases
5.3.2 Discretization in Sentences with Transitive Verbs
5.3.3 Discretization in Sentences with Unaccusatives and Unergatives
5.4 Conclusion
6 Binary Tense Structure and Adverbial Modification
6.0 Introduction
6.1 On the Role of Det and NP in a Temporal Adverbial
6.2 Syntax and Semantics of Non-deictic Modification
6.2.0 Introduction
6.2.1 The Predominance of Tense over Temporal Modifiers
6.2.2 Temporal Modification as a Form of Bounding
6.2.3 Connecting a Temporal Modifier to Indices at Different Levels
6.2.4 Non-deictic Relational Adverbials
6.2.5 Modification below S[sub(0)]
6.3 Frequency and Habituality
6.4 Syntax and Semantics of Deictic Modification
6.4.0 Introduction
6.4.1 Deictic Setting Adverbials
6.4.2 Deictic Relational Adverbials
6.4.3 A Structural Solution to the Present Perfect Puzzle
6.4.4 Comparing Solutions
6.5 Syntax and Semantics of Durational Adverbials
6.5.0 Introduction
6.5.1 Measuring below S[sub(0)]
6.5.2 Computing the Length of Indices
6.5.3 Computing Length at Higher Levels
6.5.4 Further Escapes from the in/for-Test
6.6 Conclusion
7 How to Deal Binarily with ...?
7.0 Introduction
7.1 The Semantics of the Progressive Form
7.1.0 Introduction
7.1.1 Attempts to Resolve the Alleged Imperfective Paradox
7.1.2 A Binary and Compositional Analysis of the Progressive Form
7.2 Binary Indices, Compositionality and Slavic Aspect
7.2.0 Introduction
7.2.1 pf vs [+t] and ipf vs [–t]
7.2.2 Dividing pf and ipf between Three Levels
7.2.3 Temporal Definiteness and Indefiniteness
7.2.4 Lexical and Grammatical Aspect
7.3 The Position of the Aorist in a Binary System
7.3.0 Introduction
7.3.1 The French Passé Simple
7.3.2 The Imperfective and Perfective Aorist in Bulgarian
7.3.3 Comparing Choices in Rich Tense Systems
7.3.4 The Aorist and the Third Binary Opposition
7.4 Conclusion
8 Tense, Mood and Aspect
8.0 Introduction
8.1 On the Nature of the Opposition between syn and post
8.1.0 Introduction
8.1.1 Existential Quantifiers and Modal Configurations
8.1.2 Indicative vs Subjunctive Mood?
8.2 Modality and Future: Linguistics or Philosophy?
8.2.0 Introduction
8.2.1 The Seabattle Tomorrow
8.2.2 Ockham or Peirce, Prior or Te Winkel?
8.2.3 Modal Base and Accessibility
8.2.4 Adapting the Connectives Introduced by syn and post
8.3 The Proof of the Modal Pudding …
8.4 Reaching the Top: Temporalization by pres and past
8.5 Rounding Off
Appendix
Bibliography
Author Index
Subject Index

Citation preview

THE COMPOSITIONAL NATURE OF TENSE, MOOD AND ASPECT

Bringing together fifty years’ worth of cross-linguistic research, this pioneering monograph explores the complex interaction between tense, mood and aspect. It looks at the long way of combining elementary semantic units at the bottom of phrase structure up to and including the top of a sentence. Rejecting ternary tense as blocking compositionality, it introduces three levels obtained by binary tense oppositions. It also counters an outdated view on motion by assuming that change is not expressed as having an inherent goal but rather as dynamic interaction between different number systems that allows us to package information into countable and continuous units. It formally identifies the central role of a verb in a variety of argument structures and integrates adverbial modifiers into the compositional structure at different tense levels of phrase structure. This unique contribution to the field will be essential reading for advanced students and researchers in the syntax-semantics interface. H E N K J . V E R K U Y L is Professor Emeritus at the Utrecht University Research Institute UIL OTS. This book rounds off a suite of works on tense and aspect, including On the Compositional Nature of the Aspects (1972), A Theory of Aspectuality (Cambridge University Press, 1993) and Binary Tense (2008).

CAMBRIDGE STUDIES IN LINGUISTICS

General Editors: U . A N S A L D O , P . A U S T I N , B . C O M R I E , T . K U T E VA , R . L A S S , D . L I G H T F O O T , K . R I C E , I . RO B E RT S , S . RO M A I N E , M . S H E E H A N , I . T S I M P L I

The Compositional Nature of Tense, Mood and Aspect

In this series 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134.

135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154.

N E I L S M I T H:

Acquiring Phonology Onsets: Suprasegmental and Prosodic Behaviour C E D R I C B O E C K X , N O R B E R T H O R N S T E I N and J A I R O N U N E S : Control as Movement M I C H A E L I S R A E L : The Grammar of Polarity: Pragmatics, Sensitivity, and the Logic of Scales M . R I TA M A N Z I N I and L E O N A R D O M . S AV O I A : Grammatical Categories: Variation in Romance Languages B A R B A R A C I T K O : Symmetry in Syntax: Merge, Move and Labels R A C H E L WA L K E R : Vowel Patterns in Language M A R Y D A L R Y M P L E and I R I N A N I K O L A E VA : Objects and Information Structure J E R R O L D M . S A D O C K : The Modular Architecture of Grammar D U N S TA N B R O W N and A N D R E W H I P P I S L E Y : Network Morphology: A Defaults-based Theory of Word Structure B E T T E L O U L O S , C O R R I E N B L O M , G E E RT B O O I J , M A R I O N E L E N B A A S and A N S VA N K E M E N A D E : Morphosyntactic Change: A Comparative Study of Particles and Prefixes S T E P H E N C R A I N : The Emergence of Meaning H U B E R T H A I D E R : Symmetry Breaking in Syntax J O S É A . CAMACHO : Null Subjects G R E G O R Y S T U M P and R A P H A E L A . F I N K E L : Morphological Typology: From Word to Paradigm B R U C E T E S A R : Output-Driven Phonology: Theory and Learning A S I E R A L C ÁZAR and M A R I O S A LTA R E L L I : The Syntax of Imperatives M I S H A B E C K E R : The Acquisition of Syntactic Structure: Animacy and Thematic Alignment M A R T I N A W I LT S C H K O : The Universal Structure of Categories: Towards a Formal Typology F A H A D R A S H E D A L - M U TA I R I : The Minimalist Program: The Nature and Plausibility of Chomsky’s Biolinguistics C E D R I C B O E C K X : Elementary Syntactic Structures: Prospects of a Feature-Free Syntax P H O E V O S PA N A G I O T I D I S : Categorial Features: A Generative Theory of Word Class Categories M A R K B A K E R : Case: Its Principles and Its Parameters W M . G . B E N N E T T : The Phonology of Consonants: Dissimilation, Harmony and Correspondence A N D R E A S I M S : Inflectional Defectiveness G R E G O R Y S T U M P : Inflectional Paradigms: Content and Form at the Syntax-Morphology Interface R O C H E L L E L I E B E R : English Nouns: The Ecology of Nominalization J O H N B O W E R S : Deriving Syntactic Relations A N A T E R E S A P ÉREZ - LEROUX , MIHAELA PIRVULESCU and Y V E S R O B E R G E : Direct Objects and Language Acquisition M AT T H E W B A E R M A N , D U N S TA N B R O W N and G R E V I L L E G . C O R B E T T : Morphological Complexity M A R C E L D E N D I K K E N : Dependency and Directionality N I N A T O P I N T Z I:

155. 156.

L A U R I E B A U E R:

Compounds and Compounding Communicative Functions and Linguistic Forms in

K L A U S J . K O H L E R:

Speech Interaction 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168.

K U R T G O B L I R S C H : Gemination, Lenition, and Vowel Lengthening: On the History of Quantity in Germanic A N D R E W R A D F O R D : Colloquial English: Structure and Variation M A R I A P O L I N S K Y : Heritage Languages and Their Speakers E G B E R T F O R T U I N and G E T T Y G E E R D I N K - V E R K O R E N : Universal Semantic Syntax: A Semiotactic Approach A N D R E W R A D F O R D : Relative Clauses: Structure and Variation in Everyday English J O H N H . E S L I N G , S C O T T R . M O I S I K , A L I S O N B E N N E R and L I S E C R E V I E R - B U C H M A N : Voice Quality: The Laryngeal Articulator Model J A S O N R O T H M A N , J O R G E G O N Z ÁLEZ ALONSO and E L O I P U I G - M AY E N C O : Third Language Acquisition and Linguistic Transfer I R I N A N I K O L A E VA and A N D R E W S P E N C E R : Mixed Categories: The Morphosyntax of Noun Modification A B R A H A M W E R N E R : Modality in Syntax, Semantics and Pragmatics G U G L I E L M O C I N Q U E : The Syntax of Relative Clauses: A Unified Analysis H E N K J . V E R K U Y L : The Compositional Nature of Tense, Mood and Aspect S A N D R O S E S S A R E G O : Interfaces and Domains of Contact-Driven Restructuring: Aspects of Afro-Hispanic Linguistics

Earlier issues not listed are also available

THE COMPOSITIONAL NATURE OF TENSE, MOOD AND ASPECT HENK J. VERKUYL Utrecht University

University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 103 Penang Road, #05–06/07, Visioncrest Commercial, Singapore 238467 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781108839280 DOI: 10.1017/9781108989732 c Henk J. Verkuyl 2022  This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2022 A catalogue record for this publication is available from the British Library. Library of Congress Cataloging-in-Publication Data Names: Verkuyl, H. J., author. Title: The compositional nature of tense, mood and aspect / Henk J. Verkuyl. Description: New York : Cambridge University Press, 2022. | Series: Cambridge studies in linguistics | Includes bibliographical references and indexes. Identifiers: LCCN 2021024736 (print) | LCCN 2021024737 (ebook) | ISBN 9781108839280 (hardback) | ISBN 9781108989732 (ebook) Subjects: LCSH: Grammar, Comparative and general–Tense. | Grammar, Comparative and general–Mood. | Grammar, Comparative and general–Aspect. | BISAC: LANGUAGE ARTS & DISCIPLINES / General | LANGUAGE ARTS & DISCIPLINES / General Classification: LCC P281 .V395 2021 (print) | LCC P281 (ebook) | DDC 415/.6–dc23 LC record available at https://lccn.loc.gov/2021024736 LC ebook record available at https://lccn.loc.gov/2021024737 ISBN 978-1-108-83928-0 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

To the smallest circle of warmth and love around me divided over three generations: 1. to Gina, my wife; 2. to David and Antoinette; to Judith and Ole; to Jessica and Martin; 3. to Mischa and Noah; to Tijn, Yaël and Siem; to Luna and Liza.

Contents

List of Figures List of Tables Preface 1

Introductory Chapter

1.1 1.2 1.3

Roadblocks to Compositionality Finding Our Way in Babylon: Terminological Problems A Brief Inspection of the Chapters

2

How to Deal with the Long Tradition of Going Ternary?

2.0 2.1

Introduction The Reichenbachian Matrix in Different Forms 2.1.0 Introduction 2.1.1 3 × 3 for Latin 2.1.2 Three Times 2 × 3 for Dutch 2.1.3 Reducing 3 × 3 to 7 for English 2.1.4 3 × 3 for Classical Greek 2.1.5 Two Times ((3 × 3) − 2) for French Ternary with Intervals 2.2.0 Introduction 2.2.1 The Present Perfect Puzzle 2.2.2 Topic Time as a Key for the Solution to the Present Perfect Puzzle 2.2.3 A Pragmatic Solution Points and Intervals 2.3.0 Introduction 2.3.1 Point of Evaluation 2.3.2 A Point as a Landmark 2.3.3 The Fleeting Point n

2.2

2.3

page xiv xvi xvii 1 1 6 10 12 12 13 13 14 18 19 21 23 30 30 31 32 34 36 36 37 42 44 ix

x

Contents

2.4

Conclusion

45

3

Binary Tense Structure

3.0 3.1 3.2

48 48 49 52 52 52 55 58 58 59 61 64 70 72 73 73

3.6

Introduction A Brief Survey of Te Winkel’s Binary System Binary Operators 3.2.0 Introduction 3.2.1 Dyadic Branching and Binary Tense 3.2.2 Preparing for the Semantics of Binary Operators The Present Tense Domain 3.3.0 Introduction 3.3.1 Distinguishing between Present and the Fleeting point n 3.3.2 Simple Present 3.3.3 Present Perfect 3.3.4 Taking a Snapshot at n 3.3.5 Simple Future and Future Perfect in the Present The Past Tense Domain 3.4.0 Introduction 3.4.1 Anteriority Seen as a Relation between Two Temporal Structures 3.4.2 Simple Past 3.4.3 Past Perfect 3.4.4 Simple Future and Future Perfect in the Past A Compositional Account of Tense Structure 3.5.0 Introduction 3.5.1 Ontological Preliminaries: Events or Indices 3.5.2 The Semantics of the Operators PRES and PAST 3.5.3 Negation Conclusion

4

Naive Physics and Aspectual Composition

4.0 4.1

Introduction What Did Aristotle Tell to Ryle, Vendler and Kenny? 4.1.0 Introduction 4.1.1 Formal Semantics and Aristotle 4.1.2 Tense Oppositions in Aristotle’s Metaphysics 4.1.3 Translation Problems 4.1.4 At the Bottom of the Aristotelian Notion of Motion On the Idiosyncrasy of Criteria for Aspectual Classification

3.3

3.4

3.5

4.2

74 76 78 81 82 82 83 84 90 91 93 93 95 95 96 98 102 104 106

Contents

xi

Introduction Ryle’s Criterion for Allowing Achievements: Finis A Binary Alternative to Ryle’s Exchangeability Criterion: The Report Mode 4.2.3 Vendler’s Criteria for a Quadripartition 4.2.4 Kenny’s Criteria for a Tripartition 4.2.5 Monadicity as the Disturbing Factor Features of Aspectual Composition 4.3.0 Introduction 4.3.1 Aspectual Features and Beyond 4.3.2 Doing Away with Features Conclusion

106 107

5

Levels of Interaction between Aspect and Tense

5.0 5.1

Introduction At the Bottom of a Predication 5.1.0 Introduction 5.1.1 Grounding a Verb Opposition 5.1.2 Type and Token 5.1.3 Function Format Discretization and Bounding 5.2.0 Introduction 5.2.1 Intransitive Verbs Expressing Discretization 5.2.2 Discretization and Bounding by the Internal Argument of Transitive verbs 5.2.3 Wavering between d ◦ su and su 5.2.4 The Role of the External Argument A Formal Account from Lexical Bottom to S0 5.3.0 Introduction 5.3.1 Syntax and Semantics of Noun Phrases 5.3.2 Discretization in Sentences with Transitive Verbs 5.3.3 Discretization in Sentences with Unaccusatives and Unergatives Conclusion

131 131 131 131 132 135 137 140 140 140

4.2.0 4.2.1 4.2.2

4.3

4.4

5.2

5.3

5.4

6

Binary Tense Structure and Adverbial Modification

6.0 6.1 6.2

Introduction On the Role of Det and NP in a Temporal Adverbial Syntax and Semantics of Non-deictic Modification

110 113 117 121 122 122 122 126 128

146 150 154 156 156 158 159 164 166 169 169 170 173

xii

Contents Introduction The Predominance of Tense over Temporal Modifiers Temporal Modification as a Form of Bounding Connecting a Temporal Modifier to Indices at Different Levels 6.2.4 Non-deictic Relational Adverbials 6.2.5 Modification below S0 Frequency and Habituality Syntax and Semantics of Deictic Modification 6.4.0 Introduction 6.4.1 Deictic Setting Adverbials 6.4.2 Deictic Relational Adverbials 6.4.3 A Structural Solution to the Present Perfect Puzzle 6.4.4 Comparing Solutions Syntax and Semantics of Durational Adverbials 6.5.0 Introduction 6.5.1 Measuring below S0 6.5.2 Computing the Length of Indices 6.5.3 Computing Length at Higher Levels 6.5.4 Further Escapes from the in/ for-Test Conclusion

173 173 175

7

How to Deal Binarily with ...?

7.0 7.1

Introduction The Semantics of the Progressive Form 7.1.0 Introduction 7.1.1 Attempts to Resolve the Alleged Imperfective Paradox 7.1.2 A Binary and Compositional Analysis of the Progressive Form Binary Indices, Compositionality and Slavic Aspect 7.2.0 Introduction 7.2.1 PF vs [+T] and IPF vs [–T] 7.2.2 Dividing PF and IPF between Three Levels 7.2.3 Temporal Definiteness and Indefiniteness 7.2.4 Lexical and Grammatical Aspect The Position of the Aorist in a Binary System 7.3.0 Introduction 7.3.1 The French Passé Simple 7.3.2 The Imperfective and Perfective Aorist in Bulgarian

211 211 212 212 212

6.2.0 6.2.1 6.2.2 6.2.3

6.3 6.4

6.5

6.6

7.2

7.3

179 181 181 183 185 185 186 188 189 195 196 196 197 199 202 205 209

215 221 221 222 226 232 235 235 235 237 242

Contents

xiii

7.3.3 Comparing Choices in Rich Tense Systems 7.3.4 The Aorist and the Third Binary Opposition Conclusion

246 247 251

8

Tense, Mood and Aspect

8.0 8.1

Introduction On the Nature of the Opposition between SYN and POST 8.1.0 Introduction 8.1.1 Existential Quantifiers and Modal Configurations 8.1.2 Indicative vs Subjunctive Mood? Modality and Future: Linguistics or Philosophy? 8.2.0 Introduction 8.2.1 The Seabattle Tomorrow 8.2.2 Ockham or Peirce, Prior or Te Winkel? 8.2.3 Modal Base and Accessibility 8.2.4 Adapting the Connectives Introduced by SYN and POST The Proof of the Modal Pudding . . . Reaching the Top: Temporalization by PRES and PAST Rounding Off

253 253 257 257 257 263 266 266 266 269 273 276 279 287 288

7.4

8.2

8.3 8.4 8.5

Appendix Bibliography Author Index Subject Index

290 301 321 325

Figures

1.1 1.2 2.1 2.2

Opposing Simple Past and Present Perfect with the help of R Past of the Past Jespersen’s seven tenses Vet’s division of labour between tense and aspect in phrase structure 2.3 Mapping intervals to potential evaluation points 2.4 Combining tense with [+T] or [–T] 2.5 What to expect in Chapters 3–8? 3.1 Two ways of dealing with dyadic branching 3.2 Generative syntax of tense and aspect 3.3 Tense operators expressing the three binary oppositions 3.4 The present tense domain i 3.5 Simple Present: P R E S + S Y N + I M P 3.6 The Dutch Present Perfect 3.7 Two types of situation covered by the English Present Perfect 3.8 The past domain i  and its relation to i 3.9 Simple Past: PA S T + S Y N + I M P 3.10 Past Perfect 4.1 Exchangeability of Simple Present and Present (resultative) Perfect 4.2 Terminativity at VP and S0 4.3 Construal of three aspectual classes 4.4 The butterfly model for two-place verbs 4.5 Restrictions at three levels 5.1 Continuity in the real number system R+ 5.2 Irregular or periodical actualization in the reals 5.3 Discretization: mapping into N 5.4 Interaction of two number systems: N and R+ xiv

Page 3 7 19 27 39 40 46 53 53 55 59 62 65 67 74 77 80 110 123 124 126 127 132 133 134 134

List of Figures 5.5 5.6 5.7 5.8 5.9 5.10 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7.1 7.2 7.3 7.4

Different ways of discretizing Function composition morphologically A transitive verb phrase with and without an internal argument NP structure and VP structure The intersection model of generalized quantification Factors in aspectual composition up to and including tense Modification of tense structure by adverbials Noun denotations Measuring the length of intervals Three ways of modifying α Relational adverbials with after Tense carriers in the present tense domain i in English Non-stativity changing into stativity The VP in (3a) versus the VP in (3b) Structuring perfective and imperfective aspect in Russian Sorting out the three layers of the Barentsen-Dickey theory The BD-theory applied to the absence of pro- and its presence in Russian 7.5 Token and type in different number systems 7.6 Token and type interpretation of na7.7 A O R added to the third binary opposition 7.8 The three aspectual layers in the Bulgarian aorist 7.9 Complex forms of the aorist in Bulgarian and French 7.10 Two tense systems meeting in Georgian 8.1 Branching after n 8.2 Tense, mood and aspect: three levels of binary opposition 8.3 Indicative (S Y N) vs non-indicative (P O S T)

xv 144 148 153 159 160 167 170 171 172 176 181 193 206 216 227 229 232 233 233 242 244 247 249 254 256 264

Tables

1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 4.1 4.2 4.3 5.1 7.1 7.2 8.1 8.2 8.3

xvi

Learning eight tense forms in school grammar Reichenbach’s matrix for English Madvig’s 3 × 3 matrix step 1 Madvig’s 3 × 3 matrix step 2 Kollewijn’s 2 × 3 matrix for Dutch, English and Latin Jespersen translated into Reichenbach Reichenbach in CGCG The French tense system according to Vet, in matrix form Subsystem 2 with S oriented to S Klein’s matrix for English Te Winkel’s system in Reichenbach’s notation The eight tense forms in Te Winkel’s system Aristotle’s tense oppositions Crossing tense operators Crossing two oppositions: four classes Survey of types French tense forms defined by the binary operators Lefeuvre’s proposal for harbouring the aorist in a binary system Some languages with a P R E S and PA S T form for the subjunctive Prior and Te Winkel Modal base and accessibility relations

Page 2 13 15 16 18 20 21 24 26 33 51 56 98 100 113 157 238 241 264 271 274

Preface

This book is written for linguists doing research in the domain of interaction between semantics, syntax and morphology focussed on tense, mood and aspect. The term linguists may include computational linguists, psycholinguists, SLA-linguists and even logicians focussed on the question of how their formal tools can be used for dealing with natural language. In a different use, the term linguists captures a variety of scholars from different persuasions such as categorial grammarians, minimalists, generativists in a broader sense, functional grammarians, cognitive grammarians, among many others. It also captures linguists working in the tradition of Discourse Representation Theory. For them the central notion of e(vent(uality)) is a primitive one, whereas in the present book this notion will be broken apart into different pieces of atemporal information that serve on different layers of phrase structure rendering a temporal e ultimately at the level of a tensed sentence. The book is written for all of them because compositionality has the nice property of not being bound to an ideology if one is able to see it as a technical notion. Janssen (1997:461) underscores the methodological virtue of compositionality: it requires a decision on what the basic units in syntax and semantics are, and how they are related to one another and are combined into larger units. Of course, I am committed to a theoretical position by choosing these units, especially with the help of formal semantic tools, but on the other hand it does not make sense to write about compositionality informally. Moreover, the use of tools has the rewarding effect of leading to new insights at the point where they signal inconsistency. This is because sharply defined tools are more ordaining than critical opinions of peers. Inconsistencies can never be ignored on the penalty of making the whole theoretical enterprise senseless. To not scare readers when it comes to giving formulas which ‘prove’ compositionality, I will embed them in informal text before and after, thus making it possible to skip a close inspection of them in favour of just following the main line of argument. I trust that sufficient readers remain fond of subjecting formulas to an accurate assessment. The book is easy to read for people familiar xvii

xviii

Preface

with basic notions of set theory and formal type logic including the lambda calculus which has established itself reasonably well in linguistic semantics on the basis of introductory works like Partee et al. (1990) and Gamut (1991). My Utrecht PhD thesis On the Compositional Nature of the Aspects finished in 1971 appeared without substantial corrections as Verkuyl (1972a). In the seventies, it took some time to master and apply the then-new techniques of formal semantics in exploring aspectual issues that I felt were unsufficiently accounted for in my thesis. In the eighties, my main focus was on research into the quantificational contribution of an NP to complex aspectual information at the higher levels of phrase structure resulting in A Theory of Aspectuality (1993), which contains only a brief section on tense. In the meantime, I had become acquainted with a binary tense system developed in the nineteenth century which requires compositionality. Increasingly I felt the need to connect tense and aspect on a compositional basis. This resulted in Binary Tense which appeared in 2008 and is more about tense than about aspect. However, a crucial problem had not been solved yet: what is the real contribution of a verb to the compositional process of construing phrase structure? In the Galilean perspective, motion is unbounded unless it is blocked by an external force. The present book aims at finally formalizing this Galilean angle of approach that has always informally determined my view on aspectuality. Thus, as far as Chapter 4 is concerned, the intended readership described in the first paragraph may be extended so as to include philosophers due to its rejection of the Aristotelian teleological perspective on the nature of motion which has become dominant in the current mainstream in the linguistic theory of tense and aspect on the authority of ordinary language philosophers. A consequence of research in progress is that a new publication builds on earlier work: the aforementioned books and papers, some of which were jointly written. Hence reference to that earlier work is inevitable. Combining my work on aspectuality with my work on binary tense yielded formal tools needed for cracking the contribution of the verb to aspectual information in the past decade. Therefore previous results have been adapted to a new formal setting and they are given a new perspective so that simple recycling is evaded or reduced to acceptable proportions, as I hope and also think so. This distinguishes the present book crucially from a collection of papers: the search for the basic elements of compositionality is described here for the first time in a completely new context: from bottom to top with new results. I would like to thank a number of people who have helped me in the course of writing this book or earlier. First of all, I want to express my gratitude to Marie-Eve Ritz and Hans Broekhuis for having read all the eight chapters up

Preface

xix

to and including the final version. Marie-Eve is an expert on one of the central themes, the perfect, but on another central theme – the French tense system – her being a native speaker of French made me feel protected against slipping away in wild claims about the theoretical status of the French aoristic tense forms: the Passé Simple and the Passé Antérieur. Finally, she could test the binary theory presented here in her work on Polynesian languages. Hans Broekhuis convinced me to leave the rather timid position of Verkuyl (2008) with respect to Te Winkel’s binary system where I left open that posteriority could be interpreted both temporally and modally, as Te Winkel (1866) had done. In Broekhuis and Verkuyl (2014), we found a common ground, and since then, we have had many stimulating discussions based on disagreement because it is quite hard for me to give syntax the most prominent place in a domain which, in my view, is predominantly semantic. As to the formal technical part, I owe much to Dick de Jongh, Reinhard Muskens and, at earlier stages, Harry Sitters. I feel safe in presenting the logical-semantic machinery here due to the preciseness resulting from frequent exchanges with each of them. In particular, Chapter 8 would not have achieved its present form without the many mails exchanged between Reinhard and myself both with regard to modality and to getting to the final stage of the bottom-top compositional process sketched in the present book. Thanks also to Johan van Benthem for his stimulating comment on that chapter. For their contribution to the way I have been able to write about Slavic aspect and about the aorist I would like to thank Egbert Fortuin, Jaap Kamphuis and Adrie Barentsen. They also organized a lecture for Slavicists as a check on whether the formalization of their theory on Slavic aspect in Chapter 7 does justice to the facts. I thank Maaike Schoorlemmer for checking whether I did justice to her analysis of Russian aspect. Andrei Stoevsky and Krasimir Kabakˇciev were very helpful by providing more insight in how the aorist functions in the Bulgarian tense system and how it relates to aoristic forms in Romance languages. Leonoor Oversteegen was so kind as to provide improvements in my representation of her work discussed in Chapter 2 and Geert Booij guided my small excursion to the domain of morphology in Chapter 5. I also thank Harm Pinkster for preventing elementary mistakes in my account of the connection between current linguistic theory on tense and aspect and the age-old tradition of classical, in particular Latin, grammar. The rest of the acknowledgements date back from earlier occasions. Around 2014, I felt the need to get to the original text of Aristotle’s Metaphysics 1048b in order to study it with a strictly linguistic view on the tensed verbs it contains

xx

Preface

and I wrote a paper about that which has remained unpublished: it is partly included here in Chapter 4. For comments on the paper, I would like to thank the late Emmon Bach, Olga Borik, Regine Eckardt, Antonio Fábregas, Hana Filip, Ray Jackendoff, Hans Kamp, Michael Moortgat, the late Remko Scha, Pieter Seuren, Henriëtte de Swart, Hedde Zeijlstra and Joost Zwarts. I could not have done the linguistic inspection of the tense forms in 1048b without the professional expertise of Albert Rijksbaron, co-author of the Cambridge Grammar of Classical Greek (2019), which conquered an important place in several chapters of the present book. Numerous lunches attest to the thoroughness and depth of his view on the text and its implications. I am very grateful for Albert’s support of my strictly non-philosophical and nonphilological approach to the original 1048b, even though it has led to a different conclusion for the theory of tense and aspect than he drew in Rijksbaron (1989) in which he used the aspectual classifications proposed by natural language philosophers, now countered in Chapter 4. I add to this gratitude that which I owe to Alexander Mourelatos, whose stimulating comments then and more recently were taken to heart. When Chapter 8 was written, once again I could use Albert’s reassuring help, this time with a purely linguistic approach to Aristotle’s famous passage about the sea-battle taking place tomorrow. Richard Moot played an important role around 2015 in getting a proper formal analysis of the Progressive Form in Chapter 7, which I proposed in a chapter in the Oxford University Press Handbook of Event Structure (2019) edited by Robert Truswell. I thank Richard for his valuable help and Rob for his stimulating advice to present that analysis in a larger setting. I also thank Paz González and Tim Diaubalick for their role of editors of a special issue Current Visions of TAML2: Tense, Aspect and Modality in Second Languages, for which I contributed Verkuyl (2019b) in Dutch Journal of Applied Linguistics. A part of the text of Section 5.1.1 is included in that paper. Finally, I would like to thank the commissioning editor of Cambridge University Press, Helen Barton and her staff, for guiding me so kindly and efficiently through the complex traject from book proposal to its final publication.

1 Introductory Chapter

1.1

Roadblocks to Compositionality

The present book will argue that a linguistic theory focussed on the compositional interaction of tense and aspect in sentences of natural languages is more likely to succeed in finding explanatory principles that apply universally to our dealing with time in language •

•

•

by assuming a binarily organized tense system rather than the mainstream ternary one originally proposed in Reichenbach (1947) and adapted or not by his followers; by rejecting the aspectual verb classifications proposed in Vendler (1957) and Kenny (1963) in favour of a strict compositional approach; by not allowing an eventuality e at the bottom of a sentential structure as a temporal argument of the verb, as done in event semantics following Davidson (1967), but rather by assuming a more abstract unit as the input to the computational machinery necessary for composing a complex temporal meaning at the top of a sentence.

The unifying idea behind this is that all three lines of research – on ternary tense, on aspectual verb classes and on event semantics – promote unjustifiedly (an outdated sort of) naive physics as the foundation for ontological structure and that, taken together, they stand in the way of dealing properly with compositionality by ignoring the crucial contribution of a verb to complex meaning. This does not exclude that, at the macro-level of discourse, events may function as standardly assumed in Discourse Representation Theory, but the present book is about the micro-level at which compositionality is a crucial issue. For each of the three traditions, it is necessary to get to the core of my objections in some detail and to propose a coherent whole bringing the three separate alternatives together in a strictly compositional framework. In the present chapter, I will briefly and preliminarily comment on each of the three antagonistic views in order to shed some light on the reasons why I think they stand in the 1

2

Introductory Chapter

way of a proper linguistic compositional treatment of tense, mood and aspect at the sentence level. Ternary vs binary Dutch school children master the eight tense forms of Dutch by learning a system originating in Te Winkel (1857;1866). They learn to use Dutch abbreviations such as o.v.t. for imperfect past tense and v.v.t.t. for perfect past future tense without realizing that the system is based on three binary oppositions yielding 2 × 2 × 2 = 8 tense forms.1 For children Table 1.1 Learning eight tense forms in school grammar o. Imperfect o. Imperfect o. Imperfect o. Imperfect

t. Present v. Past t. Present v. Past

– – t. Future t. Future

v. Perfect v. Perfect v. Perfect v. Perfect

t. Present v. Past t. Present v. Past

– – t. Future t. Future

learning the tense forms in Table 1.1, the three binary oppositions do not impose themselves. That is easy to understand when they are presented in (1). (1)

a. Present – Past b. Synchronous – Future c. Imperfect – Perfect

The term Future is here detached from the tripartition Past–Present–Future and taken as ‘posterior to Present or to Past’ but the term synchronous in the sense of ‘simultaneous with Present or with Past’ is not visible in Table 1.1. It is virtually impossible for language learners to see that this system of oppositions proposed nearly one century before Reichenbach (1947) automatically supplies sufficient points of reference for mediating between the speech time S and an eventuality E. It is also impossible to see that it automatically solves the problem agonizing Reichenbach’s ternary approach, namely that in spite of adding the famous point of reference R as an intermediate between S and E, a ternary system cannot account for all eight tense forms of Dutch and English without stipulating an extra point. In a binary approach, all eight tense forms are covered systematically. Within the long tradition of a primary division of tense into Past-PresentFuture, the problem of a too-direct link between E and S had bothered 1 Boldface o stands for onvoltooid ‘imperfect’ or ‘incomplete(d)’, boldface v for voltooid ‘per-

fect’ or ‘completed’, but also for verleden ‘past’, boldface t for tegenwoordig ‘current, present’ but also for toekomend ‘future’, but literally: ‘approaching’, ‘coming nearer’.

1.1 Roadblocks to Compositionality

3

generations of linguists before Reichenbach solved it.2 He decisively illustrated the difference between the English Simple Past and Present Perfect with the help of the configurations in Figure 1.1. Positioning the perspectival point

Figure 1.1 Opposing Simple Past and Present Perfect with the help of R

of reference R in the Simple Past at the eventuality point E itself, Reichenbach put this point in the Present Perfect at the point of speech S posterior to E. This made it possible to see R as the present point of perspective on what happened at point E. This technical solution to a problem that many scholars in the ternary tense tradition had been stuck with, explains why Reichenbach’s tense system became so popular. My master’s thesis in 1967 was about Reichenbach’s system, but I did not yet recognize that the binary system that I had learned at school also made use of extra points of reference preventing a direct relation between the eventuality E and S and that they did so better than Reichenbach ever could imagine. The binary system of Table 1.1 produces them automatically. It was not until the early eighties when I supervised a historically oriented PhD thesis comparing a number of nineteenth-century Dutch school grammars, that I became directly acquainted with Te Winkel (1866).3 It was an eye-opener resulting in Verkuyl and Le Loux-Schuringa (1985), which argued that a systematic comparison between Te Winkel (1866) and Reichenbach (1947) could only result in a resounding victory for a binary approach. At least for Dutch and English, and, as it turns out also for many other languages, both those with fewer than eight tense forms (Mandarin Chinese, Russian) and those with more than eight (French, Spanish, Bulgarian, Georgian), as argued in Verkuyl (2008). The first main line of the present book is therefore to get to the bottom of the difference between ternary and binary and to show that a binary approach offers the most profitable way for reaching strict compositionality. Compositionality vs Aspectual Classes An essential ingredient of the present approach is to get rid of an Aristotelian-based naive physics that 2 Chapter 2 will point out that he did not solve it but rather articulated a solution found more than

seventy years earlier. 3 The PhD thesis Le Loux-Schuringa (1984) is written in Dutch, Le Loux-Schuringa (1988) in

English.

4

Introductory Chapter

entered linguistic theory on aspectuality decades ago at the expense of a more abstract (mathematically based) ontology. This more abstract approach does justice both to the way in which individual speakers handle tense and aspect information compositionally and to the variety of choices available to languages for encoding this information in atomic elements at the lexical level and bringing them together at the different levels of phrase structure. Working on my PhD thesis, I read Vendler (1957) after I had already gone through the predominant German literature on Slavic aspect published around 1900. That put my appreciation for Vendler’s quadripartition into perspective, much in the same way in which Mourelatos (1978:418) reacted to Vendler (1957) and Kenny (1963): that they were a little late in proposing classifications of the type well-known to generations of linguists working in the domain of research into verbal aspect. Vendler’s classification of eventualites into States, Activities, Accomplishments and Achievements did not change the conclusion that I had already drawn from the linguistic aspectual classifications available in the literature on Slavic aspect, namely that they do not match with a search for atomic particles contributed by the verb and its arguments. It will be shown that only a binary view on tense makes it possible to conclude that exchangeability of tense in sentences like He wins! and He has won! – one of the showpieces of Vendler’s analysis – turns out to be purely a matter of tense rather than of aspect and that this has consequences for Vendler’s criterion for distinguishing between Accomplishments and Achievements. It was Dowty (1979) who paved the way for Vendler in linguistic theory in spite of the fact that Vendler had called his 1967 book Linguistics in Philosophy. This title suggests that the reading circle for that book was intended to consist of (analytical) philosophers. It worked out differently: it implemented Aristotle’s metaphysics as a structuring force in the domain of linguistic semantics. This allowed naive physics with an outdated view on motion and change to play a dominant role in the current theory of tense and aspect, in particular the view that each motion has an inherent goal. The second main line of the present book then is to show how Vendler’s quadripartion of aspectual classes works against the idea of compositionality, apart from the basic methodological insight that classifications generally fail when it comes to explanatory power. Atemporal vs Temporal My relation to Davidson (1967) has always been on the skeptical side because before I read that paper, I had already read the magnificent section 48 The Problem of Individuals in Reichenbach (1947:266– 74). Although many attribute the introduction of an event variable e bound

1.1 Roadblocks to Compositionality

5

by an existential quantifier to Davidson, Reichenbach made use of it in that section. Reichenbach treated this introduction in the context of a distinction he made between thing-splitting (talking about “aggregates of matter keeping together for a certain time”) and event-splitting (talking about “space-time coincidences” which do not endure), as an option for speakers to take a certain perspective in a discourse (cf. Verkuyl 1972a:156–62;1976). Davidson took the floor by pointing out that there is a logical flaw in Reichenbach’s formulas and so Reichenbach’s cognitively interesting view on perspective disappeared into oblivion at this point. In combining binary tense with aspectual composition, however, the idea of adding an extra argument to a predicate is a proper way to go in dealing with “space-time coincidences”. In that sense, I will follow Davidson’s format of predicational structure: the variable α that comes with it in the lexical characterization of a verb can be used at higher levels of phrase structure where it will be replaced by values contributed by tense operators. Davidsonian and neo-Davidsonian event semanticists use the term event as temporal without taking into account the temporal role of tense. This yields a straightforward contradiction as soon as one analyzes a tensed sentence S in terms of [S TENSE(S0 )], where TENSE stands for one or more tense operators taking a tenseless S0 so as to form a tensed sentence S . In a compositional interpretation from bottom to top, a Davidsonian event variable e is to be located in the tenseless S0 as an argument of the verb. This implies that e cannot be temporal as long as TENSE has not yet been applied. Yet, Davidsonians regard their e as temporal, the more so because they generally happen to marry their view with Vendler’s view on aspectual classes. In this way, Davidsonian eventualities are generally partitioned into four naive physical classes, or three if one uses Kenny’s classification. My criticism of this unhappy marriage leads to the third main line running through the present book. I will use the eventuality variable α as standing for a numerical value in a number system (R or N) which turns into a temporal value only after the highest tense operator has been applied yielding S . This more abstract approach opens the way for obtaining event structure in which compositionality can proceed from bottom to top without being blocked by the sort of prototyping inevitable in Aristotelian naive physics employed in the joint enterprise originating in Vendler (1957), Kenny (1963) and Davidson (1967). A final remark must be made on the use of terms like event, state, process and eventuality. They are standardly used in Discourse Representation Theory. In spite of doubts about ill- and under-defined ontological notions like eventuality expressed in Kamp and Reyle (1993:504–10), the authors can live with Davidson’s formalism with e as an argument of the verb and interpreted

6

Introductory Chapter

as an eventuality Ev. The same happens in Kamp (2019). In this respect, I think, DRT is typically a macro-enterprise, whereas the present search for compositionality in the construction of sentence meaning is a micro-matter. The question is then – using the chemical metaphor – whether having an Ev in a model at the molecular level requires that Ev (already) exist at the atomic level. Our task will be to show that the answer is negative. If the three main lines sketched here are followed, a coherent alternative at the micro-level should become visible step by step, chapter by chapter.

1.2

Finding Our Way in Babylon: Terminological Problems

An enterprise like this has to keep in mind the Babylonian confusion of speech ravaging the field. Some examples may suffice for seeing the point. The first concerns the fact that in the long tradition of research on the Latin tense system, the perfectum has been the topic of a heated debate still going on.4 Many Latinists unquestioningly oppose perfectum to imperfectum as a natural opposition, which, by the way, is also what Reichenbach did by opposing the English Present Perfect to the Simple Past in Figure 1.1. Among classical scholars there are those who defend the naturalness of the opposition by assuming that the Latin perfectum (also) expresses what in Greek is expressed by the aorist. On that semantic assumption, it is plausible that the Latin perfectum is a past tense form due to the fact that the Greek aorist was considered a past tense.5 The dominant term for expressing this pastness is praeteritum. Classical scholars often distinguish between praeteritum perfecti and praeteritum imperfecti. This practice is still visible in grammars of Romance languages. Spanish grammarians, for example, use the term pretérito as short for the aoristic pretérito indefinido also called pretérito perfecto simple. But the term pretérito imperfecto is also in use, which brings in the classical opposition between perfectum and imperfectum. Spanish grammarians also use the term pretérito pluscuamperfecto (Pluperfect) and more surprisingly also pretérito perfecto compuesto (Present Perfect).6 4 A good survey is Pinkster (1983). The heat of the debate is visible in, for example, Serbat

(1975;1976) and Rose (1984). 5 Apart from the so-called gnomic and tragic aorist; see also CGCG:419. Babylon is also visible

here: there are scholars who call the aorist use of the perfectum the historical perfect, whereas there are also those who use this term for the non-aorist interpretation. 6 cf. García Fernández (2000), Arche (2014), Fábregas (2015), González and Verkuyl (2017) and the Cactus 2000 Spanish conjugation tables on the Internet.

1.2 Finding Our Way in Babylon: Terminological Problems

7

In Germanic languages like German and Dutch, the term praeteritum is also still in use but rather as a synonym for imperfectum. When used in English it is also applied to the Simple Past. It is difficult to evade babel when the term preterit is used for aoristic forms in some languages and for imperfectum forms in other languages. Reichenbach equalizes the English term Simple Past and the French term Passé Simple: both tense forms have the same configuration for him (1947:291). Yet there are valid arguments against a translational equivalence of an English Past tense form and the Passé Simple. As argued in Molendijk et al. (2004:281f.), there is no need for seeing the English Simple Past as an aoristic form and this certainly holds for its counterparts in other Germanic languages, among which Dutch. In short, writing about aspect and tense turns out to be moving through a terminological minefield when it comes to central terms. A second example of confusion concerns the characterization of the Past Perfect as the Past in the Past, which is based on the idea of double anteriority. Let me write this as: Past1 -in-the-Past2 , to mark the problem. Without the subscripts it is more difficult to see that the term Past in the Past opposes the term Past1 Perfect to the term Present Perfect on the assumption that Perfect stands for Past2 . It also ignores the fact that this assumption requires that the Present Perfect be called Present in the Past2 , a rather puzzling term. Leech (1971:34) comes close to the equation Past2 = Perfect when saying that the Present Perfect is used “in reference to a past event to imply that the result of that event is still operative at the present time”. For Leech, the Perfect is in this case a resultative past. Why a past event should be called perfect remains unclear, because after all She wrote an angry letter to me which I received this morning is about two past terminated events without using a perfect. The Past1 -in-the-Past2 -idea can also be found in Reichenbach’s configuration E—R—S in Figure 1.2, where the relation between E and R is put on the same footing as the one between R and S: anteriority. Yet for English, the

Figure 1.2 Past of the Past

E—R-configuration is dependent on the use of the auxiliary have, whereas the relation between R and S is determined by the choice of a past tense morpheme. In other words, there are sufficient reasons for taking the difference between the members of a relation more seriously. After all, in Reichenbach’s E—R

8

Introductory Chapter

one can say that E has been completed before R, but it is misleading to say that R is completed before S in R—S. Double anteriority also presumes that R in its relation to E in the configuration E—R be given exactly the role of S in its relation to R in the configuration R—S. The next chapter will pay detailed attention to this terminological confusion arguing that it results from imposing the system of Latin tense forms to tense systems of modern languages in the past centuries. A third case in which terminology causes trouble is the distinction between the temporal use of the auxiliary will or shall in English and its modal use. The first problem is here that in sentences like (2) the form will sing is taken as a periphrastic tense of sing, where will expresses future or modality. (2)

Maria will sing in the Albert Hall (tomorrow).

The terminological difficulty here is the use of the term periphrastic tense: does its use imply that the tense of the auxiliary form will itself does not count? This question has been largely ignored in the literature. The term periphrastic tense of a (main) verb suggests that the auxilary will acts as a tense morpheme comparable with what is contributed by -ed in She walked but now pointing forward. I consider this an incomprehensible way of looking at what will really does – from a compositional point of view – because the role of PRES in the combination of PRES+willstem is ignored. If will sing in (2) expresses future in the temporal sense, there are two options: (a) the infinitival/stem form of the auxiliary will contributes temporality by projecting forward: Maria’s performance is located on the day after the utterance of (2); and (b) the tense operator PRES in will does so. Option (a) raises the question of what the present tense form of will contributes and how the expression of future by willstem is compatible with the expression of presentness by PRES. Option (b) leads to asking what the “future meaning” of will is, when posteriority can be expressed by PRES . Note that one cannot escape from an choice between (a) and (b). The second problem makes the issue even more complex because distinguishing between a temporal and a modal auxiliary will does not only require an answer to the question of why there are two verbs will but also why the same should hold for She may/must sing in the Albert Hall (tomorrow), as pointed out in Broekhuis and Corver (2016) and earlier in Quirk and Greenbaum (1973:47ff), one of the few didactic English grammars that work binarily. There are more obstacles for getting out of Babylon. Generative grammarians, for example, use the notation ‘VP’ for what is traditionally and currently often written as an S by scholars outside the generative framework. Minimalists write VP because they work with V as the head of a projection line and

1.2 Finding Our Way in Babylon: Terminological Problems

9

in this way the external argument of a sentence is seen as taking the position of a specifier and the internal argument as a complement. However, using the label VP for what formal semanticists call a proposition is problematic outside the generative syntactic framework itself. Therefore I will use the label VP for the combination of a verb with its internal argument, the label S0 for the tenseless proposition construed by combining a VP with the external argument, and the label S for the resulting tensed sentence. In a direct discussion with syntactic proposals of the generative kind, no misunderstanding will arise about the use of labels. A final case of terminological confusion concerns the use of notions like reading, meaning, interpretation, use, etc. What do scholars mean when they say that the Spanish Imperfecto has a descriptive use, a habitual use and a progressive use, as standardly distinguished in textbooks and research, as in Fábregas (2015)? For didactic grammars, it is understandable to make this distinction and to make a strong association between one of the three uses and a specific situation in which one had better apply it. But what does the term habitual use of a verb as distinguished from its episodic or descriptive use really say, theoretically? Making distinctions or not gives away a theoretical point of view. It might be typical for a verb to not have three different senses but to express just one meaning which functions differently in different contexts. Compare it with the noun bird. Do we have three nouns bird because of the sentence That bird has arrived early this spring? It allows for talking about a certain type (not a sparrow, but a stork), about a specific type, say the stork as a genus and about a ringed token stork. Would that be a reason for distinguishing three different nouns stork? In the present book, this issue will receive much attention because there is a relation between the need for distinguishing different uses of a verb and the level of abstraction at which one characterizes its meaning. Finding the real contribution of a verb to aspectual and tense information has clear consequences for the use of theoretical terms. I have given only five examples of terminological problems. There are many more. Terms like telos, culmination, result state, exchangeability, complete(d), completion, perfect, perfective, imperfective, imperfect, anterior, etc., all carry a long history with them in which they have demonstrably been used in different theoretical settings. It is not that I claim here to have solved that problem once and for all. But in sorting out the complexity of factors responsible for empirically reliable judgments about sentences, one needs to fix the theoretical terms, rejecting some terms as pretheoretical, adding some new ones because they express better what the formal tools do contribute. Some terms may qualify as useful for some languages and not so useful for others.

10 1.3

Introductory Chapter A Brief Inspection of the Chapters

Chapter 2 corrects the tendency to let any serious theory of tense start in 1947 with the publication of Reichenbach (1947). It is absolutely necessary to connect the current theory of tense with classical grammar in order to take into account the aorist or its current descendants. This leads to a discussion of different ternary grids as part of a closer inspection of notions like point, interval, fleeting n, landmark, etc. This prepares the way for showing which sort of role they have in a binary approach. Chapter 3 presents an updated version of the tense system of Verkuyl (2008) organized on the basis of the three binary oppositions. The update is needed in view of a number of improvements – substantively and notationally – due to later work. The main ingredient of Chapter 3 is the strict distinction between the notion of present (domain) and the notion of the fleeting point n, which has a counterpart in the distinction between past (domain) and then-fleeting point n  . The parallelism in a binary tense system is argued to be a dominant force in its organization. Chapter 4 sketches how the contribution of ordinary language philosophers like Ryle, Kenny and Vendler to linguistic semantics added to the terminological confusion sketched above. Their delivery of the Aristotelian legacy to linguistics consists of a sort of naive physical ontology at the cost of the principle of compositionality. The misleading translation of Greek verb forms occurring in the crucial passus of Aristotle’s Metaphysics 1048b into the English Progressive Form will be argued to have been decisive for what natural (language) philosophy handed to linguists: an outdated vision on motion. The chapter also sketches the heavy duty of a verb in taking all sorts of different arguments and argues that features are insufficient for the semantics of tense and aspect: they should be used as abbreviatory and for convenience only. Chapter 5 describes how all verbs are anchored in the system of positive real numbers R+ by focussing on the meaning of a verb without taking into account its arguments. This makes it possible to distinguish stative from non-stative verbs by assigning to each of them a (mathematical) function determining the value of the eventuality argument α of the verb. The next step is then to separate non-stative verbs expressing continuity in R+ from verbs expressing discretization in N by assigning to the latter a discretizing function mapping from R+ to N. A formal account of aspectual composition from the tenseless bottom to the tensed top S makes it possible to distinguish the (ten) factors that are in play on different levels of phrase structure.

1.3 A Brief Inspection of the Chapters

11

Chapter 6 aims at accounting for modification by temporal adverbials. The binary approach allows them to operate on different levels of tense structure above S0 . An important distinction is made between deictic and non-deictic adverbials. The variability involved in adverbial modification offers the possibility of presenting a structural solution to the Present Perfect puzzle. It also sheds light on the nature of the in/for-test: it explains why terminative sentences with a for-adverbial introduced at a higher level may be regarded as well-formed as opposed to those which require a token interpretation. Attention is given to the copula become in order to account for verbs like cool, which escape the in/for-test. Chapter 7 presents a theory of the Progressive Form in which the PROG operator is broken up into BE and - ING. This makes it impossible to maintain the central position attributed to the Progressive in the analysis of imperfectivity. The situation turns out to be more complex but can be accounted for compositionally by giving -ing its own semantic value. The chapter also shows how the binary approach to compositionality bridges the gap between the analysis of Slavic and non-Slavic aspect. It formalizes an aspectual theory which accounts for a wide variety of Slavic languages. It continues by focussing on the position of the aorist in rich tense systems where it has to survive marginally or where it has obtained an important position. A comparison is made with aoristic tense forms in systems that are (re-)organized binarily such as French. That opens the way for a deeper insight in the semantics of tense forms in languages where the aorist does not or no longer appears. Chapter 8 focusses on the nature of the second binary opposition, the one between SYN and POST. In view of the fact that POST can be argued to be modal, the leading idea is that the opposition can be understood in terms of a strict opposition between realis (indicative) and different forms of irrealis (subjunctive, conjunctive, etc.). The chapter culminates in reaching S at the end of the journey from the tenseless bottom of phrase structure to the tensed top S including all the distinctions made on the way between the different factors summarized at the end of Chapter 5. This makes it possible to see binary tense structure as expressing tense, mood and aspect in a systematic compositional way.

2 How to Deal with the Long Tradition of Going Ternary?

2.0

Introduction

The primary division between Past, Present and Future in the current mainstream ternary approach to tense has a long history, rooted in didactic classical grammar, in particular in its morphology. Learning that verbs of the first conjugation follow the pattern of laudabam ‘I praised’, laudo ‘I praise’ and laudabo ‘I will praise’, one can hardly escape from concluding that Latin morphology supports the intuitively natural tripartition between past, present and future in non-linguistic domains such as philosophy, logic, natural science and daily life. When European languages were found worthy of having their own grammar, Latin morphology remained the authoritative model even in Germanic languages lacking affixes for expressing future. The ternary approach to tense clearly does not begin with Reichenbach (1947). The present chapter goes seventy years further back into the origin of Reichenbach’s system than generally is done. This step back connects him with the tradition of Latin grammar in which the relation between tense and aspect has always been a central issue. In Section 2.1, the relation between Reichenbach (1947) and its immediate predecessors Jespersen (1924) and Madvig (1871) provides the historical background for a critical look at the two dimensions crossing in Reichenbach’s 3 × 3 matrix. Its primary vertical tripartition into Past, Present and Future makes use of the same temporal relations as the horizontal tripartition into Anterior, Simultaneous and Posterior. Section 2.1 argues that this is a source of trouble and that attempts to repair this shortcoming are doomed to fail due to the tripartite foundation of the crossings. Reichenbach introduced three points for the construction of tense configurations: a point of Event, a point of Reference and a point of Speech. Later on, proposals were made to redefine Reichenbach’s system in terms of intervals. Section 2.2 examines critically a popular proposal in which E, R and S are or 12

2.1 The Reichenbachian Matrix in Different Forms

13

may be taken as intervals and concludes that problems with this proposal again are due to the ternary design. The opposition between taking R as a point or an interval is generally seen in terms of blowing up a point and making it into an interval. This blow-up took place in the tradition of assigning a truth value to a point and so the expansion of a point into an interval opened the problem of determining what it is to assign truth to a predication with respect to an interval. This problem led many scholars eventually into event semantics. The question raised in Section 2.3 is whether the correction on Reichenbach by stretching a point to an interval is indeed the only option. An inventory is made of different sorts of points that occur or should occur in an account of tense and aspect configurations: the fleeting point n, a point as a landmark, a point of evaluation, a point as a contraction of an interval, etc. This analysis clarifies how, from Chapter 3 onwards, the notions of point, interval and eventuality will be used in a binary setting.

2.1

The Reichenbachian Matrix in Different Forms

2.1.0 Introduction Table 2.1 shows a 3 × 3 tabulation of the tenses making up the English tense system as proposed in Reichenbach (1947). Each cell contains the italicized term derived from crossing the headings. The primary division is the one between columns and will be maintained as primary in all tables which follow. The secondary division is the one between the rows. Reichenbach treats the Table 2.1 Reichenbach’s matrix for English Past R—S

Present R,S

Future S—R

1. Anterior Past E—R—S

2. Anterior Present E—R,S

I had written

I have written

3. Anterior Future E—S—R/ E, S—R/S—E—R I will have written

Simple E,R

4. Simple Past E,R—S I wrote

5. Simple Present E,R,S I write

6. Simple Future S—R,E I will write

Posterior R—E

7. Posterior Past 8. Posterior Present R—E—S/ R—S,E/ R—S—E S,R—E I would write I will write

Anterior E—R

9. Posterior Future S—R—E I will write

14

How to Deal with the Long Tradition of Going Ternary?

two tripartitions on an equal footing by assuming that the relations between E and R and between R and S are either determined by the relation ‘earlier than, anterior’ symbolized by E—R, R—E, R—S and S—R or by the simultaneity relation symbolized by the comma in E,R and R,S. In other words, the organization between the columns and the rows is temporal. The table is wellknown and is used here only as benchmark for comparing alternative ternary proposals. In the past decades, Reichenbach’s matrix has been investigated thoroughly and hence it is well known that there are many problems with it.1 Most of them simply disappear in a binary approach. For example, it makes no sense to deal with the problem of having the cells 6, 8 and 9 available for just one tense form, with the problem of having three configurations available for Posterior Past and Anterior Future and with the problem of the missing would have form, except for observing that they cannot occur in a binary approach because all these problems arise by tying the notion of future to the point of speech. Reichenbach presented his tense system as a correction to Jespersen (1924) which offered a system with seven tenses because Jespersen disagreed with a 3 × 3 tabulation proposed in an authoritative Latin grammar: Madvig (1871). It is worthwile to follow the steps from Madvig via Jespersen to Reichenbach in order to see how crucial terms in the domain of tense and aspect were (and still are) used equivocally. It is necessary to include Latin (and later on Greek) grammar in the analysis of the organization of tense forms because in proposing a ternary approach to tense systems of modern languages, grammarians tend to adopt not only the basic organization of those grammars but also the didactically established use of the key terms. It is instructive to see a sort of Echternach procession in the forward-backward-forward steps from Madvig to Jespersen to Reichenbach and how people praising Reichenbach for his new insight do not realize that Reichenbach’s system was already available in 1871, and earlier.

2.1.1 3×3 for Latin A natural beginning is to consider Table 2.2 which contains indicative tense forms found in Madvig (1871:289). Some adaptations have been made for 1 They are amply discussed in Bennett and Partee (1978), Dowty (1979), Comrie (1981),

Hornstein (1990), Stowell (1995a;1995b) for English; Verkuyl and Le Loux-Schuringa (1985), Janssen (1988), Verkuyl (2008), for Dutch; Vet (1981;2007) and Corblin and de Swart (2004), for French; García Fernández (2000) for Spanish; Prior (1967) for formal logic, among many others.

2.1 The Reichenbachian Matrix in Different Forms

15

Table 2.2 Madvig’s 3×3 matrix step 1

in praeterito R—S

in praesenti R,S

in futuro S—R

Praesens (Present) E,R

Praeteritum (Perfect) E—R

Futurum (Future) R—E

4. Praesens in praeterito E,R—S scribebam I wrote

1. Praeteritum in praeterito E—R—S scripseram I had written

7. Futurum in praeterito R—E—S scripturus eram/fui I was (then) at the point of writing

5. Praesens in praesenti E,R,S scribo I write

2. Praeteritum in praesenti E—R,S scripsi I have written/wrote

8. Futurum in praesenti S,R—E scribam/scripturus sum I will write/I am going to write

6. Praesens in futuro S—E,R scribam I will (then) write

3. Praeteritum in futuro S—E—R scripsero I will have written

9. Futurum in futuro S—R—E scripturus ero I will (then) be going to write

convenience in order to facilitate a comparison with Reichenbach. The numbering and the E,R,S-configuration of a cell in Table 2.2 are the same in a cell with the same tense form in Reichenbach’s Table 2.1. The first two columns contain the six synthetic active indicative tense forms of the verb scribo ‘write’. Latin has three distinct infinitival forms: scribere for the Praesens column, scripsisse for the Praeteritum column and scripturus esse visible in the periphrastic Futurum column. Jespersen’s criticism of the element of nearness-in-the-future in cells 7 and 9 and the absence of it in tenses in the other cells led to the proposal in Jespersen (1924) that drew Reichenbach’s attention. Jespersen’s proposal will be discussed later on in Section 2.1.3 in more detail. Quotation (1) reveals Madvig’s use of intermediate points of reference. (1)

The thing asserted is either simply referred to one of the three leading tenses, the present, past, or future, or stated (mediately, relatively) with reference to a certain past or future point of time, as being at that time present (contemporary with it), or past, or future. (p. 289)

16

How to Deal with the Long Tradition of Going Ternary?

Interestingly, Madvig uses the Latin terms praesens, praeteritum and futurum for the tripartition in the columns, not on page 289 itself where the 3 × 3 grid appears with headings in English parenthesized in Table 2.2 but, for example, on page 90 Jespersen uses only the Latin headings in discussing the grid.2 It takes some time to see that the terms in the headings stand for the Reichenbach’s Simple, Anterior (= Perfect) and Posterior, as shown by the numbering of the cells. By turning Table 2.2 a quarter turn to the right, one obtains Table 2.3 Madvig’s 3×3 matrix step 2 Past (in praeterito) R—S

Present (in praesenti) R,S

Future (in futuro) S—R

1. Anterior Past E—R—S scripseram I had written

2. Anterior Present E—R,S scripsi I have written/wrote

3. Anterior Future S—E—R scripsero I will have written

Praesens 4. Simple Past E,R E,R—S (Simultaneous) scribebam I wrote

5. Simple Present E,R,S scribo I write

6. Simple Future S—E,R scribam I will write

Futurum R—E (Posterior)

8. Posterior Present S,R—E scribam I will write

9. Posterior Future S—R—E scripturus ero I shall (then) be going to write

Praeteritum E—R (Anterior)

7. Posterior Past R—E—S scripturus eram/fui I was (then) at the point of writing

Table 2.3 which is fully comparable with Table 2.1: in praeterito must be read as Past, in praesenti as Present and in futuro as Future, all in the current use of those names in the primary ternary division of time. In other words, the upper headings of the columns in Table 2.2 are the headings of the rows in Table 2.3. Thus, Madvig’s praeteritum stands for Reichenbach’s Anterior, his praesens for Reichenbach’s Simple and his futurum for Reichenbach’s Posterior. 2 Harm Pinkster (pers. comm.) pointed out that the American translation that I used translates

praeteritum into perfect as opposed to the German one (praeteritum) and to the original Danish fortid (past). In my view, the American version matches what Madvig in fact argued as the second column contains only perfect (= E—R) forms. It shows that the term praeteritum is equivocal in being used to pertain to imperfectum, to perfectum and to imperfectum/perfectum taken as an oppositional dimension. As argued in Chapter 1, this is due to opposing past1 to past2 .

2.1 The Reichenbachian Matrix in Different Forms

17

How confusing can familiar terminology be? Regardless of the difference of terms, one may conclude that Table 2.1 and Table 2.3 are so similar that the current debate about tense systems should not be traced back to 1947 but rather be connected to a long tradition in which the terms used in the organization of Greek and Latin tense systems have been applied to modern languages. On the other hand, there are also differences. In Tables 2.2 and 2.3 the heading Praeteritum crosses in cell 2 with the heading in praesenti. Madvig characterizes the Present Perfect as follows: (2)

The Perfect is used in Latin in relating and giving information of past occurrences both in continuous history and isolated notices of events (the historical perfect† ) . . . The perfect is also used to express a thing as done and completed, presenting a contrast to the present moment, at which this thing is no longer spoken of as continuing (the perfect absolute, definite). (p. 290)

In the dagger footnote of (2), Madvig writes: “In Greek the Aorist is used in this signification” thus carrying over the aspectual force attributed to the Greek aorist to the perfectum in the Latin tense system (cf. Pinkster (2015:382– 4; 444ff.). Tables 2.1 and 2.3 differ therefore in some important respects due to the fact that the term praeteritum (= Perfect) in (2) is used to cover both anteriority and aspectual information connected with the aoristic meaning attributed to the perfectum. This reflects an important opposition made in Latin grammars between the so-called actio perfecta (cells 1, 2 and 3) and the actio infecta (cells 4, 5 and 6), which is generally taken as an aspectual one. The semantics of the Present Perfect distinguishes Madvig’s system from Reichenbach’s but classical scholars have also to deal with the opposition between Present Perfect and plusquamperfectum which runs parallel to the distinction between the Simple Present and the Simple Past. The opposition between perfectum and imperfectum (i.e. between cell 2 and cell 4) is relevant as long as the Anterior Present in cell 2 is seen as a past tense form opposed to the past tense form in cell 3: it gives room for an aspectual opposition by attributing the sense of completion to the aorist meaning of the perfectum and the sense of incompletion to the imperfectum. The opposition between perfectum and plusquamperfectum can then be seen as a temporal one. In this way, Madvig’s matrix is more appropriate for determining the nature of the oppositions in which the Present Perfect is allowed to participate on theoretical grounds: as a past tense in opposition to the Imperfect and as a present tense in opposition to a past plusquamperfectum.

18

How to Deal with the Long Tradition of Going Ternary?

2.1.2 Three Times 2 × 3 for Dutch Verkuyl and Le Loux-Schuringa (1985:251–7) gives a detailed description of a ternary proposal by Kollewijn (1892) for the description of the Dutch tense system. Kollewijn assumes a main division between Past, Present and Future, each of them forming a similar primary subdivision: Past, Present, Future. Table 2.4 pictures the Present-system containing six tenses. Again the Table 2.4 Kollewijn’s 2 × 3 matrix for Dutch, English and Latin Present Past R—S

Present R,S

Future S—R

Imperfect(-ive) E,R

4. Simple Past E,R—S Ik schreef I wrote scribebam

5. Simple Present E,R,S Ik schrijf I write scribo

6. Simple Future S—R,E Ik zal schrijven I will write scribam

Perfect(-ive) E—R

1. Anterior Past E—R—S Ik had geschreven I had written scripseram

2. Anterior Present E—R,S Ik heb geschreven I have written scripsi

3. Anterior Future S—E—R Ik zal hebben geschreven I will have written scripsero

numbering of a cell corresponds to a cell with the same tense form in Reichenbach’s Table 2.1 on page 13 including the three points E, R and S. The italicized names of the tenses in the cells are also the ones used by Reichenbach.3 Then Kollewijn multiplies the number of tables: (3)

But the present moment [i.e. Present] need not be the starting-point. That starting-point may be in the past. The two present tenses are then considered with respect to that moment in the past; the two past tenses are past with respect to the starting point in the past; the two future tenses are future with respect to that moment in the past. (p. 147, transl. hjv)

3 Latin forms are included here because Latin school grammars generally give the six tenses in

Table 2.4 in the same way. As described in Hewson (2012), the Roman grammarian Varro used the terms Infectum and Perfectum as heading for the rows and argued on morphological grounds that the Infectum-forms express tense and the Perfectum-forms aspect. Thus he reduces the number of tense forms to three. Generally, the opposition between the row headings is seen as an aspectual one, which brings the number of indicative tense forms to six.

2.1 The Reichenbachian Matrix in Different Forms

19

This says that by replacing Present by Past, one obtains a subsystem with six forms with as central point Present, which is the then-present of the Pastdomain, with respect to which there is a past and a future. This yields for Dutch the two missing tense forms Ik zou schrijven ‘I would write’ and Ik zou geschreven hebben ‘I would have written’ underlined in the quote. Now there are twelve tense forms. Putting the perspectival point at the Present of the Future domain gives eighteen tense forms. Quotation (3) shows that Kollewijn used auxiliary points in the past from which he calculated the position of the E and that he arranged the points in his system on the basis of anteriority and simultaneity. He used the Dutch terms of Table 1.1 on page 2 so that, for example, the tense form in cell 4 was abbreviated as onvoltooid (= imperfect(-ive)) verleden (= past) tijd (= tense). His system was intended as an alternative to Te Winkel’s binary system but the equivocality with respect to the term pairs Perfect/Imperfect and Perfective/Imperfective is the same in both systems. In Dutch, the upper row contains tense forms which require the auxiliaries hebben ‘have’ or zijn ‘be’ as opposed to the lower row. 2.1.3 Reducing 3 × 3 to 7 for English Now, the Echternach step backwards: Jespersen (1924:256) did not accept nine tenses. He wanted, in his words, to avoid the logical error of having a tripartition of ‘now’, which “as a point has no dimensions and cannot be divided”. He reduced the number of tenses to seven. The result is shown in Figure 2.1. I will not explain this figure in detail. It suffices to say that

Figure 2.1 Jespersen’s seven tenses

Jespersen divided time into Past (A), Present (B) and Future (C) and that he did not permit B to be split into three points Ba, Bb and Bc as he did with A and C. He identified the notion of Present with the indivisible point n. It is not difficult to see the close relationship with Kollewijn’s way of organizing a Germanic tense system, because by writing A-past, B and Cfuture bold-faced, it becomes clear that the primary subdivisions of A-past

20

How to Deal with the Long Tradition of Going Ternary?

and C-future express the same as in Kollewijn’s system. The point Ab is the then-present of A-past and Ab has a past behind it and a future in front of it. The big difference is that Jespersen refuses to divide Present into a tripartite structure. Jespersen’s aversion to a matrix organization was obviously so great that he accepted that Figure 2.1 cannot harbour the Present Perfect. On page 269 he turned this into an advantage by saying that the Present Perfect contains an element of result: the tense form is not on its own but rather “a retrospective variety of the present”. However, it is quite easy to redraw Figure 2.3 as an incomplete 3 × 3 matrix, as shown by Table 2.5. In other words, Jespersen Table 2.5 Jespersen translated into Reichenbach Past R—S

Present R,S

Future S—R

Anterior E—R

1. Anterior Past E—R—S had written scripseram

2.

3. Anterior Future S—E—R will have written scripsero

Simple E,R

4. Simple Past E,R—S wrote scribebam

5. Simple Present E,R,S writes scribo

6. Simple Future S—R,E will write scribam

Posterior R—E

7. Posterior Past R—E—S would write scripturus eram

8.

9. Posterior Future S—R—E will sing scripturus ero

turns out to differ from Madvig only in emptying two cells: 2 and 8, forgetting about his objection against the nearness expressed by the cells 7 and 9. Cell 2 is made empty because Jespersen does not allow the Present Perfect and cell 8 is empty because he sees the S,R—E configuration as expressing a non-temporal use of tense, in the case of I hope he will send the money tomorrow as a wish. This is a step back with regard to Madvig’s reorganized Table 2.3. Only in that perspective, can Reichenbach’s Table 2.1 be seen as an improvement: the Present Perfect recaptured its place and the Posterior Present in cell 8 added to the problems of crossing temporal relations with temporal relations. And in this way, we are back in 1871, four years after Te Winkel published his paper on binary tense.

2.1 The Reichenbachian Matrix in Different Forms

21

2.1.4 3 × 3 for Classical Greek It makes sense to extend the list of tables with tense systems discussed so far by presenting the indicative forms of classical Greek in order to see how its system harbours the aorist in relation to the other tenses. The standard way of presenting them so far has been ternary up to and including the most recent comprehensive and well-organized grammar Van Emde Boas et al. (2019), published as The Cambridge Grammar of Classical Greek, henceforward CGCG. This grammar has incorporated insights from current branches of theoretical linguistics. These insights are critically examined in the present book, so my interaction with CGCG is two-sided. I regard it as a valuable tool for seeing how tense forms of ancient Greek were used and are to be interpreted, but I keep room for considering the theoretical ternary basis open for a binary reorganization along the lines to be drawn. A look at Table 2.6 reveals that CGCG reserves the term perfective as heading for the middle row for the aorist and the term perfect as heading for the three forms in the upper row.4 In view of the discussion about the relation Table 2.6 Reichenbach in CGCG Past R—S

Present R,S

Future S—R

Perfect E—R

1. Plusquamperfectum E—R—S I had written egegraph¯e

2. Perfectum E—R,S I have written gegrapha

3. Anterior Future S—E—R I will have written

Perfective E–R

Aorist E–R I wrote/have written egrapsa

Imperfective E,R

4. Imperfectum E,R—S I wrote egraphon

5. Praesens E,R,S I write graphô

6. Simple Future S—E,R I will write grapsô

between these terms that will follow in later chapters, it is good to have the semantic description of major Greek tense forms as defined in CGCG. 4 Rijksbaron (2006:39) observes that the use of the future perfect in Ancient Greek is virtually

restricted to just two verbs and that periphrastic tense forms make use of eimi ‘be’. Hence this cell is left empty.

22 (4)

How to Deal with the Long Tradition of Going Ternary? The present indicative in cell 5 is described in Sections 33.14–33.21: it is used to refer to actions ongoing in the present; • it is used to refer to repeated or habitual actions, the habit being in effect at the moment of speaking; • it is used to refer to general or timeless truths which are continuously in effect; • it is used to refer to actions ongoing or to the action as a whole (arrive/have arrived, give/have given); • it is used to refer to the future. The imperfect indicative in cell 4 is described in Sections 33.22–33.26: • it is used to refer to ongoing actions in the past; • it is used to refer to repeated actions in the past (with or without an ‘end’). The aorist indicative is described in Sections 33.27–33.33: • it is used, par excellence in narrative texts, to present (the course of) main events; • it is used to present the occurrence of an action in the past as a single uninterrupted whole; • in non-narrative texts, it is typically used to describe completion of an action; • it is used gnomically in order to express general habits, tendencies, processes as a guideline. The perfect indicative in cell 2 is described in Sections 33.34–33.38: • it is used to signify that an action has been completed in the past with effects in some way relevant in the present; • it is used frequently to express a more-or-less permanent state in the present which exists as the result of a completed action in the past; • it is used in its active form to emphasize the responsibility of the subject of the verb for the result of the action. •

(5)

(6)

(7)

The aorist is seen as a Past tense marked by the augment e-. CGCG distinguishes it from the other two past tenses by taking it as Perfective. This puts it in an opposition to the Imperfectum in cell 4. It is also opposed to the Plusquamperfectum in 1 which is called a perfect tense form. In view of the binary analysis of the aorist in Chapter 7, it should be noted that the aorist in Table 2.6 distinguishes itself from the two other past tense forms by not expressing R—S. In other words, there are two different sorts of past: roughly, one bound to S in cell 1 and the other one not bound to S in the intermediate row. One question will become crucial along the way: what does the term use mean in (4)–(7) from a compositional point of view? Does each use of a tense form T represent a different meaning so that one has T1 , T2 , . . ., Tn , where each subscripted tense form has its own meaning M1 , M2 , . . ., Mn ? Or do the discerned forms T have something in common in spite of the subscripts and

2.1 The Reichenbachian Matrix in Different Forms

23

should we look at a deeper level for a more abstract meaning covering all the uses? My strategy will be to use Ockham’s razor as much as possible. Apart from providing insight into how the Greek tense system is organized ternarily, Table 2.6 and in particular the list of uses in (4)–(7) can be seen as capturing the contribution made by classical grammarians to the current theory of tense and aspect. As observed in Section 1.2, there is a price to be paid for accepting the terms used in the long tradition of classical school grammar primarily based on morphology. A challenge is therefore to see whether a wellfounded binary floor can be laid under the empirically based statements in (4)–(7).

2.1.5 Two Times ((3 × 3) − 2) for French As a Romance language, French has a rich tense system including an aoristic tense form: the Passé Simple and its past form the Passé Antérieur. This means that a binary approach with three binary tense oppositions covering eight tense forms meets the challenge of accounting for the forms not being covered. That is not really disturbing because it also holds for a ternary approach with a matrix covering only nine tense forms: French has more than nine. Actually, it is quite hard to agree on how many tense forms there are. Didactic grammars tend to restrict them to eight, but scientific grammars include other forms as well, up to fourteen as in Martin (1971). The matrix in Table 2.7 occurs on page 269 of the Handbook of French Semantics in chapter 14 ‘Tense and Aspect in Sentences’ and contains fourteen forms.5 It is an attempt by the two main authors of that chapter, Co Vet and me, to combine a binary approach with a ternary one as a way to solve the well-known problems with a 3 × 3 matrix. The stamp of Vet’s work on the French tense system, including Vet (1980;1981;1994;2001) and continued in Vet (2007;2008), is obvious. Vet is well aware of Te Winkel’s binary system and its Dutch ternary alternative in Kollewijn (1892). My present position is no longer compatible with the matrix in Table 2.7, as I made clear in Verkuyl (2008). Up to and including the last of his publications mentioned, Vet maintains his position. This gives room for improving on my 2008 objections to it due to formal tools developed in the meantime. I think it is possible to account for the richness of the French tense system in a way crucially different from the matrix presented in Table 2.7. 5 The handbook is referred to as Corblin and de Swart (2004), the chapter as Corblin and de Swart

(2004:233–70) or Verkuyl et al. (2004).

24

How to Deal with the Long Tradition of Going Ternary?

Table 2.7 The French tense system according to Vet, in matrix form Subsystem 1

Past R—S

Present R,S

Future S—R

E,R

4. E,R—S Passé Simple écrivit Passé Composé a écrit

5. E,R,S Présent écrit

6. S—R,E Futur Simple écrira Futur Périphrastique va écrire

R—E Prospective aspect

8. S,R—E Futur Périphrastique va écrire

E—R Retrospective aspect

1. E—R—S Passé Antérieur eut écrit Passé Surcomposé a eu écrit

2. E—R,S

3. S—E—R

Passé Composé

Futur Antérieur

a écrit

aura écrit

Subsystem 2

Past in the Past R—S

Present in the Past R,S

Future in the Past S —R

E,R

4. E,R—S Plus-que-Parfait avait écrit

5. E,R,S Imparfait écrivait

6. S —R,E Future du Passé écrirait Futur Périphrastique du Passé allait écrire

8. S ,R—E Futur Périphrastique du Passé allait écrire

R—E Prospective aspect E—R Retrospective aspect

1. E—R—S Plus-que-Parfait Surcomposé avait eu écrit

2. E—R,S Plus-que-Parfait avait écrit

3. S —E—R Futur Antérieur du Passé aurait écrit

Vet’s account of the French tense system builds further on Martin (1971). It combines a present subsystem 1 and a past subsystem 2 taken together in one overall system with fourteen different configurations. Most of the tense forms are used for spoken French and some of them for written French only. The Passé Simple and the Passé Antérieur have practically disappeared in

2.1 The Reichenbachian Matrix in Different Forms

25

colloquial language while surviving in written language. Vet locates them in cells 1,4 and 1,1 and regards the Passé Composé and the Passé Surcomposé as forms that are in the (long) process of replacing the Passé Simple and the Passé Antérieur in spoken French. The division into the subsystems 1 and 2 resembles Kollewijn’s primary division into subsystems A (= Past), B (= Present) and C (= Future). Kollewijn (1892) allowed each of these subsystems to have a vertical tripartition Past, Present and Future crossing with a horizontal bipartition reflecting the opposition E—R (perfect(-ive)) and R,S (imperfect(-ive)), thus obtaining eighteen tense forms. Vet takes Present as the deictic subsystem 1, splits it vertically into Past, Present and Future which cross with the horizontal division into E—R, R—E and R,S shown in Table 2.7. As a second subsystem 2, Vet takes Past. The vertical tripartition yields Past in the Past, Present in the Past, and Future in the Past and crosses horizontally in the same way as in subsystem 1. The configurations E—R and R—E of the horizontal tripartition in each of the subsystems are colored gray because Vet sees them as aspectual, as opposed to E,R-configurations. Vet does not want to see the configuration E,R as expressing that E is taking place at R and the E—R-configuration as expressing that E took place before R. Rather E in E,R is presented at R as completed and, in the case of E—R, it is only the result of E that counts at R, not its location. This should also apply to cell 3. I will discuss three of the problems that are due to the ternary organization of the French tense forms in Table 2.7. 1. The Problem of Opposing Anaphora to Deixis. Corblin and de Swart (2004:255) says that the tenses of the deictic subsystem 1 “establish a relation to S. Subsystem 2 is anaphoric because the tenses of these systems need to establish a relation with some temporal antecedent. The main perspectival point S of subsystem 2 is dependent on another point previously introduced in the discourse by which it obtains the status that S has” in system 1. This is demonstrated with the help of the sentences in (8). (8)

a. Marie entra dans la cuisine (E1 ). Pierre faisait la vaisselle (E2 ). Marie enter+PS la cuisine. Pierre do (IMP) the dishes. Marie entered the kitchen. Pierre was washing the dishes. b. Marie entra dans la cuisine (E1 ). Pierre avait fait la vaisselle (E2 ). M. entered (PS) the kitchen. P. had washed (PQP) the dishes. c. Marie entra dans la cuisine (E1 ). Pierre allait faire la vaisselle (E2 ). M. entered (PS) the kitchen. P. was going (FPP) to wash the dishes.

26

How to Deal with the Long Tradition of Going Ternary?

The orientation point S of subsystem 2 is said to be dependent on a temporal antecedent previously identified by the context. In a discourse, the underlined tense forms have the function “to provide background information or explanations about facts that were presented in the preceding context”, in the case of (8) the events E1 (2004:262). Vet’s account of the role of the tense forms of subsystem 2 ignores the token-reflexivity of the tense system as a whole. The dependency of Past on the Present has been formulated beautifully by Te Winkel (1866): (9)

In thinking one starts from two time points: either from the present or from the past. In the former case everything is considered, as it appears at the moment one is thinking; in the other, as it appeared at the point of time to which one is moving back with his thoughts. (p. 68) [translation hjv]

In a discourse, the S when taken as the fleeting point n is always there for speaker and hearer when they talk about the past, because they go back to a past domain by putting a perspectival point S there. In this way, Te Winkel makes room for taking S as the then fleeting point n  at which eventualities spoken about are being viewed as occurring, as having occurred or as projected to occur with respect to n  . As pointed out in Verkuyl and Le Loux-Schuringa (1985:248), Te Winkel’s binary analysis of past tenses in which S is always oriented to S would – phrased in Reichenbachian terms – lead to rewriting Vet’s subsystem 2 (minus the doubling and minus the dubious R—E-configuration, to which I will return later on) as shown in Table 2.8. The configuration of the Imparfait in cell 5 Table 2.8 Subsystem 2 with S oriented to S subsystem 2

Past past R—S

Past present R,S

Past S —R

E,R

4. E,R—S —S Plus-que-Parfait avait écrit

5. E,R,S —S Imparfait écrivait

6. [S —R,E]—S Future du Passé écrirait Futur Périphrastique du Passé allait écrire

E—R Retrospective aspect

1. E—R—S —S Plus-que-Parfait Surcomposé avait eu écrit

2. E—R,S —S Plus-que-Parfait

3. [S —E—R]—S Futur Antérieur du Passé aurait écrit

avait écrit

2.1 The Reichenbachian Matrix in Different Forms

27

should then be read as E,R,S —S rather than as Vet’s E,R,S and this overt inclusion of S should be extended to all cells of subsystem 2 of Table 2.7. The proper relation between Past and Present is one in which S and S are structurally related in the sense that S is automatically the then-S in the past of S, not created by anaphoricity but on the basis of the anteriority (‘going back’) relation between PAST and PRES as argued for in Chapter 3. The parallelism between the present and past tense forms stems from what is expressed in quotation (9), not from Vet’s distinction between the subsystems 1 and 2. 2. The Problem of Finding a Syntax for the Configurations. Vet (2007) again proposes the tense system discussed so far, now complemented with information about how to position the French tense forms in the syntactic structure shown in Figure 2.2. Vet locates the tripartition into the Past, Present and

Figure 2.2 Vet’s division of labour between tense and aspect in phrase

structure

Future columns in Table 2.7 at the righthand subnode of TENSE on the basis of the three ordering relations between S and R. Likewise, the tripartition into rows on the basis of the relation between E and R are located as a subnode of ASPECT . Syntactically, the structure given in Figure 2.2 is a simple translation of the configurations in the cells of Table 2.7 into tree positions. This goes wrong. Vet’s notation PRES + ANTERIOR+∅ for Elle a écrit une lettre ‘She has written a letter’, for example, justifies the question mark because Vet fails to point out how ∅ operates on S0 and how ANTERIOR operates on ∅(S0 ) to obtain ANTE RIOR(∅(S0 )) or whatever output is possible given the complex TENSE node. Apart from that, the auxiliary avoir ‘have’ is allowed to be located both at the node ANTERIOR node under TENSE and under the node RESULT of ASPECT, without any indication about how to justify that without any rule.

28

How to Deal with the Long Tradition of Going Ternary?

According to Vet, the resultative interpretation of a sentence like (10a) can be accounted for by (10b), where the verb avoir appears under the node RESULT . In the case of (10c), the sentence is taken as reporting about E itself and the Passé Composé a abattu is then exchangeable with the Passé Simple abattit. (10)

a. Jean a abattu le vieux chêne. ‘Jean has cut down the old oak’. b. PRES+∅+ [RESULT avoir]+S0 c. Ce jour-lá, Jean a abattu/abattit le vieux chêne. ‘On that day, Jean has cut down/cut down the old oak’. d. PRES+ [ANTERIOR avoir]+∅+S0 e. Je vois que Jean a abattu le vieux chêne. ‘I see that Jean has cut down the old oak’.

Vet strengthens his point by underscoring that the interpretation of (10c) is not available for (10e). According to him, (10e) proves that a resultative interpretation is uniquely expressed by the Passé Composé when avoir is connected with RESULT as in (10b). And this gives him room to assume that the Passé Composé has mimicked the essential property of the Passé Simple on its way to superseding it (cf. Caudal and Vetters 2007 for a historical analysis). Figure 2.2 can be easily shown to be inferior to the binary structure carrying aspectual and tense information. Dropping PROSPECTIVE below the node ASPECT results in a binary opposition that can be shown to make sense. Dropping it under TENSE leaves anteriority vs ∅, which turns out to duplicate the opposition between the binary opposition PAST and PRES. The same holds for the dropping of POSTERIOR. The inadequacy and imprecision in Vet’s proposal are only due to his desire to maintain a ternary approach. It should also be underlined here that the resultative interpretation of the Passé Composé is just stipulated by Vet. A speaker may have uttered (10a) somewhat agitated at the moment that the tree started to fall down, continuing with ... comme tu l’entends ‘as you hear’. In Chapter 3, it will be argued that the Present Perfect can be seen as essentially a reportive tense form and that the notion of resultativity should be disconnected from it. This also holds for the French Passé Composé. 3. The Problem of Supersedence. Theoretically it is rather surprising to see the Passé Composé occurring both in cell 1,2 and in cell 1,4 of Table 2.7 and to see the Passé Simple also sitting in cell 1,4. After all, it is a past tense form and therefore it should not be put in what is supposed to be a present deictic subsystem 1. According to the authoritative traditional grammar Grevisse (1964),

2.1 The Reichenbachian Matrix in Different Forms

29

the Passé Composé indicates “a fact achieved in a definite or indefinite period in the past and which is considered as being in contact with the present, either because that fact took place in a period not yet expired or because its consequences are seen in the present”.6 This definition is reasonably compatible with what is expressed by the E—R,S-configuration in cell 1,2. Reichenbach assigned the configuration E,R—S to the English Simple Past explicitly with the idea of “moving” R back from S to E by putting the perspective on E at E in the past, so as to distinguish the Simple Past from the Present Perfect. Having configuration E,R,S —A in cell 2,5, where A is the anaphoric anchor for S , available for the Imparfait, Vet assigns E,R—S to the Passé Simple in 1,4. According to Grevisse, the Passé Simple expresses “a fact totally achieved at a definite moment in the past without taking into consideration the contact that this fact can have with the present, in itself or by its consequences”.7 This definition conflicts with the location of the Passé Simple in cell 1,4 because the E,R—S-configuration brings E in contact with S. As noted above, Vet gives E,R a different interpretation from Reichenbach’s R,S but this does not work out well given the cells 5, in which E,R expresses that E is/was taking place at R.8 Vet’s leading idea is that the Passé Composé is in the process of superseding the Passé Simple by adopting its properties. His line of thought can be reconstructed on the assumption that the Passé Simple has an E,R—S-configuration, that the Passé Composé in cell 2 expressing an E—R,S-configuration has become polysemous being able to express E,R—S by mimicking the Passé Simple. The semantics of the Passé Composé as given in Molendijk et al. (2004:297– 305) and Borillo et al. (2004) explicitly includes the idea of a structural orientation of R on the point of speech S, which runs counter to Vet’s idea of polysemy expressed by the Passé Composé: the “French Perfect ... remains a perfect in the sense that the event in the past is viewed from the speech time S” (p. 300). This excludes the configuration E,R—S for the Passé Composé in cell 4 of Table 2.7.9

6 Le Passé Composé “indique un fait achevé à une époque déterminée ou indéterminée du passé

et que l’on considère comme étant en contact avec le présent, soit que ce fait ait lieu dans une période non entièrement écoulée ou que ses conséquences soient envisagées dans le présent.” (section 721). [translation hjv] 7 Le Passé Simple “exprime un fait complètement achevé à un moment déterminé du passé sans considération du contact que ce fait, en lui-même ou par ses conséquences, peut avoir avec le présent.” (section 719). [translation hjv] 8 Section 7.3 argues in detail why E,R—S is not a proper configuration for a Passé Simple. 9 As also argued in De Swart (2001), De Swart and Molendijk (2000) and De Swart (2003).

30

How to Deal with the Long Tradition of Going Ternary?

González and Verkuyl (2017) argues for the Spanish Pretérito – a form comparable with the French Passé Simple – that supersedence does not imply that the successful newer tense form occupies the place of the marginalized one: in some variants of Latin American Spanish but not in peninsular Spanish, the Pretérito survives by mimicking the properties of the Perfecto. When the tense system as a whole has been reorganized in favour of a stronger position of speaker and hearer with respect to location of eventualities about which they communicate, there are arguments to put the loser outside the rearranged system because it no longer participates in oppositions. In that case, the gradual reduction in dominance of the French Passé Simple and the current dominance of the Passé Composé can be understood as resulting from the increasing tendency to make the point of speech S the deictic centre of the complete tense system, so that the Passé Simple and the Passé Antérieur no longer find a place in a system that turned binary and are condemned to a niche. The three problems for Vet discussed here support the need argued for in Verkuyl (2008) to reorganize the French tense system binarily. One only has to rotate Table 2.7 clockwise, throw out the Passé Simple and the Passé Antérieur and remove the Passé Composé from cell 4, and one obtains a binary table (2008:222). This table reappears in a slightly adapted form in Section 7.3.1 on page 238 in the context of a more detailed analysis of the position of the Passé Simple in the French tense system. 2.2

Ternary with Intervals

2.2.0 Introduction So far we have been discussing proposals in which the Reichenbachian S, R and E are taken as points, in particular the point R. The present section will discuss the option of seeing the relation between E, R and S in terms of intervals. A choice between points and intervals has nothing to do with a choice between binary and ternary, because in the discussion about the difference between point and interval, the notion of truth turned out to be central: it makes quite a difference whether a predication is evaluated with respect to a point or to an interval. Bennett and Partee (1978), Taylor (1977), Dowty (1979), among others, made clear that one cannot escape from taking into account the change of truth value with the passage of the time needed for the actualization in real time of what is denoted by the predication. If one interprets Reichenbach’s system as expressing point structure, then it is quite natural to look for a solution for the problems raised in the preceding sections in terms of a system expressing interval structure.

2.2 Ternary with Intervals

31

Klein (1992) is the beginning of a series of publications centered on the unclarity of Reichenbach’s point of reference R (e.g. 1994;2000;2009). Its goal is to solve what Klein calls the Present Perfect puzzle. Klein argues that Reichenbach’s system cannot solve the puzzle and that taking R as an interval brings the solution. Because the treatment of the Perfect bears on the clarification of what so far has been brought together under the label Perfect(-ive) in the longstanding discussion about the Latin perfectum, I need to discuss this paper in some detail. This prepares the way for rejecting Klein’s ternary solution and for proposing a structural binary solution in Chapters 3 and 6. 2.2.1 The Present Perfect Puzzle The Present Perfect puzzle presents itself in sentences like (11). (11)

a. Chris has left York. b. ∗ Chris has left York yesterday/last year/two years ago. c. ∗ When has Chris left York?

The problem is that (11a) is grammatical whereas (11b) and (11c) are out. There are some exceptions such as He has just recently arrived and He has been there before. They add to the puzzle: why is this the case? The problem also involves the question: why are Simple Past sentences in (12) okay? (12)

a. Chris left York. b. Chris left York yesterday/two years ago. c. Chris was in Pontefract last year.

Klein discusses two sorts of attempt proposed in the literature. The first one – in his terms, the scope solution – focusses on the modification by the adverbials in (11b). The general idea is then that adverbials expressing pastness modify R in a configuration R—S and that deictic adverbials require R,S. Part of the problem is then that there are deictically oriented adverbs like just and recently that may occur with the Present Perfect, as in Chris has just left York. For a treatment of the Present Perfect in terms of the current relevance solution, Klein sees three problems. The first concerns the notion of current relevance itself: it is not clear how to determine relevance in the absence of a testable criterion. The second is that there is no explanation for the question of why (13a) is possible while (13b) is out. (13)

a. Chris was dead. b. *Chris has been dead.

Klein presents this problem as: “One surely cannot say that Chris’s being dead has no further relevance in (13a), nor does the current-relevance analysis

32

How to Deal with the Long Tradition of Going Ternary?

explain why (13b) is entirely impossible (unless you believe in resurrection)” (p. 531). This characterization of the problem is not very convincing because Chris has been dead for years is correct, while *Chris was dead for years is ‘entirely impossible’ when Chris was really and not seemingly dead. So the question to be put is rather why (13b) requires support from for-adverbials and from adverbials with since or ever since, while that is not needed in The gas leak has been stopped. In Section 3.3, an answer will be given in terms of what the Present Perfect distinguishes from Simple Past and Simple Present. The third problem Klein has with a current relevance analysis is that it cannot explain why the Present Perfect fails to locate eventualities in an acceptably exact way. He writes: “The speaker may even know when Chris was in Pontefract, or when he left York–but one is simply not allowed to add the appropriate adverbial without changing the construction” (pp. 531–532). Klein does not offer an explanation for this observation: one will also be given in Chapter 3 together with a solution for the problem just mentioned. 2.2.2 Topic Time as a Key for the Solution to the Present Perfect Puzzle The proposed solution of the Present Perfect puzzle requires an insight into the main features of Klein’s correction on Reichenbach. He distinguishes between (a) the time of utterance TU, (b) the topic time TT about which an assertion is made in the utterance, and (c) the time of the situation TSIT. These three temporal intervals relate to each other in a systematic way in two pairs: TT relates to TU and TT relates to TSIT, but TU does not relate directly to TSIT. Semantically, Klein’s correction on Reichenbach boils down to a switch from point structure to interval structure. This means that Klein’s tense system can make use of all sorts of relations between finite sets of points (time spans) rather than of relations between points.10 Respecting Klein’s transition from points to temporal intervals, I will write TU as STU , TT as RTT and TSIT as ETSIT so as to facilitate a comparison between Klein’s and Reichenbach’s approach. The continued use of S, R and E as labels also serves to show that the differences between the two resulting systems are not as big as claimed by Klein. 10 If time is seen as a system of time points, these points are positioned on a straight line T, where

T is a set of time points with a partial ordering. This point-based modelling represents tense in terms of a frame T = T, (RefT,AT) = E—R

The same holds for the node Asp: Asp< puts AT before EvT in (2a), Asp> puts AT later than EvT in (2c) and Asp requires an overlap between AT and EvT in (2b). These relations are exactly the ones used by Reichenbach: his tripartite configurations are systematically mapped into nodes and relations between nodes in dyadic branching syntax. In this way, the configurations in the top of the three columns of the matrix in Table 2.1 in Chapter 2 on page 13 reappear in Figure 3.2 as options for the node T in regulating the relation between RefT (Reichenbach’s S) and AT (Reichenbach’s R). Something comparable happens on the lower level with the node AT in its relation to Evt (Reichenbach’s E). The three configurations at the left-hand side of the rows in Table 2.1 are assigned to the node AsP. This inspection of what happens in syntactic approaches to tense results in concluding that syntactic dyadic branching does not necessarily lead to representing the binary oppositions in (3). (3)

a. Present (PRES) vs Past (PAST). b. Synchronous (SYN) vs Posterior (POST). c. Imperfect(-ive) (IMP) vs Perfect(-ive) (PERF).

Returning to the dyadic branching in Figure 3.1c, one can see that Op3 standing for IMP or for PERF takes (a tenseless) ϕ in order to form a tenseless ϕ at a higher level which is taken by Op2 standing for SYN or for POST to again form a tenseless ϕ which is taken by Op1 standing for PRES or for PAST in order to form a tensed ϕ  . Figure 3.3 makes this explicit by using linguistic labels, where the lowest S (from now on always called S0 ) is the tenseless predication Maria sing.7 7 As an early generative linguist I am used to letting the symbol VP (= Verb Phrase, predicate) stand for a verb plus its internal argument. From now on, the symbols S and S will be used in

a very different way from their use in the Reichenbachian notation.

3.2 Binary Operators

55

Figure 3.3 Tense operators expressing the three binary oppositions

Given a tenseless predication ϕ and going from there to the top, a sentence like Maria has sung in (4) is seen as compositionally formed by applying PERF to a tenseless S0 Maria sing so as to form the tenseless predication PERF(ϕ). (4)

a. Maria has sung. b. PRES(SYN(PERF(Maria sing)))

The output of PERF is then taken by the operator SYN. This results in the still tenseless SYN(PERF(ϕ)), which is the input for the operator PRES yielding the tensed sentence at the top of the tree, represented as PRES(SYN(PERF(ϕ))). On this account, the primary opposition in (3a) between PRES and PAST is the one by which a tenseless predication S becomes a tensed sentence S . This suggests that the notion of tense is only applicable to the opposition between PRES and PAST as proposed for Dutch in Paardekooper (1957). However, in a compositionally driven construal of structural meaning, some building blocks at lower levels obtain their full effect only at higher levels. This holds in particular for variables introduced in S0 and bound at a level higher than S0 . Therefore it would be too simple at this stage to see (3a) as a tense opposition, (3b) as a mood opposition and (3c) as an aspectual one. It will take up to Chapter 8 before it is possible to determine whether it makes sense to connect the three levels above S0 in Figure 3.3 directly to a strict distinction between tense, mood and aspect. Until then I will use the term tense structure to the ensemble of operators in configurations like (4b). 3.2.2 Preparing for the Semantics of Binary Operators Table 3.2 provides the eight tense forms captured by Te Winkel now to be analyzed in terms of the six operators introduced previously. I will begin here with first describing informally what happens when the tenseless bottom ϕ (= S0 ) in Figure 3.3 is taken by PERF or by IMP and what happens next when SYN

56

Binary Tense Structure

or POST applies. Briefly, each of these operators contributes a clause with a connective expressing a two-place relation between indices. An index stands for a semantic value taken as a set in a number system. In this first round of explaining what the operators do, I will leave out the operators and quantifiers binding the indices. The formulas for the compositional derivations in which tense operators are introduced with a lambda operator and existential quantifiers in front, are given in the formal Section 3.5. Table 3.2 The eight tense forms in Te Winkel’s system

IMP

PRES

PAST

1. Simple Present (o.t.t) Maria zingt Maria sings PRES ( SYN ( IMP (ϕ)))

2. Simple Past (o.v.t) Maria zong Maria sang PAST ( SYN ( IMP (ϕ)))

3. Present Perfect (v.t.t.) Maria heeft gezongen Maria has sung PRES ( SYN ( PERF (ϕ)))

4. Past Perfect (v.v.t) Maria had gezongen Maria had sung PAST ( SYN ( PERF (ϕ)))

5. Simple Future (o.t.t.t.) Maria zal zingen Maria will sing PRES ( POST ( IMP (ϕ)))

6. Future in the Past (o.v.t.t.) Maria zou zingen Maria would sing PAST ( POST ( IMP (ϕ)))

7. Future Perfect (v.t.t.t.) Maria zal hebben gezongen Maria will have sung PRES ( POST ( PERF (ϕ)))

8. Future Perfect in the Past (v.v.t.t.) Maria zou hebben gezongen Maria would have sung PAST ( POST ( PERF (ϕ)))

SYN

PERF

IMP POST

PERF

For the sentence Maria has sung in (4a), PERF in (4b) introduces the clause k ≺ β where the index k replaces the variable α of the eventuality argument of the verb sing in the predication S0 and where β is a variable to be replaced by j later on by the application of SYN or POST. Similarly the IMP operator introduces the clause k  β. (5)

a. b.

PERF IMP

introduces an index k such that [ϕ . . . (k) . . . ∧ k ≺ β]. introduces an index k such that [ϕ . . . (k) . . . ∧ k  β].

The connective ‘≺’ in (5a) expresses precedence: k precedes β fully in the way in which, say, the number 3 precedes the number 4 by being fully

3.2 Binary Operators

57

contained in it.8 After its introduction in the still tenseless S0 , the clause k ≺ β remains atemporal. Dependent on information in S0 itself, k may be durative or terminative, as explained in Chapter 5. Thus the notion of full actualization is neutral with respect to the aspectual opposition between durativity and terminativity. After the application of SYN in (4b) the resulting clause k ≺ j will be read as ‘k is fully actualized in j’. The clause introduced by IMP in (5b) leaves open the option of standing for k = β or for k ≺ β. This means that after application of SYN, the clause k  j is typically a clause contributing indeterminacy: the hearer cannot know which option is taken unless more information is or becomes available. This makes the third binary opposition in (3c) privative and not equipollent, PERF being the marked option. Formally, ‘≺’ differs crucially from the symbol ‘ 0, one obtains an opposition between a function f id – from now on mostly written as id – characterizing stative verbs, as defined in (8a) and a function f su – from now on mostly written as su – characterizing non-stative verbs and defined in (8b). (8)

a. id(x) = ax + b, b. su(x) = ax + b,

with a = 1 & b = 0 with a = 1 & b > 0

The identity function id in (8a) models the sense of stativity: it returns for any x in its domain the same value x in R+ . The function su in (8b) models nonstativity by returning for each x in the domain a different value x + b in R+ , with b > 0. The change expressed by su with respect to id is minimal but (8b) makes su into what can be seen as the counterpart in R+ of the successor function s in N. Defining motion expressed by a non-stative verb in terms of su, one can say that a sort of doubling of the sense of progress becomes available which is absent in the definition for id: one in the monotone increase of change expressed by su because each image differs from its original, the other contributed by the floating point n introduced by i ◦ n, which for speaker

5.1 At the Bottom of a Predication

139

and hearer has the same sort of “noiseless” forward dynamics as expressed by su (and Russell’s tiny speck).3 The choice of R+ as the domain and co-domain of f A anchors all verbs in the real number system. Stored in a mental lexicon, a verb is not connected to the time axis as long as it is not being used in a sentence given a domain of interpretation. At the lexical stage, each individual verb is assumed to be grounded in the real number system and all three verbs in (6) express unbounded continuity. Thus the contribution that a verb makes to a predication can be described as providing an anchoring into the real number system, so that the resulting predication can be connected to the time axis, given appropriate tense information provided by PRES or PAST. One immediate consequence of assuming (7) as the basic format for each verb is that for all pairs of disjoint subsets of R+ , the equation in (9) holds (with f A (A) := { f A (x)|x ∈ A}). (9)

f A (B ∪ C) = f A (B) ∪ f A (C)

The right-to-left part of (9) expresses the cumulative property as a lexical property of every verb rather than as a phrasal property stipulated from the outside, which is done, for example, in Krifka (1989;1998) and Kamp (2019:544). Both clearly remain in the tradition of seeing homogeneity and cumulativity as properties of propositions (cf. Leith and Cunningham 2001:339). The equation in (9) entails that homogeneity no longer should be seen as a defining characteristic of phrasal structure. Both homogeneity and cumulativity concern the contribution of a verb at the lexical level. This means that any form of bounding expressed at a phrasal level counts as blocking cumulativity by the presence of specific information overruling f A either in R+ itself or in N, in the case of verbs requiring rounding off to discrete values. Where the application of f A is not overruled, cumulativity and hence unboundedness remains a property contributed by the verb. By alluding to the law of inertia, this is what one may call the Galilean/Newtonian rather than an Aristotelian perspective on motion. The difference between the two functions in (8) is minimal but this minimality not only suffices for making a difference, it also appears empirically correct because a lot of verbs intuitively considered stative allow for being interpreted as non-stative, as often observed in the literature. Sometimes it is very hard to say whether sleep has a stative or a non-stative interpretation in a situation in which someone is sleeping without making movements. In I slept very restlessly last night, it is hard to think of a state, but a mother saying She has slept 3 At this point one may wonder why the slope value a in (7) is kept constant at 1. In Section 6.5.4,

it will be argued that verbs like cool and become can be dealt with as requiring a lower decimal fraction than 1 as their a-value due to the fact that su develops into id at some point.

140

Levels of Interaction between Aspect and Tense

very quietly this afternoon about her baby sleeping in a craddle without any noise can be easily experienced as talking about a state even when breastfeeding interrupted the sleep in a way pictured in Figure 5.2. Another example is think in I think that lexical aspect is a misnomer versus think in I am thinking about a proper solution. The general format in (7) makes it possible to assign the clause b ≥ 0 to verbs like sleep, hang, think, etc. rather than b = 0. Thus it makes sense to keep the function f A for verbs in need of contextual information before they can be interpreted as stative or non-stative in a given situation. 5.2

Discretization and Bounding

5.2.0 Introduction With the functions introduced so far and their shared format as the basis for defining the crucial contribution of the verb to aspectual composition, the way is free for establishing which kind of factors may restrict the unboundedness expressed by verbs. The first step in Section 5.2.1 is to treat verbs that can be pictured in terms of Figure 5.3 on page 134 in terms of function composition at the strict lexical level. Function composition will require mapping from R+ into the set of natural numbers N yielding an unbounded sequence, which may be bounded lexically or at some higher level form of bounding information. The next step in Section 5.2.2 is to focus on terminativity and durativity expressed at the level of a verb phrase headed by a transitive verb always requiring an internal argument, such as erase, reveal and discover. Section 5.2.3 treats the set of verbs like eat, draw, drink, negotiate, walk, sing, etc., which have to remain in R+ when they occur intransitively, but require mapping into N when they occur with an internal [+SQA]-argument. At several places in the present section, attention will be paid to the difference made between inaccusatives and unergatives because the distinction between the two classes involves aspectual issues. 5.2.1 Intransitive Verbs Expressing Discretization The term intransitive is often taken as applicable to a verb having just one argument, apart from the index α, as in (10). (10)

a. b.

WALK (α)(arg1 ) ARRIVE (α)(arg2 )

(= (6a))

unergative unaccusative

Yet, the argument of walk is arguably different from the argument of arrive. In the extensive literature on the lexical meaning of verbs including the literature on the morphology of complex verbs, the traditional opposition between

5.2 Discretization and Bounding

141

transitive and intransitive verbs has been subjected to a critical examination. In the sequel of publications following Perlmutter (1978) – including Hoekstra (1984), Hale and Keyser (1993;1998), Levin and Rappaport Horav (1995;1998), Broekhuis et al. (2015), Broekhuis (2019) – it has become clear that the notion of intransitivity needs refinement by making a difference between unaccusative and unergative verbs. Before Perlmutter’s publication, intransitive verbs were generally seen as transitive verbs without an internal argument. Taking into account the current view on intransitivity, the representations in (10) follow the difference made in the role of the argument of unergatives and unaccusatives. I will keep using the umbrella term intransitive when the difference does not play a role. The distinction between unergative and unaccusative verbs can be made visible in Dutch by the aspectually interesting fact that the copula zijn ‘be’ as expressing the PERF-form for the verb zingen ‘sing’ is not allowed to occur in (11a): an unergative verb requires the auxiliary hebben ‘have’. (11)

gezongen. a. Maria heeft/∗ is mooi Maria has /∗ is beautifully sung ‘Maria has sung beautifully.’ b. Maria is/∗ heeft gearriveerd. Maria is/∗ has arrived ‘Maria has arrived.’

Likewise, the auxiliary hebben ‘have’ cannot occur in a perfect form of the unaccusative verb arriveren ‘arrive’ in (11a). The difference between (11a) and (11b) does not hold for English. What Dutch and English share is that the Past Participle of an unaccusative verb may be used adjectivally as in the departed passengers/de vertrokken passagiers and the frozen fountain/de bevroren fontein whereas this is not possible for unergatives: ∗ the sung Maria/∗ de gezongen Maria of ∗ the walked man/∗ de gewandelde man.4 A number of intransitive verbs are collected in (12). The verbs before the dots in (12a) share the property of taking the verb zijn ‘be’ in the Dutch Present Perfect as in (11b) and so they are to be taken as unaccusatives. The other verbs in (12a) are unergatives. All verbs in (12) express discretization when they are used in sentences expressing a one-off eventuality. The set of English verbs 4 For Dutch, ground breaking work for this distinction was done in Kern (1912). For more

extensive comparisons concerning Dutch and English: Hoekstra (1984), Broekhuis (2019) and Schoorlemmer (1995: 29–35), which also includes a comparison with Russian. Kern already observed that the Dutch equivalents of jump and walk can be used both unaccusatively and unergatively, in the case of wandelen ‘walk’ dependent on whether it takes a directional complement.

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is split into simple verbs in (12a) and completive verbs in (12b). Some of the English verbs (12b) are translated into corresponding simple verbs in French, Spanish, German or Dutch. (12)

a. Unaccusatives: abdicate, appear, arise, arrive, break, burst, capsize, cease, collapse, depart, die, disappear, disembark, disentangle, disintegrate, dissipate, erupt, exit, expire, explode, fall, flare, happen, hatch, ignite, jump, land, merge, recover, relent, renege, resign, resurrect, return, revive, rise, sink, sneeze, startle, stumble, surface, vanish, walk (to), ... Unergatives: belch, blink, boast, caddie, cough, crow, echo, expertize, exult, exclaim, feast, jump, laugh, meddle, meditate, moulder, moult, moun, scream, sing, sleep, walk, whistle, ... b. burn up (Sp. consumirse), check in (Sp. presentarse; Du. inchecken), check out (Du. uitchecken), clear up (Fr. se dégager; Sp. escampar), come down (Sp. caer; Fr. retomber), dry out (Sp. secarse), fall asleep (Fr. s’endormir, Ge. einschlafen), fly up (Fr. s’envoler), freeze up (Fr. geler; Sp. congelarse), give in (Sp. entregarse), go away (Fr. partir), land on (Fr. atterrir), loom up (Fr. surgir), make way (Sp. pirarse), move up (Sp. correrse; Ge. aufrücken), rise up (Ge. aufstehen; Sp. resucitar), ...

Appealing to Mittwoch (1991), Husband (2012:44) asserts “that there are no simple intransitive verbs other than Achievement verbs that are unequivocally telic in their interpretation”. I read this quote as claiming that all unaccusative verbs in (12) should be seen as Achievements by those assuming Vendler classes. However, what Vendlerians call Achievement verbs is just a proper subset of the set of unaccusative verbs in (12a). The term unequivocally telic turns out to be equivocal itself at the moment Husband (2012:44) uses examples borrowed from Borer (2005) and given in (13). (13)

a. Lava erupted (from Vesuvius) on Sunday and on Monday. b. Poisonous gas exploded in Fairfax on Sunday and Monday.

These sentences do not prove that erupt and explode are unequivocally telic in the sense of expressing punctuality and requiring that both (13a) and (13b) are about two events, one on Sunday and the other one on Monday. In order to show that, it is necessary to fix the rules of the Achievement-game to be played unequivocally. These rules require strict punctuality. Actually it is quite hard to find a case in which an intransitive verb in (12) pertains unequivocally to an infinitesimal small point or to Ryle’s Finis discussed and rejected in Chapter 4.2.1. One dodges the rule of the game by classifying the unaccusative verb collapse as an Achievement verb on the ground that it is impossible to measure the time needed for a collapse. Going back to the dramatic events that happened on 9/11, 2001, one could have said

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Oh gosh, the left tower collapses while watching the TV screen, at the moment its top roof moved downward. At that moment, it would be inappropriate to say Oh gosh, the left tower has collapsed as pertaining to the same situation. This is because the collapse of the building lasted seconds and seconds and seconds before the whole structure was down and the completion of the collapse was invisible due to the dust. Yet, collapse is an intransitive verb expressing completion. To call it an Achievement verb is obviously only possible by ignoring the rule of the game just agreed on: the collapse began as a collapse and ended some seconds later as a collapse with a conventional point for marking the end. Of course, there are collapses which take nanoseconds and a human can fall within some milliseconds. On the other hand, for a human being a fall from a flight of stairs can take seconds. In other words, verbs used for describing discrete eventualities allow for a sort of span width or leniency at odds with the Finis convention.5 Another example is the vanishing cat in Alice in Wonderland. It took time for the cat to become invisible and there is a conventional point at which people may agree that the cat is no longer there. Obeying the strict rule of the game one needs to have two verbs vanish, one for expressing a sudden disappearance, the other one for expressing gradual completion. The same holds for the verb fall: Alice’s fall down the rabbit-hole at the beginning of the book took also a very long time. The proper way to go then, is to ban vanish and fall from the Ryle-Vendler list of Achievements. This also holds for the verb erupt in (13a) in which case it suffices to have a look at a broadcast of an eruption on TV in which one sees rocks being spit out for minutes. And (13b) may be about a series of explosions on Sunday and just one explosion on Monday. These counterexamples against the claim that all intransitive verbs expressing completion in token eventualities are Achievements in the Ryle/Vendler sense, should suffice, so that we are allowed to leave aside the surfacing of submarines, the process of two companies merging, the moulting of birds, the disintegration of the Roman Empire, etc. That verbs can lexically express discretization, requires function composition in the lexicon, in particular a rounding-off function applying to Ran(su), the output of su, and mapping from the system of real numbers R+ into the system of natural numbers N. An essential difference between the two number systems is that in N there is no number at all between 0 and 1, between 1 5 Vendlerians may argue that the verbs are at least Accomplishments, which would be quite rea-

sonable in the case of lava eruptions. As pointed out in Chapter 4, Accomplishment verbs in the strict sense do not exist in Vendler’s quadripartition.

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and 2, between 2 and 3. Void in the strict sense. This makes the numbers in N discrete. If there is a mapping from R+ to N for a verb like erupt in (12a), one can understand why this verb can also express an unbounded sequence of discretely ordered eruptions: the set N is infinite. In order to model this interaction between R+ and N, Verkuyl (2019a) proposed a generalized ceiling function gc : R+ −→ N defined as: (14)

⎧ ⎨ 0 < x ≤ x  −→ gc(x) = 1 x  < x ≤ x  −→ gc(x) = 2 gc(x) = ⎩ ...

It is easy to follow the steps in definition (14) by inspecting the x-axis of Figure 5.5a and seeing that all originals in the interval (0, x  ] are mapped to the y-value 1 and all originals in the interval (x  , x  ] to the y-value 2, etc. However, the function gc turns out to be too specific for dealing with situations

Figure 5.5 Different ways of discretizing

sketched in Figure 5.5b, which accounts for Figure 5.3. In view of adverbial modification as discussed in Chapter 6, it will be necessary anyhow to treat the set Ac as an indexed family of intervals and therefore a more general discretizing function will be defined.6 For a finite set Ac of intervals a written as in (15a), it will be assumed to be always possible to take the union over its members as given in (15b), where Ac is finite. (15)

a. Ac = {a

1n, a2 . . . , an } ai = a1 ∪ a2 ∪ . . . ∪ an such that for any ai , a j : i < j, b. ac := i=1 where ai < a j means that ∀x ∈ ai and ∀y ∈ a j : x < y

6 In writing Section 5.1, I did not realize that gc does not properly capture the Figures 5.1–5.3

without additional clarification, as pointed out by Dick de Jongh (pers.comm.). Therefore gc will be replaced by a more generally defined function.

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For an infinite set Ac = {a1 , a2 . . .}, the same will be assumed. Taking the union over Ac yields the boldface ac as a subset of R+ generalizing over exits and eruptions in Figure 5.5 allowing to measure the total length of the union.7 Given this generalization it is possible to define a discretizing function d : + R −→ N as in (16).8 (16)

d(x) = i iff x ∈ ai

The partial function d is defined over the elements ai of Ac in (15a) and undefined over the elements ai of the set Ac such as the interval between x  and x  in Figure 5.5. As said, d can only occur as yielding a composite function with the function su. This is obtained by defining the composite function d ◦ su : R+ −→ N as: (17)

d(su(x)) = i iff su(x) ∈ ai

This function covers Figure 5.3 where the set Ad is construed on the basis of the number of a-intervals in Ac . Given (17), one can now make a lexical distinction between verbs requiring only the function su because they do not express discretization such as walk, sail, work, etc., and the verbs expressing discretization and requiring d ◦ su, as defined in (18) and exemplified in (12). The difference is shown in (18). (18)

a. V(α)(arg) ∧ α = Ran(su) b. V(α)(arg) ∧ α = d(Ran(su))

The index α in (18a) is unbounded in R+ because Ran(su) ⊆ R+ . It is assigned to verbs fitting in Figures 5.1 and 5.2. The range d(Ran(su)) of the composite function d ◦ su(x) in (18b) is the output of applying d to Ran(su). In the absence of more information, α is unbounded: d(Ran(su)) ⊆ N. It is bounded if and only if there is a number m such that all natural numbers in d(Ran(su)) are smaller or equal to m. In that case, d(Ran(su)) is called a bounded sequence, possibly just a singleton. In the absence of [+SQA]information about the argument arg, the range d(Ran(su)) remains unbounded in N. This makes verbs like arrive suitable for occurring with a bare plural NP as their external argument, as in Guests arrived and Patients here died within a month after their arrival. In other words, both types of verb in (18) express 7 The notation in (15) is here restricted to verbs but it will also be used in the analysis of adverbial

modification and measurement in Chapter 6 when it comes to computing the length of a union. 8 Here again it is necessary to observe that the subscripts i and j in a and a are crucially i j

different from the lower case i, j and k in the representations of tense structure. On the other hand, the latter indices are written in lower case and therefore the sets ac and ai are also written in lower case because type-logically they are of the same type as the tense indices.

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unboundedness lexically because verbs need to accommodate differences in their arguments as well as the difference between α as a token or a type. Summarizing, the function d introduces discretization at the lexical level. Discretization is essentially an ingredient of the notion of terminativity in the sense that bounding provided by the contribution of a [+SQA]-argument in (18b) is a necessary condition for creating a bounded sequence in N. In the case of a [−SQA]-argument, the sequence remains unbounded, hence equals N, in principle, dependent on contextual information. This means that no verb is stored in the mental lexicon so as to pertain to a uniquely actualized bounded index α, not even the verb die, which is characterized in the same way as arrive. 5.2.2

Discretization and Bounding by the Internal Argument of Transitive verbs The list in (19) contains transitive verbs which need an internal argument for obtaining terminativity at the level of VP. (19)

abolish, actualize, adapt, adduce, acquire, appoint, begin, betray, break, bury, build, cancel, cease, cheat, chisel, chop, close, cobble, conceal, convert, convince, cook, cover, cure, cut, damage, deliver, deposit, destroy, devastate, dig, disable, discharge, disclose, discover, distort, divide, draft, draw, drink, drive, eat, elect, erase, erect, escape, excoriate, find, finish, found, frame, get, hear, hide, hit, kill, knit, leak, leave, lift, lose, lurch, melt, miss, negotiate, notice, nullify, obliterate, order, park, pass, perform, petrify, photograph, play, prove, resume, see, tear, reach, read, rebuild, receive, recite, recognize, record, refund, reimburse, rend, render, repair, repeal, rescind, return, repeal, reveal, reverse, revoke, ruin, safeguard, score, sell, seat, serve, shatter, shell, shred, sing, smell, spot, start, stop, stun, stupefy, succeed, swallow, taste, tear, tell, tell, terminate, throw, touch, transcribe, transfer, transmit, transpose, turn, uncover, understand, unearth, unlock, unravel, unveil, vent, whack, win, write, . . .

Some are not afraid to see the italicized verbs as Achievement verbs. Again, if we apply the strict rules for the achievement game, dodging is inevitable. To repair a shoe cannot seriously be called an Achievement in spite of Ryle’s claim and even Vendlerians will also not easily call drink a wine or overcome writer’s block an Achievement. As argued in Chapter 4, they see this sloppy use of terms as a negligible inconvenience and assume that build, drive, draw are Accomplishment verbs by calling them Accomplishments and – a practice beginning with Dowty (1979:69) – by giving examples as build NP, drive NP a mile, draw (a picture), thus trading the linguistic notion of verb for a philosophical one.

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Returning to the strict linguistic perspective on what a verb contributes apart from its arguments, we need a closer look at the format for the verbs in (19) given in (20) where arg2 is the internal argument and arg1 the external one.9 (20)

V(α)(arg2 )(arg1 ) ∧ α = d(Ran(su)) ∧ |α| ≤ |arg2 |

The two clauses following the main predication connect α to the internal argument arg2 by making a cardinality condition in the third clause. Recall that α is a set and the same holds for the quantificational information expressed by an internal argument NP, as argued for in Verkuyl (1993:69–189). The bounding instruction imposed by [+SQA] on the range of the composite function d ◦ su provides a natural number m as a bound such that the cardinality of the set α is smaller than or equal to the cardinality of the internal argument. This blocks the non-stative continuation of the function su, as illustrated by (21a) and (21b), informally and provisonally written as |α| ≤ |tr|. When an internal argument is [–SQA], the information about the unboundedness expressed by the NP is also connected to the index α, as illustrated by (21c) and (21d) in their last clause. (21)

a. John discover a treasure. DISCOVER(α)(tr)(j) ∧ |tr| = 1 ∧ α b. John discover three treasures. DISCOVER(α)(tr)(j) ∧ |tr| = 3 ∧ α c. John discover treasures. DISCOVER(α)(tr)(j) ∧ |tr| > 1 ∧ α d. John discover no treasure. DISCOVER(α)(tr)(j) ∧ |tr| = 0 ∧ α

= d(Ran(su)) ∧ |α| ≤ |tr| = d(Ran(su)) ∧ |α| ≤ |tr| = d(Ran(su)) ∧ |α| ≤ |tr| = d(Ran(su)) ∧ |α| ≤ |tr|

In (21a), John stands in a (still tenseless) discover-relation between the internal argument denotation and an index α, the cardinality of which is determined by the clause |α| ≤ |tr|. This clause works more interestingly in (21b): John may have found the three treasures one-by-one, or first one and then two simultaneously, or first two and then the last one, or all three at once.10 In (21c), the [−SQA]-specification of the internal argument in the form of |tr| > 1 makes it impossible to limit the unbounded sequence in N expressed by the verb, because there is no way to determine a finite cardinality |tr|. Only when the PAST operator actualizes the tenseless predication in real time, can 9 Mass nouns are left outside the scope of the present book. They were treated formally in Verkuyl

(1993:177ff.) in terms of a measure function rather than a cardinality function. It is easy to connect the two functions in terms of expressing an absolute value. 10 All variations provided by the use of a [+SQA]-plural NP as an argument of a verb have been analyzed in detail in papers about distributivity and collectivity collected in Verkuyl (1999). The larger the cardinality of arg2 , the more room is available for partitioning the set denoted by it.

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John discovered treasures be interpreted as about John’s discovery of an unknown finite number of treasures. Finite by implication, due to the anteriority relation expressed by PAST. In (21d), the information that the cardinality of α is zero means that no discover-eventuality took place. The list in (19) contains verbs with Latin prefixes like ad- (by assimilation sometimes appearing as ac-, af-, etc.), con-, de-, re-, trans-, most of which have or had an aspectual load comparable with what is expressed by particles like in, off, away, out, etc. in obtaining terminativity in predicates with an internal [+SQA]-argument. The split in the lists of verbs in (12) and (19) into (a) and (b) shows that verbs with a prefix in one language often have simple translational equivalents in other languages or translations in which the prefix finds a translational equivalent in a particle, and reversely so. This makes it plausible that the function d cannot only be attributed to affixes but also to particles which are part of a phrasal verb expressing discretization (rather than perfectivization). Along that line of thought, one may consider generalizing over, for example, DIS - and OUT in [V DIS + -cover] and [V blot + OUT], respectively, where both affix and particle are seen as contributing to discretization. Captured under the heading X D , they would both stand for the presence of the function d as pictured in Figure 5.6. In the case of Figure 5.6a, the particle OUT can be seen

Figure 5.6 Function composition morphologically

as providing the internal argument with discretizing information at the level of V , after which the VP is formed by combining the complex verb blot out with the internal argument. Figure 5.6b is interesting because it shows function composition (d ◦ su) as running parallel to morphological composition, much in the way in which in Russian a perfective prefix na- can be seen as taking a verb stem -pisat’ ‘write’ in order to yield a perfective verb V napisat’ lit: ‘write up’ in the sense of finishing. I will return to that issue in more detail in Section 7.2. In the case of discover, DIS- might be interpreted as a bounding morpheme producing a V by taking a V0 -cover. However, English-speaking children

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learning the word discover will assign α = d(Ran(su)) directly to discover as a whole, in the way shown in Figure 5.6c. Lexical structure of the form given in Figure 5.6b may become visible for them later on after having met a much larger number of dis-verbs bringing them to the question why all these verbs begin with dis-. Figure 5.6c may also be used for verbs like resurrect, reveal, revive where no verb stem is available (∗ surrect, ∗ veal, ∗ vive), for verbs like blink, die, rise, burst, etc. where no affix is visible and for verbs like arrive, erupt, actualize, etc. where those learning these words will not recognize prefixes. Historically, there is ample empirical room for the hypothesis that the verbs may have lost the discretizing force they had in earlier stages of the language in which they appear by transferring it to other parts of the sentential structure. In English, it is impossible to assume a 1:1 relation between having a prefix like dis- and expressing the discretizing function d because alongside discover, disaffect, disaffirm, etc., one has disbelieve, disregard, disagree, etc., where dis- does not allow for function composition. In German, prefixes and particles such as er- ‘re-’, ent- ‘dis’, aus- ‘out’, auf- ‘up’, ab- ‘off’, etc. still have a perfectivizing force more or less comparable with the role of a number of perfective prefixes in Slavic languages, but there are also clear cases in which prefixes have lost this force, as in leuchten ‘enlighten, radiate’ vs erleuchten ‘illuminate, enlighten, radiate’. As to Dutch, I cannot absent myself from joint research in 1966 with Jan Luif into the perfectivizing force of prefixes like her- ‘re-’ in modern Dutch. The question was: to which degree are the verb oppositions dekken ‘cover’ vs ontdekken ‘discover’ vs herontdekken ‘rediscover’, bouwen ‘build’ vs herbouwen ‘rebuild’, etc. comparable with Slavic oppositions expressed by the systematic absence of prefixes in imperfective and the presence of prefixes in perfective verbs? We went back to the then-available oldest sources of Middle Dutch and found that many modern Dutch prefixes must have lost their original perfectivizing force because in modern Dutch they do not express perfective aspect in a way comparable with their Slavic counterparts.11 Parallel to the process of losing perfectivizing force was the process of obtaining articles. From Schönfeld (1954:141), we learned that the article de ‘the’ entered early Middle Dutch as a weakened form of the demonstrative

11 The immediate cause of this research was Schultink (1964), which reported about the produc-

tivity of the Dutch prefix her- ‘re’ in neologisms. Our work helped our supervisor in writing Kraak (1967). Hoekstra (1984) showed that a substantial part of Dutch verbs beginning with be-, ver- and ont- still have the perfectivizing force comparable with dis- in discover.

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pronoun in the same way in which the French article le has been established itself as a weakened form of the Latin demonstrative pronoun ille. In Dutch, the article gradually took over the task of flection and gender to render a noun into an NP, and so it obtained the role of expressing quantificational information previously played by verbal prefixes.12 The combination of the two developments – the decrease of the perfectivizing contribution of verbal suffixes and the increase of the role of providing nominal determiner information – led me to the compositional perspective of Verkuyl (1972a), namely that the absence of articles, and consequently the lack of bounding by a verb, can be compensated for by verbal prefixes and that the loss of discretizing power of prefixes may run parallel to the development of determiners expressing [+SQA]-information. In the case of [–SQA]-NPs there is no bounding. The conclusion of the present section is that all transitive verbs in (19) are properly accounted for by scheme (20). There is a division of labour between the verb and its arguments in terminative (still tenseless) predications. The verb contributes non-stativity (by su) and discretization (by d ◦ su) creating unbounded sequences in R+ and N, respectively. The [+SQA]-feature contributed by the internal argument in sentences like (21) provides the bounding limit by cardinality information. This means that the notion of terminativity is essentially quantificational in the case of [+SQA]-NPs with count nouns without any nearby ingredient in sight for assuming a telos. 5.2.3 Wavering between d ◦ su and su The list in (22) is a selection of verbs occurring both transitively and intransitively: (22)

chisel, cook, draft, draw, dig, drink, eat, hear, knit, leak, melt, negotiate, perform, play, push, read, operate, recite, serve, saw, sing, swallow, tell, write, ...

Verbs in (22) do not require an internal argument because they are often used intransitively. Terms available for them are pseudo-transitive or pseudointransitive. The general picture is that when they occur without an internal argument, they do not discretize. In other words, they occur as unergatives, which means for Dutch that they all require hebben ‘have’ rather than zijn ‘be’ as a PERF-auxiliary. 12 Cf. Kabakˇciev (1984; 2000) for the relation between the absence of the article and perfectiviz-

ing prefixes in Slavic languages. For a modern elaboration of this idea applied to Germanic languages, see Philippi (1997).

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Judith in (23a) may eat alone for an hour, but one may also negotiate for weeks and read for months without a need to provide an internal argument. (23)

a. Judith ate alone. b. Judith ate a sandwich with cheese and then went to her work.

In occurring with an internal argument, the verbs in (22) express discretization when they satisfy the Plus-principle, as exemplified in (23b). At first sight, the aspectual difference between the sentences in (23a) and (23b) can be simply accounted for by the difference between their α, i.e. between α = Ran(su) and α = d(Ran(su)), respectively. This raises the question of whether one is bound to have two different verbs eat. This question is appropriate because there are languages that have two verbs for the opposition between (23a) and (23b) as, for example, in Mokilese reported about in Harrison (1976:159).13 (24)

a. Ngoah kang mwumwwo. I ate fish ‘I ate (some of) that fish.’ b. Ngoah mwinge. I ate ‘I was eating.’ c. ∗ Ngoah mwinge mwumwwo. I ate fish ‘I ate (some of) that fish.’ d. Ngoah kohkoa oaringkai I am grinding coconuts ‘I grind these coconuts.’ e. Ngoah ko oaring I grind coconuts ‘I am grinding coconut.’

The examples in (24) show that a language may opt for two different verbs in presenting boundedness or not. However, having two verbs instead of one is not a general pattern, even in Mokilese where many verbs have two forms one of which is morphologically marked. The English throw in its transitive use is peid in Mokilese, whereas its intransitive counterpart is peidek. In a number of cases, two verb forms differ because one of them results from noun incorporation. One could see the reduplicative verb form in (24d) as a form of adding a particle forcing the internal argument oaringkai into being interpreted as a [+SQA]-NP. 13 Marie-Eve Ritz drew my attention to that publication, after which I got in contact with Sheldon

Harrison who was so kind as to give me the examples (24a)–(24c).

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In view of these considerations, one could defend a distinction between eat1 in (23a) and eat2 in (23b) coming close to the situation in Slavic languages where a verb may have a perfective form and an imperfective form. In other words, the verb form eat in (23a) could indeed be defined as having the clause k = Ran(su) as opposed to the verb form eat in (23b) having the clause k = d(Ran(su)). Such a solution would be supported by the fact that a large number of verbs in (22) have the property of being able to occur overtly with prefixes or with particles. Dutch has pairs such as eten ‘eat’ vs opeten ‘eat up’, schrijven ‘write’ vs opschrijven ‘write up’, onderhandelen ‘negotiate’ vs uitonderhandelen ‘negotiate until a settlement is reached’, etc. These complex verbs cannot occur intransitively. Whether one considers the Mokilese pair peid and peidek or the Russian pair napisat’ and pisat’ one verb with two forms or two different verbs, is decisive for the question of whether one includes morphology or syntax as the prime factor in the analysis. In the former case, it is arguable that the lexical entry of a verb like eat, when it takes its internal argument, contains a particle PRT D which overtly triggers the application of d, as illustrated in Figure 5.6b and represented in (25b). (25)

a. eat three sandwiches. b. [VP [V PRT D (V0 EAT)]([NP three sandwiches])(x) ∧ α = d(Ran(su))] c. ∗ [VP [V ∅(V0 EAT)]([NP three sandwiches])(x) ∧ α = Ran(su)]

If this operator is absent, as in (25c), the verb eat is intransitive and cannot occur with an internal argument. In this way, PRT D represents the discretizing function d preparing the verb for interaction with the internal argument. In other words, rather than having two verbs eat, a plausible hypothesis is to connect the presence of an internal argument with the phrasal function composition d ◦ su. This means that Judith ate a sandwich, Judith ate three sandwiches, Judith ate sandwiches and Judith ate no sandwich are to be treated in the same way as the four discover-sentences in (21) be it with a different lexical history in the sense that transitive eat is a complex verb and discover a simplex one as shown in Figure 5.6c. I will not follow this line of reasoning because a simpler solution announces itself: every transitive verb that is able to take a [+ SQA]-NP as its internal argument will be lexically defined as a d(Ran(su))-verb. This means that the sentences in (26) differ by the absence of quantificational information about the internal argument in (26a) preventing [+T VP ]-information at the VP level on the basis of the Plus-principle discussed in the preceding chapter.

5.2 Discretization and Bounding (26)

153

a. Judith ate alone. EAT(α)(arg2 )(arg1 ) ∧ α = d(Ran(su)) b. Judith ate a sandwich and then went to her work. EAT(α)(arg2 )(arg1 ) ∧ α = d(Ran(su)) ∧ |α| ≤ |arg2 |

There are some arguments in favour of this solution. The first is that (26a) may appear in discourses like (27a). (27)

a. Judith prepared her daily sandwich. This time with cheese. She ate alone because Ole had been called away for a suddenly scheduled meeting, and then she went to work. b. In those weeks, Judith ate alone in her room.

In that case, the earlier context provides information about the number of sandwiches involved. It also makes the period of Judith’s eating alone finite by the fact that she went to work. Given that, it is not unreasonable to assume that She ate alone is to be interpreted comparable to the interpretation of She ate sandwiches where sandwiches is a [–SQA]-NP, be it that the absence of an overt NP evokes the lexical knowledge of the verb eat (distinguishing it from drink, say). Dutch has the word iets ‘something’ for this to supplement the underinformation in She ate alone, a word escaping from the distinction between count and mass. In this way, a [–SQA]-marking is called for, leading to a durative interpretation in spite of the α = d(Ran(su))-marking of the verb. A second argument is given by (27b). As long as Judith is a human being it is hard to interpret this sentence as being about a form of eating permanently going on for weeks. The most appropriate interpretation of (27b) is being about a series of discretely and regularly organized eating eventualities in which Judith is involved, not excluding the exceptional interpretation in which it is assumed that (being hospitalized) when Judith was able to eat, she did that alone. In both cases, the discretizing function d is called for. Figure 5.7a pictures the way of accounting for the terminative interpretation of (23b) on the basis of Figure 5.6c. Figure 5.7b pictures the durative

Figure 5.7 A transitive verb phrase with and without an internal argument

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interpretation of (23a) in terms of accounting for the durativity in spite of the presence of the function d. The absence of an NP has the same effect as the presence of an [–SQA]-argument. At a later stage, this will be formally accounted for. 5.2.4 The Role of the External Argument Two main issues have to be dealt with now before we can get to a formal account. The first is the question of which information about the external argument should be stored in the lexical semantics of a verb. The question is relevant due to the division between unergative verbs and unaccusative verbs and the effect of this on the aspectual information contributed by the verb. Are they marked for a difference with respect to their external argument (if they have one), or not? The second issue concerns the question of how the external argument of a transitive verb relates to its VP. The representations of sentences given so far in the present chapter have a singular NP as their external argument. Plural NPs have to be taken into account as well. The difference made between unaccusative and unergative verbs can be understood as crucially being a syntactic one. It is based on the opposition between attributing the thematic role of agent to the external argument and the role of theme (patient) to the internal argument. Having in mind the observations just made, we should say more about the semantic relation between an NP and the VP with which it occurs to form an S0 . I will first discuss the main idea about this relation with the help of sentence (28a) in which the external argument is singular.14 (28)

a. Judith ate a sandwich. b. eat a sandwich  [EAT(α)(s)(x) ∧ |s| = 1 ∧ α = d(Ran(su)) ∧ |α| ≤ |s|] c. Judith eat a sandwich  [EAT(α)(s)(ju) ∧ |s| = 1 ∧ α = d(Ran(su)) ∧ |α| ≤ |s|]

The format of the predication itself requires that the external argument relate to the VP as a whole and that it be connected to the quantificational information contributed by the internal argument. This requirement is met by making Judith dependent on the same verbal index on which a sandwich is made dependent, namely α. With the denotation of Judith having cardinality 1, this requirement is easy to fulfill: there is one person to which α is connected and the cardinality 14 I will continue the practice in the present chapter so far to simplify the formalism so as to

give room to the underlying idea by suppressing the type-logical requirement for matching the proper types until the next section.

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of α is at most 1. This means that the relation between ju and α can be seen as multiplicative, as made visible by the ×-sign in Figure 4.5 on page 127. As soon as the external argument is plural as in (29), it is necessary to assign an α to each of the two members of the set J2 = {Judith, Jessica}. (29)

Judith and Jessica ate a sandwich.

This sentence may be about a situation in which Judith and Jessica each ate a sandwich, but it might as well apply to a situation in which they shared one. In both cases, each member of the set J2 is mapped to “her own VP”, so to say, but nothing prevents sharing the α-index with just one and the same sandwich. The latter is what I have called kolkhoz-collectivity in some of the papers in Verkuyl (1999): Judith and Jessica are allowed to say afterwards We ate a sandwich but none of the two is allowed to say I ate a sandwich. In the case of a singular external argument arg1 and a singular argument arg2 as in (28), the mapping involved has some unnaturalness about it, but this is absent in sentences like (30). (30)

a. b. c. d.

Four men lifted a piano. Three men lifted four tables. Three girls bought a boat. Hammerstein, Rodgers and Hart wrote some musicals.

Sentences like these were investigated in detail in several of the studies collected in Verkuyl (1999).15 The formalism used there is different from that used in Section 5.3 due to the fact that the notion of index and its role in the tense structure above the level of S0 has become more articulated in later work. In the present informal account, it suffices to observe that the relation between the external argument and its VP can be seen in terms of the (non-commutative) multiplication scheme (31), which informally captures the gist of the current analysis. (31)

|arg| × |VP| = m, where m ≤ |arg|

The idea behind such a function is that it multiplies the denotation of the VP because each of the members of the external argument set is mapped to “its own” VP. This means that each member has its own index α even though it happens to share this α with other members of the set. In thematic idiolect, 15 In particular, in its chapters 6 Multiple Quantification and 7 Collectivity and Distributivity.

These studies originated in joint work with Jaap van der Does – Van der Does and Verkuyl (1996) and Verkuyl and Van der Does (1996) – based on Van der Does (1993) and related to Scha (1981). I refer to the references in these papers for discussions on collectivity and distributivity going on in that period.

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this means that each member of the external argument set has its own path and that it can share that path with respect to α and/or to members of the internal argument set in a variety of ways. In (30a), the four men may have lifted the same piano in a collective effort but in other interpretations of this sentence two, three or four piano’s may have been lifted. In (30b), there is a range from four to twelve different tables that may be have been involved in the lifting(s). Sentence (30c) may be about the purchase of one boat or two boats. In the latter case, one boat was bought by two girls and the other one by the third girl. If we do not know who Hammerstein, Rodgers and Hart were, we are allowed to interpret (30d) as expressing that each of them wrote some musicals. But this is not what happened: Rodgers and Hammerstein wrote a number of musicals in the period in which Hart and Rodgers no longer formed a team. This can be captured by assuming that the multiplication relation in (31) is expressed by a function. This function is essentially different from the function involved in combining a verb with its internal argument. 5.3

A Formal Account from Lexical Bottom to S0

5.3.0 Introduction The preceding sections shed some light on principles guiding compositionality from the bottom to the top of a tenseless predication S0 . The first aim was to understand the contribution of the verb without taking into account the contribution made by its arguments. The second aim was to investigate the combination of a transitive verb and its internal argument arg2 . The third aim was to delineate the relation between the argument arg1 and the VP. The present section summarizes the outcomes by showing formally how compositionality operates from the lexical bottom to the phrasal top at S0 . The compositional procedure of getting from S0 to S by following the three binary oppositions was already outlined in Chapter 3 but adverbial modification needs to be taken into account to sharpen that picture. That will happen in Chapter 6. The capstone of the compositionally formed phrase structure will be fixed in Chapter 8 after having included a formal account of the opposition between SYN and POST . Extending the type-logical machinery employed in Chapter 3 on the basis of Definitions 1 and 2 on page 84 requires new variables. Table 5.1 provides each variable with a type. The notational difference between variables is important. For example, X is of type e, t representing a set of entities e, whereas X of type e, i, t takes as its value a relation between an (eventuality) index α of type i and an entity e (the external argument in the relation). Likewise there is a big type difference between P and P. This difference will be explained when the variable P occurs for the first time in a derivation. Transitive verbs do not

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Table 5.1 Survey of types Variable

Type

Example

x, y, z α, β, γ , δ  X,Y, P, Q X, Y, Z , . . . P, Q – P, Q, . . . φ, ψ p,q

e i i, t e, t e, i, t e, i, t, i, e, t, t e, i, t, i, t, e, i, t e, i, t, i, t i, t t

r, m i, i , j, k hour, day, week, . . . girl, house, table, circle,. . . walk, build a house . . . – draw, lift, eat, be, . . . the table, two tables . . . Mary walk, Judith eat a sandwich Mary walked

Operator

Type

Example

∃a ∀a λa

a = x, α, k, X, P a=x a = x, α, X, P, P, φ

∃k[. . . k . . .] ∀x[. . . x · · · → . . . x . . .] λX λα.X (g)(α)

need a variable. The variable  of type i, t stands for sets of indices. This type will be treated in Chapter 6. Table 5.1 also includes the operators occurring in the derivations. Essential for proving that representations are compositionally construed is the use of the lambda-calculus. This was already done in Section 3.5 for the three tiers of the tense structure on top of the tenseless S0 . In the present section, the lambdacalculus will also be used to get from the lexical bottom to the top of S0 so as to get a connection with the lowest level of binary tense structure beginning right above S0 , as described in Section 3.5. The lambda operator λa (with the metavariable a) will occur with many of the types distinguished in the upper part of the table. The type-logical matching involved requires all sorts of techniques which are quite forbidding even though one is trained in reading them, due to the need of checking parentheses and square brackets, proper binding of quantifiers, evading type clashes and so on. On the other hand, the formulas do not go beyond what was promised informally in the preceding sections. In that sense, they just confirm what has been discussed so far. Therefore, the strategy followed for making the present section bearable is to break up the derivations in comprehensible numbered steps with sufficient explanation, not so much about the technicalities of lambda-calculus but rather about how pieces of information find themselve back in more comprehensive constructions. Readers who trust that the derivations are correct may look at the first and the last line of the

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formulas of a step and read the comments given before or after the formulas. Full derivations are given in the appendix. 5.3.1 Syntax and Semantics of Noun Phrases The formal machinery for getting from bottom to top is anchored in the Theory of Generalized Quantification. This theory has been successful in extending the range of quantifiers that helped logicians to translate sentences of natural language into logical expressions. Until Barwise and Cooper (1981), quantifiers involved in regimenting natural language expressions into the format of first order logic were the existential quantifier (∃) and the universal quantifier (∀) and their interaction. This had resulted in a close association between the indefinite article a and the quantifier ∃ and between the determiner all and the quantifier ∀.16 It had also led to a thorough study of scope in view of the fact that these operators may jointly appear in one formula, as ∀x∃y or ∃x∀y, or in the case of the article the as ∃x . . . ∀y. Generalized quantification made an end to the restriction to just articles by drawing words like some, three, most, few, many, etc. into the research of quantification, words that may clearly co-occur with articles, as in The two new tables are in the garden, The many meetings we had led to a number of improvements, Three of the five attempts failed, etc. This has resulted in a broader use of the notion of determiner. In this extension, there is some area of tension between a linguistic perspective and a logical-semantic one relevant for the present analysis: there are two ways of parsing (32a) of which the adjectival treatment of two in (32b) is quite popular in linguistic syntax.17 (32)

a. the two tables b. the(two(table)) c. the(two)(table)

In that approach, two operates on table to form TWO(TABLE) which is then taken by the indefinite ∅ or by the definite article THE. It is called adjectival because two is treated in the same way as the adjectives energetic, helpful, etc., namely, type-logically as modifiers of type e, t, e, t. Such a position was also taken in the dyadic X-bar syntax proposed in Verkuyl (1981). However, the adjectival approach meets a problem signaled in Van Benthem (1986:52): in an expression like ∃X[X ⊆ Y ∧ |X| = 2] the ‘at least’-meaning 16 That all is not an article linguistically was explained by seeing it as a combination of all the. 17 See: Barwise and Cooper (1981), Scha (1981), Link (1983;1991), Van Benthem (1984),

Westerståhl (1984;1989), Keenan and Faltz (1985), Van der Does (1993) and Peters and Westerståhl (2006), among many others.

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159

of the existential quantifier over X overrules the exactly 2 information provided by |X| = 2. This means that one cannot be sure about how many tables are involved in this expression. This problem led Verkuyl (1993) into opting for the structure in Figure 5.8a. The basic idea underlying that approach is

Figure 5.8 NP structure and VP structure

that it regards DET2 as combining two semantic elements: the [± DEF]-feature expressed by SPEC and the numerical information provided by DET, modified or not. This information is the crucial contribution of the NP to interpreting a sentence and in this way two in Figure 5.8 is the main element of the determiner. In the absence of modifiers like at least, most and exactly but also nearly and more than, it contributes the clause |T| = 2 to be read as ‘exactly two’.18 I will not include modifiers in the scope of the present analysis. 5.3.2 Discretization in Sentences with Transitive Verbs Sentences like (33) have received a lot of attention in the theory of generalized quantification. We will now derive (33) compositionally in that framework. (33)

The three girls lifted two tables.

Figure 5.9 shows the crucially important intersection model of generalized quantification. In terms of the explanation of Figure 5.8a just given, Figure 5.9 expresses that in the universe of interpretation E, the symbol A stands for the 18 Mathematical logicians easily forget that when they order two croissants in a bakery they will

pay for two croissants and that when they truthfully say that they have three children, there is no fourth or fifth available to make the at least-meaning of three appropriate. Figure 5.8 assumes that I saw three children means ‘I saw exactly three children’ by default and that modifiers like at least and at most are used for marked cases. This means that if we say Three girls lifted two tables, the number of k’s involved for all the girls is at most 6. The analysis corresponding to Figure 5.8a treats at least, at most and exactly as modifiers of two either used explicitly or implicitly depending on the situation.

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Figure 5.9 The intersection model of generalized quantification

set of girls in E, the symbol B for the set of those who lift two tables and that the intersection A ∩ B warrants that there are three entities belonging to A which also belong to B. That neither definiteness nor indefiniteness is decisive for connecting A to B shows that the (in-)definiteness of an NP is not a central element of DET2 in terms of computing the value of the intersection. The difference between [+DEF] or [–DEF] – to use handy features – is local in the sense that [+DEF] requires that the existential quantifier be reduced to a specific subset of A which enters into the connection with B in the same way as is the case with [–DEF]-NPs, namely by intersecting with B. A complicating factor is that the external argument has wide scope over the VP due to the asymmetry inherent to the relation between external and internal argument. This will make it necessary to give an account of the difference in thematic roles played by NPs occurring as external or internal argument. The thematic role of the internal argument is located in the VP as pictured in Figure 5.8b. The first steps consist of obtaining the NP two tables. This begins with the insertion of TABLE in the formula for the determiner [∅ [two]]. The node SPEC in Figure 5.8a stands for [–DEF], i.e. the absence of a definite article. Thus an NP like a table is analyzed as A(SG)(CHILD), where SG introduces the cardinality information 1. A bare plural NP like tables is analyzed as ∅(PL)(TABLE), where PL stands for ≥ 2. In both cases, an indefinite set of tables is existentially introduced. For convenience I will introduce SPEC(NUM)-expressions syncategorematically. The full derivation of (33) is given as (1) in the Appendix on page 290f. It includes the specification of the crucial types involved. The noun table refers to the set of tables in the domain of interpretation. 1. table  TABLEe,t The determiner two is analyzed as SPEC ( NUM ) and introduced in 2. 2. ∅(TWO)  λXλX λβλP[P ⊆ X ∧ |P| = 2 ∧ ∀x[P(x) → X (x)(β)]]

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It takes TABLE, which replaces the λ-bound variable Xe,t yielding the formula in 3. 3. ∅(TWO)(TABLE)  λX λβλP[P ⊆ TABLE ∧ |P| = 2 ∧ ∀x[P(x) → X (x)(β)]] Step 4 consists in defining the Theta-role attributed to the internal argument of a transitive verb. 4. int  λQλY λα∃Q[Q(Y )(α)(Q) ∧ |α| ≤ |Q|] This is a crucial step in the composition because in this way the argument α of a verb is connected to one of its co-arguments. Seen in this way, int has the task of connecting the internal argument – which after step 3 is still “on its own” and open to being inserted in all sorts of position – specifically to the eventuality index α of the transitive verb. This connection is made in the form of contributing the clause |α| ≤ |Q| which warrants that the cardinality of α never exceeds the cardinality of Q when this is given by the NP. The application of int to the NP of step 3 is shown in step 5, the last line of which is of type e, i, t, i, t. This can be read as expressing a relation between an index i and a pair consisting of an index i and an entity e. In other words, the thematic role of an internal argument requires that the index involved in the relation between the internal argument and the verb, be connected to the relation between the external argument and this index. 5. int (∅(TWO)(TABLE))  λQλY λα∃Q[Q(Y )(α)(Q) ∧ |α| ≤ |Q|] (λX λβλP[P ⊆ TABLE ∧ |P| = 2 ∧ ∀x[P(x) → X (x)(β)]]) ... = λX λβ∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀x[Q(x) → X (x)(β) ∧ |β| ≤ |Q|]] The next step in 6 is to introduce the verb lift which is fronted by the variable P of type e, i, t, i, t.This is exactly the type of the last line in step 5. 6. LIFT  λPλzλα(P(λvλα  [LIFT(α  )(v)(z) ∧ α  = d(Ran(su))])(α) Applying LIFT to the internal argument NP results in the last line of step 7. 7. LIFT(int (∅(TWO)(TABLE)))  λPλzλα(P(λvλα  [LIFT(α  )(v)(z) ∧ α  = d(Ran(su))])(α)) (λX λβ∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀x[Q(x) → [X (x)(β) ∧ |β| ≤ |Q|]]]) ...

162

Levels of Interaction between Aspect and Tense = λzλα∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀x[Q(x) → [LIFT(α)(x)(z) ∧ α = d(Ran(su)) ∧ |α| ≤ |Q|]]]

This formula looks for an entity z of type e so as to form S0 of type i, t. At this point, the Van Benthem problem should no longer haunt us. I think this is the case. The crucial aspectual clause is |α| ≤ |Q|. Suppose that the existential quantifier in ∃Q allows for more sets Q of tables than just one. Then for each of these sets Q, it is the case that it contains exactly two members (in the absence of modifiers, as observed previously). In terms of Figure 5.9, for each x in the set A there are only and precisely two tables that are lifted either with respect to one α or with respect to two indices α. The following steps concern the introduction of the external argument NP, where ext should be seen as accounting for the thematic role of the external argument as a carrier of nominative case.19 Before these steps can be taken, something should be said about the definiteness of an article. In the present analysis, the DET2 -node covers two semantic factors: quantity by DET, (in-) definiteness by ±DEF. Definiteness of an NP is determined by context. As in Verkuyl (1993), I will make use of the notion of a context set C, which is considered a nominal element in the sense that it needs not be introduced existentially. In this way, the three will be introduced as in step 8.20 8. THE(THREE)  λXλX λβλP[P ⊆ X ∧ |PC | = 3 ∧ ∀x[P(x) → X (x)(β)]] The operator λP introduces a set of sets P which are all a subset of the set X such that the contextual information represented by the context set C of all things known to speaker and hearer with respect to the ongoing discourse intersects with P yielding three P-entities identified for speaker and hearer either anaphorically or deictically. Note that this context set is abstractly defined as long as tense has not yet been applied. This allows for applying the NP the three girls to a past domain or to the present domain without fixing which girls are involved. In other words, the actualization of set C in the real time of the domain is completely dependent on the application of PRES or PAST. In view of the fact that sentences may pertain to episodic and non-episodic sentences, this seems to be the correct way to follow. In John kept the receipts, the set of receipts can only be settled upon when it is clear in the discourse that 19 Many scholars see the internal argument as the theme, so I guess they would like to have

a different symbol here. But I use ext here leaving in the dark whether it concerns Agent, Patient, or in the case of unaccusatives Theme. 20 Rather than writing P ∩ C I shall write P to be read as ‘P restricted by the context set C’. C

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the sentence is about one eventuality index k or about a series of these indices. Moreover in sentences with a plural external argument, each of the participants “may have its own context set C”, so to say. The next step applies the formula in step 8 to the noun girl which substitutes for the variable X. 9. THE ( THREE )( GIRL )  λX λβλQ[Q ⊆ GIRL ∧ |PC | = 3 ∧ ∀x[Q(x) → X (x)(β)]] At that point, the NP must be given its position and role. In our case, this is the position of external argument. Therefore the formula in step 9 is the input for ext defined in 10. 10. ext  λPλX λα∃P[P(X )(α)(P)] This operator ensures that the individual participants in the plural NPdenotation are properly connected to the α-argument of the verb as shown in 11. 11. ext (THE ( THREE )( GIRL ))  λPλX λα∃P[P(X )(α)(P)] (λX λβλQ[Q ⊆ GIRL ∧ |QC | = 3 ∧ ∀x[Q(x) → X (x)(β)]]) ... = λX λα∃P[P ⊆ GIRL ∧ |PC | = 3 ∧ ∀x[P(x) → X (x)(α)]] The external argument NP the three girls takes the VP of type e, i, t which replaces the variable X to form a predication of type i, t. Note that e, i, t stands for a relation between a value of type i and a value of type e. This relation (in fact a function) can be seen as a set of pairs (α, y), where y is contributed by the internal argument. The application of ext to the formula in 11 yields 12. 12. ext (THE ( THREE )( GIRL ))(LIFT(int (∅(TWO)(TABLE))))  = λX λα∃P[P ⊆ GIRL ∧ |PC | = 3 ∧ ∀x[P(x) → X (x)(α)]] (λzλα  ∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀y[Q(y) → LIFT(α  )(y)(z) ∧ α  = d(Ran(su)) ∧ |α  | ≤ |Q|]]) ... = λα∃P[P ⊆ GIRL ∧ |PC | = 3 ∧ ∀x[P(x) → ∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀y[Q(y) → LIFT(α)(y)(x) ∧ α = d(Ran(su)) ∧ |α| ≤ |Q|]]]] This is exactly the point at which the representation stands for S0 . The formula says (tenselessly) that there is a set P of girls such that this set contains three girls identified in the discourse (by speaker and hearer) and such that for each

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girl x in P there are two tables y such that x lifts y either with regard to one index α or with regard to two indices α. In this way, P and Q are bounded sets in N so that S0 is terminative. Applying SYN and PAST as defined in Section 3.5.2 on page 89 yields (34). (34)

∃i ∃j∃k∃P[P ⊆ GIRL ∧ |P ∩ C| = 3 ∧ ∀x[P(x) → ∃Q[Q ⊆ TABLE ∧ |Q| = 2 ∧ ∀y[Q(y) → [LIFT(k)(y)(x) ∧ k = d(Ran(su)) ∧ |k| ≤ |Q| ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]]]]

This says that there is a past domain i  and a contextually identified set P of three girls such that for each x of P there is a set Q of tables with two members y such that x lifts y relative to the eventuality index k and k ⊂ N and the cardinality of k is less or equal to the cardinality of Q and (by the application of IMP) there is underinformation about actualization of k in j and hence in the domain i  , which is anterior to i. In (34), the relation between the external argument NP and the VP is seen as a function, say f ext , with as its domain the set P of girls. This function relates g1 to Q1 , g2 to Q2 , and g3 to Q3 not excluding Q1 = Q2 = Q3 .21 For the same reason, nothing prevents Q1 ∩ Q2 ∩ Q3 = ∅ or Q1 ∩ Q2 ∩ Q3  = ∅. This variable output of the function f ext is due to the role of the index k in its interaction with members of the internal argument denotation. It allows there to be just two tables t1 and t2 lifted consecutively by all three girls, at different times. It also allows for six different tables lifted at the same moment and for all sorts of intermediate configurations. This is because the function f ext does not map directly to a set of tables, but to a set of pairs of indices and tables. In this way, table t1 in the pair (1, t1 ) is counted as different from t1 in the pair (2, t1 ).22 5.3.3 Discretization in Sentences with Unaccusatives and Unergatives The question is now how unaccusatives and unergatives fit in the present analysis, in particular whether they show a different behaviour with respect to the multiplication scheme (31) on page 155. If so, this should follow from comparing the tenseless underlined S0 -parts of the sentences (35a) and (36a). 21 In the metaphor of the thematic framework in Gruber (1976), one could say that each of the

girls has her own individual path and that paths may overlap with regard to the eventuality index as well as to the sets of entities denoted by the internal argument. 22 This way of counting resembles a traffic count where the number of cars passing are counted during the whole day. A car passing twice will be counted as two cars, as discussed in Verkuyl (1984); cf. also Krifka (1990). I refer here to several studies in Verkuyl (1999), in particular to its chapter 8.

5.3 A Formal Account from Lexical Bottom to S0 (35)

a. Three girls arrive(d at the hotel this afternoon). b. ARRIVE(α)(arg2 ) ∧ α = d(Ran(su)) c. λα∃P[P ⊆ GIRL ∧ |P| = 3 ∧ ∀x[P(x) → [ARRIVE(α)(x) ∧ α = d(Ran(su)) ∧ |α| ≤ 3]]]

(36)

a. Three girls walk(ed along the river this afternoon). b. WALK(α)(arg1 ) ∧ α = Ran(su) c. λα∃P[P ⊆ GIRL ∧ |P| = 3 ∧ ∀x[P(x) → [WALK(α)(x) ∧ α = Ran(su)]]]

165

Starting the compositional process with the verb arrive, it requires an argument. In (35b), the argument occupies the position taken by the internal argument in a transitive configuration and so it will be subscripted as arg2 . The lexical characterization of an unaccusative therefore triggers the clause |α| ≤ |arg2 |. In this way, the cardinality information about the internal argument three girls is made available resulting in the clause |α| ≤ 3 in (35c). In this way, the NP three girls in (35a) happens to be promoted to the position of the external argument because that position is empty due to the absence of arg1 but the NP retains the specification of its relation to the eventuality index α obtained by int . As to unergatives, they fall into two groups. The first is the group of verbs represented in (36b): walk, eat, swim, sail, etc. They are characterized by the clause α = Ran(su) which, as a subset of R, fails to provide any bounding information due to the absence of an internal argument. Representation (36c) allows for all sorts of walking along the river: together, on different occasions, one walk+ a joint walk for the other two, etc. The second group unergatives contains verbs like belch, blink, boast, cough and knock as exemplified in (37). (37)

a. Three girls knocked (on the door). b. KNOCK(α)(arg1 ) ∧ α = d(Ran(su)) ∧ |α| ≥ 1 c. λα∃P[P ⊆ GIRL ∧ |P| = 3 ∧ ∀x[P(x) → [KNOCK(α)(x) ∧ α = d(Ran(su)) ∧ |α| ≥ 1]]]

They have in common that the cardinality of the external argument does not have a restricting effect on the index α. This means that the cardinality of α is left in the dark as to whether it is 1 or more than 1. The lexical definition in (37b) explains also why – pace Smith (1991: 55–7) and in her trail Li (2017) – there is no need for coercive reinterpretation in sentences like John knocked for five minutes. In John knocked without the durational adverbial it is left in the dark whether he knocked once or more than once, not excluding that John may be a robot in a science fiction story knocking endlessly on the door to make captives crackers, say. The context in which John knocked is used, is decisive for whether or not the sentence in the

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larger context of a discourse expresses boundedness. The speaker may continue with . . . and his knocking scared me or with . . . until the door opened. Or with . . . for five minutes. In other words, this is a case of α being an unbounded subset of N. This also holds for verbs like waggle, flutter, glimmer, spatter, etc. The difference between the first and second group of unergatives is sometimes subtle. Some see the Dutch verb wandelen ‘walk’ as a frequentative (a constant repetition of steps) and historically this may have been the case, but in current Dutch the verb wandelen is on a par with rijden ‘drive’, vliegen ‘fly’, zwemmen ‘sail’, etc. The present framework does not include the historical development of verbs, but it is easy to see that fading out the element of discretization inherent to frequentatives by removing the function d from the lexical entry may lead to a long-term change from (37b) to (36b). 5.4

Conclusion

The conclusion of the present chapter is that it is possible to formally account for aspectual composition from the lexical bottom up to and including S0 . This prepares the ground for proceeding from S0 to the tensed top S with the help of the tense operators formally accounted for in Chapter 3. The formal machinery is also applicable in marking the difference between unergatives and unaccusatives in a quite natural way. Syntactically they occupy the same position in the dyadic tree: on the left side of the VP node they take. Semantically they differ, dependent on the relation the argument k has to the argument arg1 for unergatives and the relation k has to arg2 in the case of unaccusatives. All in all, there seem to be quite different factors involved in the aspectual composition of tensed terminative sentences as illustrated for the PAST ( SYN ( IMP (ϕ)))-configuration in (33), repeated here as (38). (38) The three girls lifted two tables.

The full derivation of this sentence was given in twelve main steps and resulted in representation (34). It may help to connect this representation with the syntactic structure underlying the compositional procedure from bottom to top and to point at the places where the relevant information is introduced at the different levels of phrase structure. Figure 5.10 combines Figure 4.2 on page 123 with Figure 3.3 on page 55 and provides a list of factors that play a role in aspectual and tense composition with references to the pages where they were discussed: 1.

quantificational information contributed by a [+SQA]-NP as given in Figure 5.8a and described informally in Sections 4.3.1–4.3.2

5.4 Conclusion

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Figure 5.10 Factors in aspectual composition up to and including tense

2.

3.

4.

5.

6. 7.

and formally in steps 1, 2 and 3 of the derivation of (33) on page 159; application of int to the NP two tables as accounted for by step 5 of the derivation. It requires d as a discretizing function operating on Ran(su) and it relates α to the cardinality of Q on the basis of step 4 on page 161; discretization at the lexical level by the composite function d ◦ su providing an unbounded sequence {0, 1, 2, 3, . . .} in N as defined in (17) on page 145 and informally illustrated in Figure 5.3 on page 134; phrasal terminativity compositionally obtained at VP[+T] and putting a bounding instruction of the unbounded sequence {0, 1, 2, 3, . . .} using the cardinality information |arg2 |, as accounted for in steps 5, 6 and 7 of (33); bounding the denotation of the NP the three girls by cardinality 3, identifying this set as uniquely defined for speaker and hearer and made into an external argument by ext due to steps 9 and 10 on page 163; multiplication starting with step 11 of the derivation and resulting in a terminative tenseless predication obtained in (34) on page 164; underinformation about the actualization of d ◦ su by the application of IMP replacing the index α by k in the clause k  j, as sketched formally in Section 3.5;

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choice for an indicative tense form and not a subjunctive or modal one introduced by SYN and to be discussed in detail in Chapter 8; anteriority to n by PAST as formally accounted for in Section 3.5; actualization in the real time of the domain i  due to its isomorphic connection to the present domain i and so to the clause i ◦ n, also to be treated in Chapter 8.

It goes without saying that at all levels of this figure there are other options available than those presented here, but I will not spell out these options because all of them are covered by the formal machinery presented so far. There is more to say about the consequences of organizing aspectual and tense information in this way, but that will be done in the following chapters, when appropriate.

6 Binary Tense Structure and Adverbial Modification

6.0

Introduction

Rather than supplying an exhaustive account of temporal adverbial modification in general, this chapter aims at accounting for how temporal modification interacts with structures discussed at the end of the preceding chapter while meeting the requirements of compositionality. Hence its scope is limited to temporal adverbials with a Prepositional Prase or just a Noun Phrase with a covert preposition, as in (1). (1)

a. setting and relational adverbials like in 1678, in the morning, then, during the meeting, after the war, before breakfast, this week, next week, before last week, tonight, yesterday, etc. b. frequency adverbials like every morning, often, always, etc. c. durational adverbials like for an hour, in an hour, the whole day, throughout the war, since 1945, etc.

The adverbials in (1a) will be partitioned on the basis of the difference between setting and relational prepositions proposed in Verkuyl (1973). Setting adverbials are those with prepositions such as in, on, at, during, etc.; relational adverbials occur with prepositions like since, after, before, etc. The main partition to be made with regard to (1a), however, is the one between non-deictic adverbials (e.g. in the morning, before breakfast) and deictic adverbials (e.g. this week, yesterday).1 I will use the notation TADV for the adverbials in (1a). All adverbials in (1a) share that syntactically they may be inserted at three levels of tense structure, as shown in Figure 6.1. In Figure 6.1a, TADV c-commands S0 and its internal structure as indicated by fat lines and 1 Verkuyl (2008:91–124) provides a detailed analysis of adverbial modification of tense structure,

detailed in the sense that it discusses a number of ternary proposals in a binary setting. I will not repeat that discussion here, because the focus in the present chapter is on the role of adverbial modification in the compositional procedure followed so far.

169

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Figure 6.1 Modification of tense structure by adverbials

boldface. In Figure 6.1b, TADV takes the structure PERF(S0 ) to form the input for the SYN operator whereas in Figure 6.1c the structure SYN(PERF(S0 )) is in the scope of TADV. The main syntactic distinction originally made by Jackendoff (1972) between verb phrase adverbials, and sentence adverbials, and maintained in Broekhuis et al. (2015) and in Broekhuis and Corver (2016) for Dutch, is reflected in the difference between Figure 6.1a and 6.1b. As we shall see, it is also possible for a TADV to be inserted at the level between SYN and PAST shown in Figure 6.1c. The position of a TADV in tense structure determines the interpretation. The type-logical characterization of temporal adverbials gives a more precise view of the syntactic structure in which they operate. All are expressions of type i, t, i, t: they take a ϕ to yield a ϕ.2 Type-logically, they are therefore of the same type as IMP, PERF, SYN and POST : they may take S0 in order to form TADV (S0 ) and then be taken by PERF yielding PERF(TADV(S0 )), etc. Section 6.1 explores the internal structure of an NP in temporal adverbials, Section 6.2 analyzes the syntax and semantics of the non-deictic adverbials in (1a), Section 6.3 accounts for the frequency adverbials in (1b) and Section 6.4 for the deictic adverbials in (1a). That section also includes a solution to the Present Perfect puzzle. The adverbials in (1c) will be analyzed in Section 6.5. 6.1

On the Role of Det and NP in a Temporal Adverbial

All adverbials in (1) are analyzed on the assumption made by Katz and Postal (1964) that a temporal adverbial can be seen as a prepositional phrase even 2 The preposition of adverbials in (1a,b) is of type e, i, t, i, t, i, t, i, t. It takes an

NP to form a modifier of type i, t, i, t.

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though some of them appear without an overt preposition, as in the case of this week, which is syntactically analyzed as [PP [P ∅] this week]. They are also analyzed on the assumption that their introduction into phrase structure takes place without PRES and PAST having been applied. This means that they are analyzed in terms of number systems in the same way as was done with indices in S0 predications and at higher levels. The role of a preposition in a temporal adverbial will be argued to relate a certain index (α, k, j, i, i  , ai , . . .) to the index introduced by its NP. Section 5.1 started with three figures illustrating the structure in which an eventuality index α may occur on the lexical or phrase level. These figures were connected with the notion of an indexed family of sets. The present section discusses a similar figure on the side of a temporal adverbial. The Nouns occurring in the NP of temporal adverbials were organized into different categories in Verkuyl (1973), where a distinction was made between Type I Nouns and Type II Nouns. Figure 6.2 categorizes nouns occurring in

Figure 6.2 Noun denotations

adverbial modifiers by distinguishing between units in a continuously organized measuring system (Type I) and units that are organized discretely, either with equally large intervening intervals (Type IIa) or with irregularly intervening intervals (Type IIb). It was used to illustrate some observational facts. The sentences in (2) with the setting preposition in show that the determiner DET of the NP with a Type I Noun like week needs a much stronger referential force to isolate a week on the time axis than the determiner of NPs containing Type II Nouns like afternoon and reception. (2)

a. Ik zag hem in ∗ een week/∗ in de week/in die week. I saw him in ∗ a week/∗ in the week/ in that week. b. Ik zag hem op een zaterdag/op de receptie/die avond. I saw him on a Saturday/at the reception/that evening.

That a weak determiner like een ‘a’ when combining with a Type II Noun has referential force preventing measurement is shown in (3b). (3)

a. For an hour he was a terrible nuisance to me. b. ∗ For a reception/a weekend he was a terrible nuisance to me.

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Yet it is possible to measure with Type II Nouns when the NP is a bare plural. (4)

a. Ik heb daar drie weekenden lang gezeild. I have sailed there for three weekends. b. Ik heb daar drie uur gezeild. I have sailed there for three hours.

Sentence (4a) combines the discretization expressed by Type II units with a durative predication. In that respect, (4a) is comparable with For hours she sailed from this bank to the other side where duration is on the side of the adverbial and discretization on the side of the predication. In (4a), formeasurement allows for summation, whereas it is required in (4b) because what is measured in a Type II pattern must eliminate the empty space between the units being measured. It is striking to see how much the structures in Figure 6.2 resemble those in Figure 6.3, which brings the first three figures in Section 5.1 together, allowing for a direct comparison with Figure 6.2. It will

Figure 6.3 Measuring the length of intervals

be argued that Figure 6.2 can be dealt with in terms of an indexed family of sets in the same way as in the case of Figure 6.3. A direct consequence is that a noun like hour can be seen as denoting the set of hours in the domain of interpretation. This set H is introduced as a predicate over indices. ∃δ[H(δ)...] says that there is a δ belonging to the set H of hours, where H is of type i, t and δ of type i. Thus δ obtains the status of an index just like k and j. This provides the way to relate δ to k or to j and to see the upper line in Figure 6.2 as a well-ordered set of δ’s. The interrupted line for Type IIa Nouns represents sets whose members δ are periodically ordered. It

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opens the way for applying summation in order to get the total length of individual δ’s taken together. The irregularly interrupted line for Type IIb Nouns is the least organized one. Seeing this as shorthand for the structures pictured in Figure 6.3c, one can see that δ is an indexed member of a family of sets. This opens the way for summation in the case of sentences like I’ve worked fifteen hours this week totalling the number of hours spread over the week, as discussed later on in detail in Section 6.5.1. The specific contribution of a determiner will be discussed when appropriate. 6.2

Syntax and Semantics of Non-deictic Modification

6.2.0 Introduction We begin in Section 6.2.1 with the question of whether it is possible for adverbials to be inserted above PRES or PAST. This question will be answered in the negative. In Section 6.2.2, the crucial connective relating the modifying index of a setting adverbial to the modified index will be investigated. This results in leaving the spatial metaphor of locating some unit into another one behind in favour of seeing adverbial modification as a form of intersecting. Section 6.2.3 investigates how the insertion of setting adverbials on each of the three levels of tense structure proceeds. Relational adverbials are discussed in Section 6.2.4. Section 6.2.5 analyzes modification below the level of S0 . 6.2.1 The Predominance of Tense over Temporal Modifiers Essential for the present analysis is that all three sorts of adverbial in (1) are subordinated to PRES or PAST. Many have followed Partee (1973) – underscored in Partee (1984a) – in subordinating tense to temporal adverbials due to the fact that tense forms may be seen as “pronominal” with respect to these adverbials. It will be argued that there is no problem in taking PRES or PAST as c-commanding temporal adverbials. It is indeed attractive to use the term temporal for the denotation of the morning and a Thursday in sentences like (5) because an eventuality of Ron seeing Mary is experienced as taking place in a unique temporal unit called the morning of a certain day and having the structure of an interval, say (0,1).3

3 I am using Dowty’s example (5a) because one may interpret (5a) as being about a very

short eventuality so that Ron saw Mary for hours can be understood as terminative, say ‘Ron saw Mary (regularly passing by the door of his office) for hours’. But (5a) also allows for being interpreted duratively as about a meeting in which Ron and Mary discussed all sort of matters. This leniency of the verb see make this example useful because it permits me to

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Ron saw Mary in the morning. Ron and Mary flew to Paris on a Thursday. The Queen was born on 21 April 1926. Ron and Mary presented their paper at a conference.

However, this is not what is unequivocally expressed in the sentences (5). Technically, this can be shown by representing (5a) roughly as PAST(ϕ) where ϕ is tenseless and hence atemporal. As a consequence, the temporal status of the morning in ϕ is to be reduced to the neutral term interval. This means that in the tenseless Ron see Mary in the morning the denotation δ of the morning is an interval in R+ , hence an index, just like k and j. On a collective interpretation, the adverbial in (5b) may denote a particular Thursday on which Ron and Mary flew to Paris, either together or in different planes. On a distributive interpretation, (5b) may pertain to two different Thursdays. In both the collective and distributive interpretations, it is also possible to assume two series of Thursdays in a larger period in which Ron and Mary happened to fly regularly to Paris. It is not excluded either that Ron and Mary are pilots flying from Schiphol to Paris and that each of them flew to Paris twice or even three times on a particular Thursday, or regularly. Even in the case of (5c) one is not bound to see tense as anaphorically related to a more dominant adverbial.4 Sentence (5d) shows that the multitude of interpretations is not due to the fact that (5a)–(5c) use calendar names. It would be strange to take at a conference dominant to PAST if one does not know whether two or more conferences are involved or just one. The decision about what counts as the precise denotation of the morning, a Thursday and a conference in the present domain i can be only resolved by preceding discourse and by the relevant knowledge of speaker and hearer. That the decision is dependent on i is an extra argument for assuming that actualization of kor a series of k’s in real time is a matter of applying PRES or PAST because these operators introduce i. In the case of PAST, this is done by the . . . i  < i and ◦n. Unique actualization is achieved when no λ-operator fronts the formula, which occurs by the application of PRES or PAST. skip clauses like k = d(Ran(su)) or k = Ran(su) which do not play a role in the examples with Mary and Ron. 4 According to Mellor (1981:23), the adverbial in sentence (5c) should be seen as typically requiring the B-series because “dates, in short, are temporally unqualified attributes of events and things and tenses are not. That is the essential difference between the B-series and the A, indeed the only difference”. Mellor’s position in which the fleeting point n belongs to the A-series allows for giving tense its own dominant place at the top of the tree: (5c) is said in the A-series about some event fixed in the B-series in the past of n. Oversteegen’s Two Track Theory discussed in Section 2.3.1 also excludes dominance of the B-series over the A-series.

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The status of an eventuality index k as the argument of a verb, the fact that k is modified on an atemporal level by adverbials of the type under analysis and the fact that PRES or PAST are decisive for making the index k temporal by providing unique actualization in the real time, substantiate the position that tense is not subordinate to a temporal adverbial. I think that this alternative to Partee’s position strictly follows from the prominence of the first binary opposition between PAST and PRES. In Chapter 8, it will be shown that these operators can be held responsible for the mapping of atemporal phrase structure into the actual time axis of the domain of interpretation. 6.2.2 Temporal Modification as a Form of Bounding While writing a previous version of this chapter, I relied on Verkuyl (1973) without looking at it intensively, assuming that I still knew what it had proposed. Therefore, I took the preposition IN – generalizing over in, on, at, during – as a natural starting point for explaining the notion of setting in terms of a two-place relation IN(α, δ) between indices α and δ by locating the value of α directly in the value of δ; as I had done in Verkuyl (2008). In this way, IN(α, δ) was semantically interpreted as in (6). (6)

[[IN(α, δ)]] = 1 iff [[α]] ⊆ [[δ]]

It was only when the intuitively natural idea of locating one unit into another led to a structural problem in relating indices that I had a much closer look at the IN-definition and noticed that my 1973 analysis of temporal modification had evaded the metaphorical spatial pitfall of seeing it as a form of inclusion. Essential for temporal setting adverbials there is that they “are characterized by the fact that their NP necessarily refers to a limited stretch of time” (1973:596). This limiting force was illustrated by sentences like (7). (7)

a. During the existence of the universe stars emit light. b. During the flight of the spacecraft this computer will collect data.

The use of the setting preposition during puts an implicit restriction on the existence of the universe and although a spacecraft may fly eternally, the adverbial in (7b) requires that the flight be a limited one for which the predication holds. Note also that ??During the eternal existence of the universe ... is semantically ill-formed. The 1973 perspective on the restricting role of modifiers makes it necessary to redefine (6) in terms of a relation O(α, δ) where the eventuality index α is the α-part of δ. After all, the computer in (7b) may continue to collect data after the flight and the same sort of continuation of the predication is even explicitly expressed in sentences like (8).

176 (8)

Binary Tense Structure and Adverbial Modification a. On Monday, Jacob was sailing on the North Sea (as he did on Tuesday). b. On Monday, her condition was constant and also in the rest of the week, I see here.

In both sentences, the modifier δ (= Monday) presents just a slice of a longer period δ  for some reason constraining the predication itself to just this slice. In (8a), the speaker may use the restriction in order to prepare for saying something about other things that happened on that particular Monday. Sentences like (9) differentiate between Figure 6.4a and 6.4b. (9)

a. On Monday, Mary wrote her letter of resignation. b. The pumping station worked on Monday.

Due to the terminative predication Mary write a letter of resignation, sentence (9a) positions the writing of letter on Monday (= δ) so that α is properly included in its δ, as sketched in Figure 6.4a. However, the durative predication

Figure 6.4 Three ways of modifying α

The pumping station worked in (9b) may apply both to a situation in which the pumping station worked 24 hours per day without any interruption as illustrated in Figure 6.4b but also to a situation in which the station functioned on Monday even though the pumping itself was restricted to just a couple of hours, the case one has in Figure 6.4a. Figure 6.4c illustrates the situation already exemplified in (8) and for (9b) the situation in which Monday is just a slice because its 24 hours belong to a larger contextually given domain δ  in which the pumping machine was working. With respect to the eventuality index k, emphasis on the limiting role of adverbials is in line with the Galilean view on motion discussed in Chapter 4: the role of temporal modification can be seen as providing a bound to indices occurring in the binary tense structure such as k but also j, i and i  . Given the different levels at which a modifier may enter tense structure, the index α in the relation O(α, δ) does not have only k as its value: it may also stand for j, i and i  . These indices have no discrete structure and so they require a limiting stretch restriction directly. Modification restricts the unboundedness of the time axis to a specific stretch of time for which the modified index is relevant. What

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happens before or after is irrelevant (for the time being). Therefore, O(α, δ) will be interpreted as in (10): (10)

[[O(α, δ)]] = 1 iff [[α]] ∩ [[δ]] = ∅

This definition captures the three configurations in Figure 6.4. Even though in the majority of cases an inclusion relation between α and δ is empirically justified, the intersection relation in (10) is type-logically more appropriate. This means that in the case of, say, the relation expressed by O(i  , δ), the modification contributed by the index δ involves the restriction of i  to δ given the predication modified by δ. This leaves the rest of i  , if any, outside the modification itself. In the case of O(k, δ), a terminative k is included in δ, as exemplified by (9a), but in this case the ⊂-symbol amounts to [[k]]∩[[δ]] = [[k]]. The interpretation of O holds for adverbials like during the meeting, at night, at a conference, on Tuesday morning, etc. There is also no objection to analyze between two and four as an O-adverbial. The adverbial in the morning in (5a) Ron saw Mary in the morning is broken up into two pieces: (a) the NP the morning denoting an interval δ; and (b) the preposition in denoting the relation O which connects an eventuality index α to δ. Both elements are visible in (11), which locates the eventuality index α in δ. (11)

in the morning  λϕλα∃δ[M(δ) ∧ O(α, δ) ∧ ϕ[α]]

This definition introduces a set M (of type i, t) of mornings of which δ (of type i) is a member. We write M(δ) in order to express [[δ]] ∈ [[M]]. As observed earlier, the modifier δ can be embedded in a larger index. Let δ stand for the morning in (5a). Then δ can always be embedded in a larger interval δ  , perhaps denoted by on that day or on April 28, possibly already identified by available discourse information, otherwise simply assumed as being an unnamed subset of the present domain i  . If (5b) is about an internship at Air France KLM somewhere done by Ron and Mary, δ  may be identified by that month or their internship, which makes (5a) pertain to a series of Thursdays. Earlier discourse information shared by speaker and hearer decides upon this, so one should always be prepared to allow for embedding the δ of a sentence in a larger δ  unnamed in that sentence but named earlier in the discourse.5 5 I do not consider the assumption of a larger domain δ  always available for δ pragmatic. By

systematically making room for a factor dependent on the shared knowledge of speaker and hearer, the semantic representation can account for structural relations in the temporal structure construed in the course of discourse. Moreover, lexical knowledge of morning already implies

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In view of the derivations of sentences with adverbial modification that will follow below, the relation between δ and δ  will have to be made as precise as possible to avoid mismatch of types. Rejecting IN(α, δ) in (6) as accounting for temporal modification does not mean that the IN-relation disappears from the scene. In all three configurations of Figure 6.4 there are two modifiers, δ and δ  . I will use IN(δ, δ  ) as defined on the basis of (6) in order to account for a situation in which a modifier δ is included in a larger δ  . In Figure 6.4, the index α is pictured as an interval, a set, just like the indices δ and δ  . This means that one can write α ⊂ δ ⊆ δ  for Figure 6.4a (with α ∩ δ = α). And that we write W(δ  ) for naming δ  by the noun week and for expressing that δ  is an element of the set W of weeks. Let I be an indexed set of sets spelled out in (12a), then the general notation for such a set is given in (12a) where the subscripted index i of Ai generalizes over the subscripts of the sets in (12b), which are all natural numbers. (12)

a. I = {M1 , W2 , Y3 , 4 , . . .} b. I := { Ai }i∈N

Let an arbitrary i be the set as given in (13): (13)

i = {k, j, i  . . .}

Because i is of type i, t, each of the indices i, j, k, δ, δ  , etc., used in formulas in earlier chapters is allowed to be a member. The -symbol will be used for a set of indices having no name in natural language or having a name used earlier in a discourse but not in the sentence under analysis itself. Let M stand for the set of mornings in the model, W for the set of weeks, Y for the set of years, etc. If A is used as a variable of type i, t ranging over the elements of I, then the postulate in (14) can be said to hold for temporal adverbial modification. (14)

Monotone increasing domain postulate ∀Ai ∈ I∃A j ∈ I[δ ∈ Ai ⇒ ∃δ  ∈ A j [δ ⊆ δ  ∧ Ai ⊆ A j ]]

This warrants, for example, that W ⊂ Y holds as well as δ ⊆ δ  , with δ ∈ W and δ  ∈ Y. It also holds for M ⊂  for any  being a superset of M. This is exactly what is needed in order to account for the flexible insertion of adverbials in the tense structures of Figure 6.3: the higher the location, the more inclusive should an adverbial be as compared with a lower one. The preceding discourse determines what counts as the highest named or unnamed interval so that each morning is embedded in a natural day. Semantics seems to me to have the task of accounting for that.

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far. The empirical grounding of postulate (14) is hampered by the fact that normally sentences do not contain more than two temporal adverbials, but on the other hand a puzzling sentence like Jan left a 3:00 p.m. last year will automatically call for some covert δ’s between δ and δ  to close the bridge. 6.2.3 Connecting a Temporal Modifier to Indices at Different Levels Returning now to sentence (5a), we will give (the outline of) its derivation in (15) which corresponds to Figure 6.1a. The full derivation is given as (2) in the appendix on page 293. (15)

a. Ron saw Mary in the morning. (= (5a)) b. S0  λα  [SEE(α  )(m)(r)] c. IN - THE - MORNING λϕλα∃δ[M(δ) ∧ ϕ[α] ∧ O(α, δ)] d. IN - THE - MORNING(S0 )  . . . = λα∃δ[M(δ) ∧ SEE(α)(m)(r) ∧ O(α, δ)] e. IMP(IN - THE - MORNING(S0 ))  . . . = λβ∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  β] f. SYN(IMP(IN - THE - MORNING(S0 )))  . . . = λα∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  α] g. PAST(SYN(IMP(IN - THE - MORNING(S0 ))))  . . . = ∃i ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]

In (15e), the overlap O restricts α to δ (Figure 6.4a,b) or it restricts the modification by δ to a subset of α (Figure 6.4c). Footnote 3 on page 174 left open the possibility of interpreting (15a) as a case of modifying a terminative S0 or a durative S0 . The uncertainty about which of the two is the case in (15a), would be resolved by the clause k = d(Ran(su)) in which k is included in δ. The durative interpretation is justified as soon as it is captured by Figure 6.4c. In that case, j may be seen as already being identified in earlier discourse as the day of which the morning δ is just a part, which would become clear by adding to (15a): ... in her office and after lunch they went on somewhere else in the building. That δ may appear in a different O-relation from the one in (15) is shown in the last line of the derivation for the configuration pictured in Figure 6.1b, the full derivation of which is given in the Appendix as (3) on page 293. (16)

a. Ron saw Mary in the morning. (= (5a)) b. IN - THE - MORNING(IMP(S0 ))  ... c. = ∃i ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ k  j ∧ O(j, δ) ∧ j  i ∧ i < i ∧ i ◦ n]

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The difference is the restriction of j to δ in (16c). It follows that k must be positioned in δ even on a durative interpretation either as in Figure 6.4a or as in Figure 6.4b. As discussed later on, the configuration O( j, δ) is quite natural for contexts in which k occurs habitually. The third option available for a temporal adverbial in Figure 6.1c is given in (17b). (17)

a. Ron saw Mary in the morning. (= (5a)) b. IN - THE - MORNING(SYN(IMP(S0 )))  . . . c. ∃i ∃δ∃j∃k[M(δ) ∧ SEE(k)(m)(r) ∧ k  j ∧ j  i ∧ O(i , δ) ∧ i < i ∧ i ◦ n]

At this level of insertion, the “slicing” property of modification shows itself. The relevance of the predication is constrained to the morning δ positioned in the past domain i  . The third option may not be a natural one for (17a) but given the fact that insertion of δ takes place at a level very close to the introduction of PRES or PAST, we have to wait until the treatment of deictic adverbials in order to see whether a high level of insertion is structurally related to deixis or not. The leveled tense structure provides a natural way for assigning more than one temporal modifier to a predication, as shown in the derivation of (5a) given in (18), the full version of which appears as (4) in the Appendix on page 294. (18)

a. Ron saw Mary at nine o’clock in the morning. b. S0  λα  [SEE(α  )(m)(r)] c. AT- NINE - O ’ CLOCK  λϕλα∃δ[N(δ) ∧ ϕ[α] ∧ O(α, δ)] d. AT- NINE - O ’ CLOCK(S0 )  . . . = λα∃δ[N(δ) ∧ SEE(α)(m)(r) ∧ O(α, δ)] e. IMP(AT- NINE - O ’ CLOCK(S0 ))  . . . = λβ∃k∃δ[N(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  β] f. IN - THE - MORNING λϕλα∃δ  [M(δ  ) ∧ ϕ[α] ∧ O(α, δ  )] g. IN - THE - MORNING(IMP(AT- NINE - O ’ CLOCK(S0 )))  . . . = λα∃k∃δ∃δ  [N(δ)∧ SEE(k)(m)(r)∧ O(k, δ)∧k  α ∧M(δ  )∧ O(α, δ  )] h. SYN(IN - THE - MORNING(IMP(AT- NINE - O ’ CLOCK(S0 ))))  . . . = λα∃j∃k∃δ∃δ  [N(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ M(δ  ) ∧ O(j, δ  ) ∧ j  α] i. PAST(SYN(IN - THE - MORNING(IMP(AT- NINE - O ’ CLOCK(S0 )))))  . . . = ∃i ∃j∃k∃δ∃δ  [N(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ M(δ  ) ∧ O(j, δ  ) ∧ j  i ∧ i < i ∧ i ◦ n]

(18i) says that k overlaps with δ called 9’oclock where k is restricted to δ and it says that k precedes or equals j in so far j is restricted to δ  called the morning. This accounts for the relation between the two adverbials in terms of

6.2 Syntax and Semantics of Non-deictic Modification

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a difference of level in tense structure.6 Syntactically, this outcome is as to be expected for Dutch as pointed out in Broekhuis and Corver (2016:1161). 6.2.4 Non-deictic Relational Adverbials Relational adverbials like after breakfast in (19a) can be considered complex O-adverbials ordered by an anteriority relation, illustrated in Figure 6.5.

Figure 6.5 Relational adverbials with after

(19)

a. Ron saw Mary after breakfast. b. after breakfast  λϕλα∃γ ∃δ[B(γ ) ∧ (δ) ∧ γ < δ ∧ O(α, δ) ∧ ϕ[α]]

In (19b), the adverbial is defined as looking for a predication ϕ (here, Ron see Mary) the eventuality index k of which substitutes for the variable α in O(α, δ) and is restricted by δ. The named index γ precedes the unnamed δ. In (20), δ remains unnamed and δ  (= the morning) comprises both γ and δ. (20)

Ron saw Mary in the morning after breakfast.

This is an argument for assuming that (19a) involves three intervals interacting in the modification: (i) γ (= breakfast), (ii) δ locating α, and (iii) δ  comprising the named γ and the unnamed δ, where the third adverbial δ  can be understood as pertaining to the morning, as in (20), although not necessarily so. In view of a discussion following later, it is appropriate to note here that the relation between γ and α is defined by the anteriority-connective < and not by the abut-connective ⊃⊂, which expresses anteriority as well but requires that α be adjacent to γ . This is not required in (19) and (20). 6.2.5 Modification below S0 Adverbial modifiers have been analyzed so far on the assumption of their sharing the logical type i, t, i, t. This explains the λϕ at the beginning of their 6 Adverbials like 9 o’clock are interpreted as landmark in the sense of Chapter 2. That is, there is

room for seeing its denotation as standing for an interval larger than 9 o’clock sharp.

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definition, because ϕ is of type i, t. It also explains why the tense structure above S0 is the domain in which modification takes place: the operators of the second and third binary opposition take type i, t to form i, t. In terms of interpretation, treating non-deictic adverbials as yielding the same type as their input was shown to result in empirically correct observations about different interpretations of the sentences under analysis dependent on the level of application.7 Writing i, t, i, t for the characterization of the logical type of temporal adverbials allows for the use of a more general notation a, t, a, t, where a is a variable over types. In doing so, the modification is given a broader application. This opens the way for taking into account modification at a lower level than the tenseless top S0 as in (22a). (21)

a. To eat fish on Friday was quite normal in those days. b. We were asked not to interrupt during the meeting. c. Ron has decided to call Mary in the morning from now on.

(22)

a. [VP to call Mary in the morning] b. λzλα  [CALL - MARY(α  )(z) ∧ α  = d(Ran(su))] c. in the morning  λPλxλα∃M[|M| ≥ 1 ∧ ∀δ[M(δ) → [P(α)(x) ∧ O(α, δ)]]] d. λzλα∃M[|M| ≥ 1 ∧ ∀δ[M(δ) → [CALL - MARY(α)(z) ∧ α = d(Ran(su)) ∧ O(α, δ)]]

The VP in (22a) is of type e, i, t. By the variable a in the generalized type a, t, a, t, the modifier in the morning defined in (22c) is allowed to count as being of type e, i, t, e, i, t taking (22b) in order to yield (22d). Applied to the sentences in (21), VP-modification differs from S0 -modification. On Friday in (21a) is used for making a semantic unit EAT- FISH - ON FRIDAY independent of the external argument. Given the restriction to just the VP, (21b) cannot be paraphrased as ‘During the meeting we were asked not to interrupt’ because the ban on interrupting may have been expressed before the meeting took place. In fact, the meeting may still be in the process of being planned. In (21c), Ron decided on morning calls without any referential force expressed by in the morning. These examples show that modification below S0 is marked in the sense that Friday, the meeting and the morning do not refer to a specific interval uniquely located on the time axis. 7 This makes the present analysis of adverbials quite different from the one in Rathert (2012),

which locates positional adverbials like in the morning below S0 even though her syntax can be understood as type-logically translatable into the type-logic applied here.

6.3 Frequency and Habituality 6.3

183

Frequency and Habituality

Adverbials like three times and often can be seen as quantifying over indices in their scope. I will use the set  in order to indicate that three times, often, always, frequently, seldom, etc. express m × δ as the cardinality of , where m is a natural number which may be given overtly or must be estimated as corresponding to a certain level of frequency. Thus, three times and often are analyzed as in (23) and (24), where the adverbials have the pair of quantifiers ∃ j∃k in their scope. (23)

a. Ron saw Mary three times. b. three times  λϕλα∃[|| = 3 ∧ ∀δ[(δ) → ϕ[α]]] c. PAST(FADV(SYN(IMP(S0 ))))  . . . ∃i ∃[|| = 3 ∧ ∀δ[(δ) → ∃j∃k[SEE(k)(m)(r) ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

(24)

a. Ron saw Mary often. b. often  λϕλα∃[|| > m c ∧ ∀δ[(δ) → ϕ[α]]] c. PAST(FADV(SYN(IMP(S0 ))))  . . . ∃i ∃[|| > m c ∧ ∀δ[(δ) → ∃j∃k[SEE(k)(m)(r) ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

In both cases, multiplication is expressed in terms of cardinality. Taken in a linguistically adapted sense of 3 × δ, the adverbial three times can be seen in (23b) as providing the cardinality 3 of an unnamed set  of intervals δ. In the same way, often can be defined as in (24b), where the clause || > m c in (24) expresses that the number of k’s is ‘above average’ given a contextually determined value m.8 This is due to the fact that often in (24b) requires a set  with sufficiently many δ’s for ending high in a scale between 0 and 1 from which m is derived. The adverbial every morning also multiplies by means of universal quantification over δ’s. In (25a), it introduces a set M of mornings δ and says that in each δ Ron saw Mary. The full version of (25) is given in (5) on page 295. (25)

a. Ron saw Mary every morning. b. S0  λα[SEE(α)(m)(r)] c. IMP(S0 )  . . . = λβ∃k[SEE(k)(m)(r) ∧ k  β] d. SYN(IMP(S0 ))  . . . = λα  ∃j∃k[SEE(k)(m)(r) ∧ k  j ∧ j  α  ] e. EVERY MORNING  λϕλα∃M∀δ[M(δ) → [ϕ[α] ∧ O(α, δ)]] f. EVERY MORNING(SYN(IMP(S0 )))  . . . λα∃M∀δ[M(δ) → ∃j∃k[SEE(k)(m)(r) ∧ k  j ∧ j  α ∧ O(α, δ)]]

8 A formula along this line of thought was used in Verkuyl (1999:99) as an alternative to proposals

in De Swart 1991, Pratt and Francez 2001, Von Stechow 2002, Artstein and Francez 2006, Francez and Steedman 2006.

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Binary Tense Structure and Adverbial Modification g.

PAST ( EVERY MORNING ( SYN ( IMP (S0 ))))  . . . ∃i ∃M∀δ[M(δ) → ∃j∃k[SEE(k)(m)(r) ∧ k  j ∧ j  i ∧ O(i , δ) ∧ i < i ∧ i ◦ n]]

The last line of the derivation says that for each morning δ there is a j and a k making the predication true and that each morning δ overlaps with the past domain i  . The set M will generally be taken as contextually determined dependent on the previous discourse. This determines the range of the universal quantifier. If the discourse concerns Mary’s one-week visit to New York where Ron works at an office, the set M will be restricted to days of that week often with a marginal leniency as to the number. The question that arises is how the frequency interpretation of (25a) relates to the interpretation of (5a) Ron saw Mary in the morning when this is clearly about a series of mornings in which Ron saw Mary. Take, for instance, a situation previously discussed in the discourse where the speaker and not the hearer was informed about a semester in which Ron stayed at CSLI where Mary has a position. In relating that to the hearer, sentence (5a) may be about that semester or a part of it in which Ron saw Mary every morning. There is another way of expressing that meaning, as shown by the derivation in (26). (26)

a. Ron saw Mary (always) in the morning. b. S0  λα  [SEE(α  )(m)(r)] c. IN - THE - MORNING(S0 )  . . . = λα∃δ[M(δ) ∧ SEE(α)(m)(r) ∧ O(α, δ)] d. IMP(IN - THE - MORNING(S0 ))  . . . = λβ∃δ∃k[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  β] e. SYN(IMP(IN - THE - MORNING(S0 )))  . . . = λα∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  α] f. ∅∀  λϕλα∃∀δ  [(δ  ) → ϕ[α]] g. ∅∀ (SYN(IMP(IN - THE - MORNING(S0 ))))  . . . = λα∃∀δ  [(δ  ) → ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  α]] h. PAST(∅∀ (SYN(IMP(IN - THE - MORNING(S0 )))))  . . . = ∃i ∃∀δ  [(δ  ) → ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

Up to and including (26e), the derivation proceeds as in the derivation (15) for Ron saw Mary in the morning. To obtain a habitual or frequency interpretation there are two ways to go: an overt and a covert one. If ALWAYS∀ is the representation for the overt universal quantifier expressed by always, then the covert occurrence of this quantifier will be written as ∅∀ , both having the representation in (26f). This results in a derivation that accounts for the type interpretation of (5a). The detailed version of (26) is given as (6) in the Appendix on page 296.

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The difference between (26h) and (25g) is clear: in (25g) a set M of mornings δ is given and for each δ Ron saw Mary in δ. In (26h) there is a set  of unnamed indices δ  such that each δ  is mapped to a member δ of a set M of mornings in which Ron saw Mary. This may lead to interpreting (26a) covertly as Every day Ron saw Mary in the morning, but also as Every workday Ron saw Mary in the morning or Every working appointment, Ron saw Mary in the morning. The Monotone Increasing Domain postulate in (14) warrants the inclusion relation between δ and δ  . Summarizing over the different forms of temporal modification by an adverbial containing the noun morning, one can conclude that there is a diversity of ways in which it can be shaped dependent on the levels of tense structure as visible by comparing the last lines of the derivations. Three of them are: •

•

•

M may be introduced as a predicate as in ∃δ[M(δ) ∧ . . .]. This is the format suitable for token interpretations, as in (15)–(18). M may be introduced in front of the derivation in the form of ∃M∀δ[M(δ) → . . .]. This is the format in which the adverbial contains a determiner expressing quantification, as in (25). M may be introduced in the scope of a quantifying frequency adverbial in the format ∃∀δ  [(δ  ) → ∃δ[M(δ) . . .]], as in (26).

This inspection of non-deictic adverbials suffices to meet the aim set in the introduction of the present chapter, namely to account for the interaction of temporal adverbials with phrase structure made available to them as part of a compositional procedure to get from the bottom to the top of a tensed sentence. In the remaining sections, the information provided about this form of modification will be augmented when necessary. 6.4

Syntax and Semantics of Deictic Modification

6.4.0 Introduction Temporal adverbials like last week, this week, tonight, next weekend, yesterday, tomorrow, recently, soon, last Tuesday, now, nowadays, these days, within a week from now, during that meeting, etc. clearly involve deixis due to the way their denotation relates to the speaker of the sentences in which they occur. Yet, to say that these adverbials are all deictic is not a foregone conclusion. For example, during that meeting may be used to refer anaphorically to an earlier introduction of a meeting in the preceding discourse and so locating k is not dependent on its position with respect to n. Also, this week in I’ll call you this week may pertain to the i ♦ -part of the present domain i, whereas in I

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prefer to have it this week said by someone pointing at the screen of a computer to the one scrolling through the calendar in order to fix a date for a meeting with a client some months later, this week does not refer to the week in which the sentence is uttered. Because yesterday is one of the adverbials used in formulating the Present Perfect puzzle, the present section cannot escape from offering a solution. This will be done in steps by first discussing deictic setting adverbials in Section 6.4.1 and by establishing in Section 6.4.2 that yesterday should be treated differently from setting adverbials and from relational adverbials like before last week. This result will be applied in Section 6.4.3 where a structural binary solution to the Present Perfect puzzle will be given in terms of why English yields this problem and other Germanic languages do not have it. 6.4.1 Deictic Setting Adverbials Our analysis of deictic adverbials begins with observing a difference between the Dutch sentences in (27) en (28), which also holds for the English translations. (27)

a. Vorige week logeerde Mary in Hotel Europa. ‘Last week Mary stayed in Hotel Europa.’ b. Een paar uur geleden reed ze langs ons huis. ‘A few hours ago she drove past our house.’

(28)

a. Deze week logeerde Mary in Hotel Europa. ‘This week Mary stayed in Hotel Europa.’ b. Vanavond reed ze langs ons huis. ‘Tonight she drove past our house.’

The temporal adverbial vorige week ‘last week’ in (27a) means ‘in the week preceding the present week’ and een paar uur geleden ‘ a couple of hours ago’ positions k in a period j preceding n with a distance of some hours between k and n. Such a distance is also required for the interpretation of sentences in (28): k is located in an earlier period of this week or tonight. The adverbials in (27) can only occur with a past tense, whereas the adverbials in (28) may also occur with the Simple Present, as shown in (29). (29)

a. Deze week logeert Mary in Hotel Europa. This week stays Mary in Hotel Europa ‘This week Mary is staying/stays/will stay in Hotel Europa.’ b. Vanavond rijdt ze langs ons huis. Tonight drives she past our house ‘Tonight she is driving/will drive past our house.’

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In (29), the speaker may map forward as is made clear by the English translations. The terminative (29b) allows not only for the interpretation of just one passage past our house but also for a “going on at n” interpretation. Without further context, this is a little odd because it requires a series of passages going on tonight, as in the case of a so-called “cycle race around the church”. The oddness disappears in a sentence like Vanavond vaart ze langs Texel ‘lit: Tonight she is sailing/sails past Texel’, which has a going-on-interpretation because Texel is a large island. The dominant interpretation of (29b) is the one looking forward in which she is expected to drive past our house just once. What do the deictic temporal adverbials contribute to the meaning of (28) and (29)? The answer to this question depends on the level of tense structure on which the adverbial is inserted. Left aside aspectual and quantificational information contributed by S0 , application of IMP to S0 in (28a) and (29a) leads to (30a) and application of SYN to (30b). (30)

a. b.

IMP (S0 )

 λβ∃k[STAY(k)(h)(m) ∧ k  β]  λα∃j∃k[STAY(k)(h)(m) ∧ k  j ∧ j  α]

SYN( IMP(S0 ))

The modifier this week is introduced in (31). (31)

THIS WEEK

 λϕλα∃δ[W(δ) ∧ ϕ[α] ∧ O(α, δ) ∧ δ ◦ n]

This introduction of δ is made deictic by the clause δ ◦ n, which requires that the nominal element n be located in δ so that δ is deictically dependent on the utterance of the speaker at n. As a modifier of α, the index δ intersects with α. Applied to (30b), THIS - WEEK yields (32). (32)

THIS - WEEK ( SYN ( IMP (S0 )))  λϕλα∃δ[W(δ) ∧ ϕ[α] ∧ O(α, δ) ∧ δ ◦ n] (λα  ∃j∃k[STAY(k)(h)(m) ∧ k  j ∧ j  α  ]) . . . = λα∃j∃k∃δ[W(δ) ∧ STAY(k)(h)(m) ∧ k  j ∧ j  α ∧ O(α, δ) ∧ δ ◦ n]

This output waits for being taken by PRES or PAST. Application of obtain PRES results in (33). (33)

PRES ( THIS - WEEK ( SYN ( IMP (S0 ))))  . . . ∃j∃k∃δ[W(δ) ∧ STAY(k)(h)(m) ∧ k  j ∧ j  i ∧ O(i, δ) ∧ δ ◦ n ∧ i ◦ n])

The final line of (33) leaves us in the dark whether Mary is staying in the hotel at n or will stay in the hotel later on this week. The PAST-sentence (28a) Deze week logeerde Mary in Hotel Europa ‘This week Mary stayed in Hotel Europa’ is derived with (34) as its final line. (34)

PAST ( THIS - WEEK ( SYN ( IMP (S0 ))))  . . . ∃i ∃j∃k∃δ[W(δ) ∧ STAY(k)(h)(m) ∧ k  j ∧ j  i ∧ O(i , δ) ∧ i < i ∧ δ ◦ n ∧ i ◦ n]

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The definition of this week in (31) leads in (34) to the clause O(i  , δ). This restricts the past domain i  in which k is located due to the clauses k  j and j  i  to the intersection it has with the interval δ denoted by this week. The clause δ ◦ n connects δ to the fleeting n, hence to the present domain i which determines the deictic nature of the modification. The last line of (34) expresses that Mary stayed in Hotel Europa earlier this week due to the clause i < i. The application of PERF instead of IMP in (35a) results in (35b). (35)

a. Deze week heeft Mary in Hotel Europa gelogeerd. ‘Mary has stayed in Hotel Europa this week.’ b. PRES(THIS - WEEK(SYN(PERF(S0 ))))  . . . ∃j∃k∃δ[W(δ) ∧ STAY(k)(h)(m) ∧ k ≺ j ∧ j  i ∧ O(i, δ) ∧ δ ◦ n ∧ i ◦ n]

The clause j  i provides the room for locating k beyond n, which is correct for Dutch but not for English. It will be re-examined in Chapter 8 in discussing the opposition between SYN and POST. 6.4.2 Deictic Relational Adverbials Non-deictic relational modification discussed in Section 6.2.4 requires two indices: δ and γ . In (19a) Ron saw Mary after breakfast, the clause BREAK FAST (γ ) identifies the interval of the breakfast where δ is the unnamed successor to γ . The relation between γ and δ represented as γ < δ expresses anteriority. Deictic relational modifiers also express anteriority but the picture is more complex as shown by the sentences in (36). (36)

a. Mary will take a decision after next month. b. Mary took her decision before last week.

The adverbials in (36) behave in the same way as the non-deictic relational adverbials due to the overt occurrence of the relational prepositions after and before by locating k in an unnamed interval following or preceding a named one. Thus (36a) seems to be correctly pictured by Figure 6.5 on page 181, the relational character of the modification in (36) being attributed to the anteriority relation γ < δ. However, it is not possible to characterize the adverbials last week and next week in (37) as simple setting adverbials even though they allow for extension with a setting preposition: in the last week and during the next week. (37)

a. Last week Mary stayed in Hotel Europa. (= (27a)) b. Mary will stay in Hotel Europa next week.

Both sentences presume an anteriority relation between the present week and the week after or before. In fact, last week in (37a) names an interval while

6.4 Syntax and Semantics of Deictic Modification

189

leaving the anchoring unit (i.e. this week) unnamed. Last week is defined in (38a), next week in (38b) with γ as the week preceding or following this week δ. (38)

a. last week  λϕλα∃γ ∃δ[W(γ ) ∧ W(δ) ∧ O(α, γ ) ∧ ϕ[α] ∧ δ = s(γ ) ∧ δ ◦ n] b. next week  λϕλα∃γ ∃δ[W(γ ) ∧ W(δ) ∧ O(α, γ ) ∧ ϕ[α] ∧ γ = s(δ) ∧ δ ◦ n]

The deictic nature of the adverbials in (38) is accounted for by the clause δ ◦ n. This means that the denotations of adverbials get their temporal value at the moment at which PRES or PAST applies. There is no need to assume in (36a) and (36b) that the period after next month is itself a month: it may be any interval. In contrast to that, last week in (37a) requires this week δ as the anchoring unit immediately following γ and in (37b) δ as the anchoring unit immediately preceding γ . Nouns like week, month and year denote sets of units that are well-ordered when organized in an indexed family of sets. This is accounted for in (38) by introducing two members of the set W of which δ is the immediate successor or predecessor to γ . This distinguishes these adverbials from adverbials with Type II nouns like last Friday, next summer and during the last meeting. In those cases, the notation δ < γ or γ < δ would be more appropriate with δ taken as the anchoring unit containing n, say some part of today or this week or this year. Next summer, when said in the present summer, may automatically take the γ = s(δ)-form with δ as the present summer rather than today.9 6.4.3 A Structural Solution to the Present Perfect Puzzle The introduction of the adverbial yesterday in a derivation is similar to the one of last week in (38a): (39)

yesterday  λϕλα∃γ ∃δ[D(γ ) ∧ ϕ[α] ∧ O(α, γ ) ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n]

We have now arrived at an answer to Klein’s question of why (11b) ∗ Chris has left York yesterday discussed in Chapter 2 on page 31 is ungrammatical. The literal translations of (11b) are grammatical in Dutch and German. (40)

a. Chris heeft York gisteren verlaten. (Dutch) b. Chris hat York gestern verlassen. (German)

9 I will not further explore these differences because they are part of the lexical semantics of

the adjectives and nouns involved in temporal modification not relevant to the solution of the Present Perfect puzzle.

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This extends the Present Perfect puzzle to the problem of explaining why (40a) and (40b) are grammatical and to the problem of explaining why sentences with a Simple Past in Dutch, German and English may occur with a deictic modifier as shown in (41a), (41b) and (42a), respectively.10 (41)

a. Chris verliet gisteren York. b. Chris verließ gestern York.

(42)

a. Chris left York yesterday b. PAST ( TADV ( SYN ( IMP(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(k, γ ) ∧ k  j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i < i ∧ i ◦ n] c. PAST ( TADV ( SYN ( IMP(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(j, γ ) ∧ k  j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i < i ∧ i ◦ n] d. PAST ( TADV ( SYN ( IMP(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(i , γ ) ∧ k  j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i < i ∧ i ◦ n]

The grammaticality of (42a) can be explained at three levels by the fact that Chris’s departure yesterday is anterior to today (= δ) due to the intersection relation O(k, γ ). There are two anteriority relations involved in these representations. Firstly, the PAST operator locates i  anteriorly before the present domain i due to the definition of PAST. Secondly, δ = s(γ ) says that γ is anterior to δ because δ is the successor of γ in the well-ordered set of days. These two forms of anteriority are brought together by the fact that γ is located in i  due to the clause k ≺ j and j  i , in (42b) by O(k, γ ), in (42c) by O(j, γ ) and in (42d) by O(i , γ ). As observed before, the intersection at different levels of insertion corresponds to different interpretations. The clause O(j, γ ), for example, gives room for continuation of sentence (42a) by further reporting about what Chris did after leaving York connecting those eventualities to Chris’s departure by shaping a common present domain j. The clause O(i , γ ) may be used to embed yesterday in a larger past before yesterday, so that yesterday is the relevant “slice”. We are now committed to explaining the ungrammaticality of (43a) in English, where the three representations in (43b,c,d) are to be compared with those in (42b,c,d). (43)

a. ∗ Chris has left York yesterday. b. ∗ PRES ( SYN ( IMP ( TADV(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(k, γ ) ∧ k ≺ j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i ◦ n] c. ∗ PRES ( SYN ( IMP ( TADV(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(j, γ ) ∧ k ≺ j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i ◦ n]

10 The German Simple Past has dramatically lost ground to the Present Perfect. Yet, (41b) is fully

grammatical. The literal English counterpart of (41) is: Chris left yesterday York.

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d. ∗ PRES ( SYN ( IMP ( TADV(S0 ))))  . . . [D(γ ) ∧ LEAVE(k)(y)(c) ∧ O(i, γ ) ∧ k ≺ j ∧ j  i ∧ D(δ) ∧ δ = s(γ ) ∧ δ ◦ n ∧ i ◦ n]

Due to PRES, the anteriority-relation i  < i in (42) does not occur. What remains is the anteriority relation between γ and δ expressed by the clause δ = s(γ ). Note that the clause O(α, γ ) in all three cases defines the intersection between α (= k in (43b), = j in (43c) and = i in (43d)) and γ . In all these cases, k ≺ j holds and j is said to synchronize with i by the clause j  i. What is missing is the clause γ ◦ n crucial for connecting γ to the present domain i. In other words, δ ◦ n prevents γ from being located in i. This is the first part of the structural solution to the Present Perfect puzzle, which also works for the more specific comparison between (44) and (45).11 (44)

a. Chris left York this morning. b. PAST(SYN(IMP(TADV(S0 ))))  . . . [M(δ) ∧ O(k, δ) ∧ LEAVE(k)(y)(c) ∧ k  j ∧ j  i ∧ i < i ∧ δ ◦ n ∧ i ◦ n] c. PAST(SYN(IMP(TADV(S0 ))))  . . . [M(γ ) ∧ (δ) ∧ δ = s(γ ) ∧ LEAVE(k)(y)(c) ∧ O(k, γ ) ∧ k  j ∧ j  i ∧ i < i ∧ δ ◦ n ∧ i ◦ n]

(45)

a. Chris has left York this morning. b. PRES(SYN(IMP(TADV(S0 ))))  . . . [M(δ) ∧ O(k, δ) ∧ LEAVE(k)(y)(c) ∧ k ≺ j ∧ j  i ∧ δ ◦ n ∧ i ◦ n] c. ∗ PRES(SYN(IMP(TADV(S0 ))))  . . . [M(γ ) ∧ (δ) ∧ δ = s(γ ) ∧ LEAVE(k)(y)(c) ∧ O(k, γ ) ∧ k ≺ j ∧ j  i ∧ δ ◦ n ∧ i ◦ n]

The clause δ = s(γ ) in (44c) and (45c) says that an unnamed anchoring unit δ ∈  is the successor of γ (= this morning). Sentence (44a), when uttered in the morning, is grammatical and that holds also for a situation in which (44a) is uttered in the afternoon. However, in the latter case, only representation (44c) is allowed, not (45c). In the grammatical (44b) and (45b), there is no intervening γ : the deictically anchored δ intersects with k (and includes k) and the clause k ≺ j warrants full actualization in j which in both cases is connected to i. As said, this cannot be the whole story: it should be made clear why other languages allow the Present Perfect in sentences with the translational equivalent of yesterday or the unnamed δ in (45c). Verkuyl (2008:83–8) made a comparison between the Present tense in Dutch and English and concluded that in developing a tense system based on binary oppositions, a language is free to make choices when it comes to a division of labour between the tense forms. Within this degree of freedom, for example, binary oppositions are allowed to waver between equipollent and privative contrasts. 11 I restrict myself here to just looking at the lowest level of insertion, because the comparison

holds as well for the two higher levels.

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English has opted for developing the Progressive Form as a very dominant form taking away some of the duties performed by the Simple Present or Simple Past in other languages. As to the latter, this might mean for past sentences that the IMP-form k  j has become less important as a form underinforming about full actualization of k. English speakers have Mary was walking directly available in cases where Dutch speakers use Mary wandelde ‘lit: Mary walked’. Consequently, Dutch hearers need to wait for more information about full actualization of k. When English speakers use the past form walked, they can be expected to having ignored the Progressive option in favour of talking about a fully actualized walk. In this sense, anteriority is made a more prominent feature for PAST than it has in Dutch. Another choice in which languages may vary, concerns the sense of falling within the time-sphere of the present in the use of the Present Perfect. A wellknown term used in the literature is the term current relevance but as this term is too often interpreted as close to the notion of result, I will not use it. The English Perfect is often used when Dutch uses the Simple Present as in Ron and Mary have known each other for years and Ron en Mary kennen elkaar al jaren ‘lit: R. and M. know each other already years’. Result is not the proper term in this connection. Rather one has to do with the fact that in the use of the Present Perfect the point of perspective at n in English is only backwards whereas Dutch maintains the backward, going-on and forward perspective. This also holds for the use of the Simple Present heeft ‘has’ in a Present Perfect construction Chris heeft York achter zich gelaten ‘Chris has left York behind’ which in Dutch may project forward into i ♦ . In particular, these sort of differences can be expected to have different outcomes per language with regard to modification. There are more differences concerning the division of labour between tense forms in the present and past domains. The present domain i in Figure 6.6 shows that English has delegated this division in i to two auxiliaries and a copula rather than to the main verb itself.12 Except for verbs not requiring the Progressive Form, the Simple Present form of an English main verb is generally used for expressing neutrality or habituality, or perhaps more precisely: for expressing that the tense form of a main verb is used at a type level rather than at the token level. This does not seem to hold for the Simple Present forms of auxiliaries such as has and is. They have the possibility of occurring in the Progressive: is having and is being in the case of a 3rd person singular but this is only possible when they occur as a main verb. This means that a 12 The same applies to the past tense forms had, was and would divided over the past domain i  .

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Figure 6.6 Tense carriers in the present tense domain i in English

speaker opting for has in has left York uses the auxiliary as signaling a choice for full actualization, while opting for is in is leaving York signals the absence of full actualization of k. For has as an auxiliary and is as a copula a token interpretation is quite natural in view of the factual nature of the Present Perfect in English discussed in Chapter 3 and of the going-on actualization of the Progressive. In Dutch, the Simple Present form of the main verb can easily handle what is expressed in English by the Progressive Form and by the POST operator introducing will both at the type and at the token level.13 As shown in Sections 3.3.3 and 3.3.4, the Dutch hebben ‘have’ may cover the whole present domain i by locating k in i ♦ . This makes a crucial difference with English with regard to the present domain j of k. (46)

a. Over een half uur hebben we de tien kilometerpaal bereikt. In half an hour have we the ten kilometer mark reached ‘In half an hour we will have reached the ten kilometer mark.’ b. Over een half uur bereiken we de tien kilometerpaal. In half an hour reach we the ten kilometer mark ‘In half an hour we will reach the ten kilometer mark.’

(47)

a. Over tien minuten rijden we al twee uur. In ten minutes drive we already two hours ‘In ten minutes we will have been driving for two hours.’ b. Over tien minuten hebben we al twee uur gereden. In ten minutes have we already two hours driven ‘In ten minutes we will have already driven for two hours in a row.’

In Dutch the a- and b-sentences in (46) en (47) are (extensionally) exchangeable. This is not the case in English. From this it follows that the auxiliary has 13 Interestingly, older generations in the Netherlands are still familiar with the use of zullen ‘will’

learned at school as a temporal auxiliary but nowadays experienced as rather genteel in spoken language. Moreover, as pointed out in Broekhuis and Verkuyl (2014) when it is used, it can be shown to be modal, as also argued in Chapter 8.

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in Chris has left is to be interpreted with an eye on i a because has shares the property of the English Simple Present of main verbs of not looking forward, except for a planned k. Looking only backward from n is enforced in English, of course, by the sense of full actualization expressed by PERF. For the Present Perfect this means that j is to be synchronous to i a so that n is the point at which it is informative to say that k has been fully actualized in j. As a fact or in the report mode. As observed earlier, English has strengthened the anteriority relation expressed by PAST due to the fact that the Progressive Form takes over a part of the going-on interpretation which in other languages can be expressed by the Simple Past. If the task of the English Present Perfect is to report about a fact that holds at n, the clause δ = s(γ ) in (45b) can be seen as prohibitive for that due to the absence of the clause γ ◦ n, as explained in the analysis of (43). This shows immediately in (48) in which the adverbial at nine o’clock has been added to (44a) and (45a) which are both grammatical when said in the morning. (48)

a. Chris left York at nine o’clock this morning. b. ∗ Chris has left York at nine o’clock this morning.

The Simple Past sentence (44a) allows for a more specific adverbial, as shown in (48a). This is not possible for (45a) as shown in (48b). This can be explained by assuming that at nine o’clock has brought in a clause δ = s(γ ) introducing an anteriority relation. The proper interpretation of a Present Perfect sentence requires the absence of the clause δ = s(γ ). Inserting one leads to trouble. More in general, one may see this in terms of predominance of PRES + PERF over modifying adverbials: the Present Perfect as a tense form may obtain its factual nature by including the adverbial in the factuality as well. It expresses factuality with regard to the full domain i a rather than to an intersected part of it. In this way, the difference between Dutch and English with respect to the choice for a Present Perfect can be seen as difference between two ways of speaking about eventualities. In Dutch, both the Present Perfect and the Simple Past can be used as alternative ways to phrase a story also due to the broad use of the Dutch Simple tenses which has led to a minimal role for the Dutch counterpart of the Progressive Form. The structural solution to the English Present Perfect puzzle presented here requires no appeal to aspectuality: the nature of k in the formulas is indifferent to the factors opposing (42) to (43). This makes it unnecessary to characterize the so-called universal perfect in sentences like (49) as a separate form of the Present Perfect dependent on durativity.

6.4 Syntax and Semantics of Deictic Modification (49)

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a. The meaning of the perfect has been debated for more than 200 years. (Mittwoch 2008) b. I’ve known Max since 1960. (McCawley1971) c. I have always known Max as kind. d. He has lived in London all his life. e. We’ve been sitting in a traffic jam for more than an hour.

That they seemingly form a group is simply due to the distinction between interpreting a durative predicate and interpreting a terminative one. This also occurs in past tense sentences. When Michaelis (1994) assumes that in sentences like (49e) a temporally modified durative predication expresses that a state obtains throughout the interval i a plus n as its upper bound, then the answer is that He lived in London all his life also expresses a state throughout an interval with as an upper bound, the end of his life. There is no reason for calling this a universal Simple Past nor is there any reason for calling the Simple Present universal in Max is employed by IBM since 1960. Given the fact that the sentences in (49) are exactly the ones where Dutch uses the Simple Present, their analysis is captured by the present analysis of the Present Perfect in English. The universal use of the Present Perfect follows from the analysis proposed in Section 3.3.3 in which the Present Perfect is seen as ‘reporting so far’, ‘to my knowledge so far’ with respect to the domain i a . 6.4.4 Comparing Solutions The solution of the Present Perfect puzzle proposed in Klein (1992) introduced the notion position-definite discussed in Chapter 2 on page 33. For Klein, a present tense form has is [+p-definite] because it specifies a definite position for the eventuality on the time axis with respect to the speaker as opposed to a past tense form which is [–p-definite]. On the other hand, yesterday is also p-definite because it is connected to the speaker but it modifies Klein’s topic time, which in this case contains the deictic centre n. For Klein, the key for the solution of the problem is that the covert modifier of the eventuality ‘Chris leave York’ in (43a) ∗ Chris has left York yesterday is different from yesterday. It is p-definite but independent of yesterday. At that point, Klein invokes a pragmatic principle, the P-definiteness constraint, which says that in an utterance the expression of topic time (here modified by yesterday) and the expression of eventuality time – modified by a covert modifier and made p-definite by the use of has – cannot go together because the two are not dependent on each other. This constraint rules out (43a). Klein’s approach is dependent on a ternary approach to tense, which makes it very difficult to see where his solution shares elements with the one proposed

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in the present section. I think that the binary approach is more suitable for prying out the deeply hidden factor which can be held responsible for the ungrammaticality of (43a) ∗ Chris has left York yesterday and not to forget ∗ Chris has walked yesterday and ∗ Chris has left York this morning when said in the afternoon. This factor is hidden behind several others, including the predominant role of the Progressive Form and, with it, the increasing use of the Simple Past for expressing anteriority leading to a decreasing role of k  j in expressing underinformation. Also included is the specialization of the English Present Perfect into a backward-looking tense form expressing factuality by expressing what counts at n for i a as a whole, among other factors, as discussed. From these factors, it follows that it is not allowed to express anteriority between the two temporal units involved in a deictic adverbial by the clause δ = s(γ ) for Type I Nouns or γ < δ for Type II Nouns. As far as I can see, this solution has a much larger explanatory power than Klein’s ternary solution, certainly with respect to sentences like (44a) and (45a). Moreover, it is in full harmony with the idea of compositionality and accounted for at different levels of tense structure. 6.5

Syntax and Semantics of Durational Adverbials

6.5.0 Introduction There is a long-standing sort of litmus test for distinguishing between perfective and imperfective aspect: the in/for-test. It separates the a-sentences in (50) and (51) from the b-sentences. (50)

a. Mary waited for an hour. b. ∗ Mary waited in an hour.

(51)

a. #John discovered that treasure for an hour. b. John discovered that treasure in an hour.

The test is so well-known that (50) and (51) should suffice for serving as the point of departure for a formal account of this distinction.14 That speakers react to the in/for-test in a predictable way, points in the direction of a cognitive basis for it. In my own experience, when “innocent” native speakers of Dutch are confronted with the in/for-test (for the first time in their life), they clearly reject 14 It appears in practically all works on aspect in Slavic (Filip (2012), Gvozdanovic (2012), Lind-

stedt (1985), Dimitrova-Vulchanova (1996)) and non-Slavic languages (Finnish: Heinämäki (1984), Hungarian: Kiefer (2009), Greek: Anagnostopoulou (2003), Giannakidou (2003), Chinese: Tai (1984), Basciano (2015), French: Vet (1980), De Swart (2012)), among many others; Verkuyl (1972a) gives some German examples from Herbig (1896) and Leskien (1919).

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the one-event interpretation for Dutch #-cases and agree on the possibility of a queer sort of repetition or a forced stretching interpretation.15 Verkuyl (2008:96–104) argues that two measure functions are involved: an additive function and a non-additive μ-function. The best way to understand the difference is to get back to the definition of the functions id and su in Section 5.1.3 and to have a look on page 139 at the definition (9) of cumulativity assigned to verbs lexically defined by id and su, repeated here as (52a). (52)

a. f A (B ∪ C) = f A (B) ∪ f A (C) b. μ(B ∪ C) + μ(B ∩ C) = μ(B) + μ(C)

That definition reflects the possibility for an additive μ to measure the length of Mary’s waiting in (50a) on the basis of (52b). As sketched in Chapter 5, the cumulativity expressed by a su-verb can be overruled by the discretizing function d either at the lexical level of at the phrasal level. It follows that additive μ then can no longer be applied. This makes the present analysis different from proposals in Dowty (1979) and Krifka (1989:98ff.;1998:214ff.), among others. Kamp and Reyle (1993) holds that the two adverbials under analysis express the same measure function μ where the μ of for an hour is unbounded and the μ of in an hour is bounded. Like Krifka (1989), they appeal to pragmatic considerations, rejected in Verkuyl (2008:99f.). The present analysis describes the meaning of for three hours in terms of the paraphrase ‘the number of temporal units hour is three’ on the basis of a one-dimensional additive duration measurement along the line of (52). In Section 6.5.1, the two measure functions at a level below S0 will be introduced as was done in Verkuyl (2019a).16 6.5.1 Measuring below S0 A duration-measuring adverbial is welcome in sentences like (53a). Verkuyl (2019a) proposed the measure function μ attributed to the for-adverbial in (53b) providing the length of the interval Ran(su) construed by the application of the function f A . 15 One proviso should be made at this point: sentences like The soup cooled in ten minutes

and The soup cooled for ten minutes are both well-formed. This issue will be taken up in Section 6.5.4. 16 Section 6.5.1 gives a brief capitulation of this proposal before fitting it into the format of modification proposed earlier in the present chapter. This has the advantage of analyzing the key notions involved in the measurement invoked by for- and in-adverbials in terms of the basic empirical facts playing a role in the for/in-test. The next step in Section 6.5.2 is then to account for their introduction at higher levels of tense structure.

198 (53)

Binary Tense Structure and Adverbial Modification a. Mary walked for three hours. b. for three hours  λPλxλα[P(α)(x) ∧ μhour (Ran( f A )) = 3] c. walk for three hours  . . . λxλα[WALK(α)(x) ∧ α = Ran(su) ∧ μhour (Ran(su)) = 3]

The for-adverbial in (53b) is of type e, i, t, e, i, t which means that it operates on the VP. It introduces the measure function μ which excludes the output of d as a possible input. The formula in (53c) shows how the adverbial has taken the VP in order to form the VP waiting for the external argument. The in-adverbial in (54a) is of the same type and introduces a measure function ν in (54b) requiring an inverse mapping from N to R+ . (54)

a. Ron discovered that treasure in three hours. b. in three hours  λPλxλα[P(α)(x) ∧ νhour (d -1 (α)) ≤ 3] c. discover that treasure in three hours  . . . λxλα[DISCOVER(α)(tr)(x) ∧ α = d(Ran(su)) ∧ |α| ≤ |tr| = 1 ∧ νhour (d -1 (α)) ≤ 3]

The clause α = d(Ran(su)) in (54c) is part of the lexical definition of the verb discover and provides the domain for this mapping, α being a subset of N. As explained in Chapter 5, d(Ran(su)) is the output of a composite function d ◦ su where Ran(su) being a subset of the co-domain of the function su is the domain of the function d. Mapping inversely from d(Ran(su)) to Ran(su) yields a proper subset of R+ . In this way, having obtained a number m in N by applying d to the output of su, it is a natural thing to be able to compute the distance between 0 and m in the “underlying” real number system R+ (i.e. the domain and co-domain of su) in terms of some measuring function. In order to get back to R+ for measurement of a three-hour interval, the function ν needs the range of d -1 as its domain. This requirement is made concrete by letting νhour apply to the range of d -1 , which is the inverse of the function d. That is, d -1 (d(Ran(su))) = Ran(su), that is, R+ restricted to the length of three hours modulo the leniency generally allowed by speakers and hearers with regard to rounding off, say, 58 minutes and 14 seconds to 1 hour. The measure function ν tells how much it cost in real time to actualize k as a discrete unit. The result of applying in three hours to discover that treasure results in a measurement of the output of d -1 , which means loss of information because d -1 is not a function but a relation. Spelled out for d as defined in Chapter 5 on page 145, the inverse d -1 applied to 1 yields the interval a1 as a unit not sensitive to (52b), making the measurement by ν different from that by μ. The next step is to account for the asterisk in (55a) and the #-sign in (56a).

6.5 Syntax and Semantics of Durational Adverbials (55)

a. ∗ Mary walked in three hours. b. λxλα[WALK(α)(x) ∧ α = Ran(su) ∧ νhour (d -1 (α)) = 3]

(56)

a. #John discovered that treasure for three hours. b. λxλα[DISCOVER(α)(tr)(x) ∧ α = d(Ran(su)) ∧ |α| ≤ |tr| = 1 ∧ μhour (α) = 3]

199

In (55b), there is a simple mismatch between the underlined parts of the representation: the function ν cannot see d and d −1 cannot take an α in R+ . The story in (56b) is different. Here the clause α = d(Ran(su)) makes α an index in N, whereas μ requires α = Ran( f A ) as an index in R+ , according to (53b). This incompatibility blocks the one-event interpretation, because there is no way to get from N to R+ , as in the case of an in-adverbial. The characteristic feature of the #-reinterpretation is a “next best” interpretation involving a sometimes mechanical sort of repetition, as in #She broke her glass for hours, or an unnatural sort of stretching, as in #She emptied her cup for five minutes. The forced repetition can then be accounted for by assuming that μhour “decides” to opt for staying in the unbounded N thus obtaining an interpretation with k = {1,2, . . .} analogous to the interpretation of John knocked on the door for some minutes. Which satisfies the requirement expressed by a for-adverbial at a higher type level. 6.5.2 Computing the Length of Indices In (53), the for-adverbial is positioned as a modifier below the level of S0 with the same type-logical characterization as in the morning in (22b) when it occurs in sentences like To do your exercises in the morning makes a lot of sense. Given Sections 6.2 and 6.4, a generalization is now possible, also in view of the need to account for the (re-)interpretation in sentences like (57a) with for an hour. (57)

a. (#)For more than two hours they sung the Marseillaise. b. They sung the Marseillaise for days here at the Place de la Concorde. c. For many years, the family arrived in the hotel in the first week of October.

There is no need to place the #-sign (57b) in the regular frequency interpretation when it occurs with for days. The more so when the adverbial pertains to a much longer period in the habituality interpretation of (57c). It is only the one discrete token event interpretation that is excluded by a duration-measuring adverbial. Note that the pattern sketched in (53a) and (57) is fully covered by the three figures at the beginning of Chapter 5 taken together in Figure 6.2 on page 171 in Section 6.1. The measurement for three hours involves the upper

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two situations in that figure. Sentence (53a) Mary walked for three hours may pertain to the situation sketched in Figure 6.2a when she walked without any interruption. Or to Figure 6.2b, where the sentence may be comparable with the one in which a fitness gadget reports about daily walking hours in terms of 11.378 steps in total allowing for interruptions such as breakfast, lunch and dinner. Or with the Fitbit measuring sleep. In sentences like Ron stuck to his position for hours, the default interpretation is the discrete token one. Sentences like (58) require summation both for the evenings or meetings involved and for the durative predication. (58)

a. Ron bleef avondenlang bij zijn standpunt. ‘Ron maintained his position for evenings.’ b. Zes vergaderingen lang bleef Ron bij zijn standpunt. ‘Ron maintained his position for six meetings.’

The sentences show a reverse picture of the situation in which for an hour with a continuous δ relates to a terminative k (= d(Ran(su))) expressing discretization, as in the sentences (57). In (58), a durative predication k (= Ran(su)) relates to a discretely organized index δ. In Figure 6.2b on page 171, the configuration led us to distinguish between Ac = {a1 , a2 , . . .} and Ac = {a1 , a2 , . . .} such that Ac ∪ Ac = R+ . The set Ac is the set of intervals separating the intervals belonging to Ac . This means that if we think of for-measurement in terms of summation, we need to operate on Ac . This can be done quite easily by seeing Ac as an indexed family of sets a, as written in (59). (59) Ac := {ai }i∈I

Because Ac is a set of sets, one may see the sum total of all its members in terms of the summation already demonstrated in (15) on page 144 and here generalized to all indices involved in temporal modification: α, β, γ , δ, i, j, k, etc. In order to increase the readability of the formal representations of the relation between indices that modify and indices that are modified, I will simplify the notation. Thus instead of writing . . . ∃H∀δ[|H| = 3 ∧ H(δ) → . . .], I will generally write . . . ∃H3 ∀δ[H(δ) → . . .]. This makes it more natural to see that in the type-logical representation, a noun like morning or week or hour, etc. denotes a family of indices δ, as illustrated by three hours in (60a). (60)

a. H3 := {δi }i∈I , with I = {1, 2, 3} 3 δi = δ1 ∪ δ2 ∪ δ3 b. δ := i=1

In (60b), δ is defined as the set resulting from the union of all the three subsets of H3 : δ1 , δ2 and δ3 . The boldface notation is just for convenience because δ is

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of the same type as δ: type i. It will only be used in contexts in which taking the

1 union is at issue. Definition (60b) allows for a singleton: when δ = i=1 δi = δ1 or when Ac in (59) has just one singleton member a1 . Note also that (60b) meets the requirement of an additive measurement: μ(δ1 ∪ δ2 ) + μ(δ1 ∩ δ2 ) = μ(δ1 ) + μ(δ2 ). This holds for any δi , δ j whether δi is adjacent to δ j or not. Taking the union is important because it allows for the fact that for three hours may pertain to the first three units located on the continuous line at the top of Figure 6.2 on page 171 but also to the summation applying to three discretely organized hours in the Type II patterns of that figure. For modifiers with a Type II head noun, summation will be necessary in the case of Type IIa and default in the case of Type IIb. Intervals in a summation do not need to have the same length: all situations in Figure 6.2 are covered. Type-logically the indices k, j, i, i  and n are all intervals of type i and so they are elements of the set  introduced in Chapter 5, as indicated in Table 5.1 on page 157. Using the variables over indices of that table one can say that each δi in (60b) may be seen as an open interval ( 1 , 2 ) marked by the points 1 and 2 with 1 < 2 where < is a linear ordering on R+ . (61)

a. ( 1 , 2 ) < ( 3 , 4 ) := 2 ≤ 3 b. ( 1 , 2 ) ∪ ( 3 , 4 ) ∪ ( 5 , 6 ) = ( 1 , 6 ) c. O(( 1 , 2 ), ( 3 , 4 )) := 3 ≤ 1 and 2 ≤ 4

The notation in (61) makes it possible to be more specific about the internal structure of indices by writing the intersection relation O(α, δ) as (61c). On top of that, we need a more general notation for comparing indices which have a different role to play, for example, the eventuality index k and the modifying index δ. For any two indices α and β one can say that the most right-hand point of the interval α is equal or anterior to the leftmost point of β. (62)

a. α < β := r (α) ≤ (β) b. ∀α((α) ≤ r (α))

These stipulations about the internal structure of indices are necessary because this structure is measured by μ. Apart from that, they obey the conditions under which the isomorphic mapping from index structure into temporal structure triggered by PRES or PAST may take place, as will be made clear in Chapter 8. Getting back to the measurement μα itself, it is convenient to define the length of the sum of intervals in terms of the largest number m of the index set I on the basis of knowing that it is the point r (am ). The length of δ in (60) in terms of hours can be measured by applying the function μh resulting in (63), where m = r (am ). (63)

μh (δ) = m − 0 = m

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Applied to (60c), this results in m = 3. If Mary walked for three hours, the summation of the eventuality index k of sentence (53a) is computed by μ, its output yielding a certain absolute value m in a set of measuring values. (64)

μδ (α) = m iff there is a set  of units δ such that the measured length of α equals the length m of δ.

Applying the notation in (64) to (53b) would give the clause μh (Ran(su)) = 3 for saying Mary walked for three hours. The modifier contributes the measuring unit ‘hour’ and the number of them as the absolute value and says that the length of taking three units equals the length of (the summation of) the eventuality index k(= Ran(su)). 6.5.3 Computing Length at Higher Levels The insertion of the for-adverbial below S0 faces the same problem as the insertion of the adverbial in the morning in Section 6.2.5: the exclusion of the external argument. Therefore it is necessary to account for the insertion at higher levels. By inserting for three hours in (53a) at the level above S0 , one obtains the derivation in (65). The durational adverbial is of the same type as the adverbials treated in previous sections: i, t, i, t. (65)

a. Mary walked for three hours. (= (53a)) b. S0  λα[WALK(α)(m) ∧ α = Ran(su)] c. FOR - THREE - HOURS  λϕλα∃H∀δ[H(δ) → [ϕ[α] ∧ μδ (α) = 3]] d. IMP(FOR - THREE - HOURS(S0 ))  . . . = λβ∃H∀δ[H(δ) → ∃k[WALK(k)(m) ∧ k = Ran(su) ∧ μδ (k) = 3 ∧ k  β]] e. SYN(IMP(FOR - THREE - HOURS(S0 )))  . . . = λα∃j∃H∀δ[H(δ) → ∃k[WALK(k)(m) ∧ k = Ran(su) ∧ μδ (k) = 3 ∧ k  j ∧ j  α]] f. PAST(SYN(IMP(FOR - THREE - HOURS(S0 ))))  . . . = ∃i ∃j∃H∀δ[H(δ) → ∃k[WALK(k)(m) ∧ k = Ran(su) ∧ μδ (k) = 3 ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

Taking into account the abbreviations made in (64), the last line of the derivation says that there is a set H of three hours δ such that for each element δ of H, there is a j and its k such that the length of this union equals the length 3 of the union δ of the indices δ. In terms of Figure 6.3, this means that intervals ai constituting k are grouped together into one interval the length of which is three hours. In other words, sentence (65a) may be about two walks which taken together have the duration of three hours. In the case of one walk, the cardinality of H is just 1.

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The analysis of for-modification in terms of (65) makes it possible to account for the attenuation of the blocking force associated with the #-sign in (56a) and (57a), as illustrated in (66), the shortened version of (9) in the appendix on page 297. (66)

a. For three years, Ron saw Mary in the morning. b. S0  λα  [SEE(α  )(m)(r)] c. IN - THE - MORNING  λϕλα∃δ[M(δ) ∧ ϕ[α] ∧ O(α, δ)] d. IN - THE - MORNING(S0 )  . . . = λα∃δ[M(δ) ∧ SEE(α)(m)(r) ∧ O(α, δ)] e. IMP(IN - THE - MORNING(S0 ))  . . . = λβ∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  β] f. SYN(IMP(IN - THE - MORNING(S0 )))  . . . = λα∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  α] g. FOR - THREE - YEARS  λϕλα∃Y∀δ  [Y(δ  ) → [ϕ[α] ∧ μδ  (α) = 3]] h. FOR - THREE - YEARS (SYN(IMP(IN - THE - MORNING(S0 ))))  . . . = λα∃Y∀δ  [Y(δ  ) → ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  α ∧ μδ  (α) = 3]] i. PAST(FOR - THREE - YEARS(SYN(IMP(IN - THE - MORNING(S0)))))  . . . = ∃i ∃Y∀δ  [Y(δ  ) → ∃j∃k∃δ[M(δ) ∧ SEE(k)(m)(r) ∧ O(k, δ) ∧ k  j ∧ j  i ∧ μδ  (i ) = 3 ∧ i < i ∧ i ◦ n]]

This says that there is a set Y of three years γ for each of which there is a set M of mornings δ such that each δ harbours a j and its k and the length of the union of the indices δ  is the measured length of i . It should be noted here that the measured length of i  is not necessarily the total length of i  . Turning now to the unwellformed sentence (55a), here given as (67a), we see that the problem of a stretched or forced repetition interpretation also occurs at the level above S0 . (67)

a. #Ron discovered that treasure for three hours. b. ∃i ∃H∀δ[H(δ) → ∃j∃k[DISCOVER(k)(tr)(x) ∧ k = d(Ran(su)) ∧ |k| ≤ |tr| = 1 ∧ μδ (k) = 3 ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

The eventuality index k is not the proper input for measurement because the μ-function requires R+ as its domain, whereas k is a singleton in N. As shown in (54), measuring can be done by the converse relation d −1 which maps back the information carried by k = d(Ran(su)) to a number system where measurement of length is possible (i.e. to R+ ). In other words, if α = d(Ran(su)), then d −1 (α) = Ran(su). Only after the application of d −1 may one measure in R+ . The resulting value of the measurement is finite and must be given as a whole. This is because d −1 is not a function. Applied to (68a) this yields the derivation in (68).

204 (68)

Binary Tense Structure and Adverbial Modification a. John discovered that treasure in three hours. b. S0  λα∃tr[DISCOVER(α)(tr)(j) ∧ |α| ≤ |tr| = 1 ∧ α = d(Ran(su))] c. IN - THREE - HOURS  λϕλα∃H∀δ[H(δ) → [ϕ[α] ∧ μδ (d −1 (α)) = 3]] d. IMP(IN - THREE - HOURS(S0 ))  . . . = λβ∃H∀δ[H(δ) → ∃k[DISCOVER(k)(tr)(j) ∧ |k| ≤ |tr| = 1 ∧ k = d(Ran(su)) ∧ μδ (d −1 (k)) = 3]] e. SYN(IMP(IN - THREE - HOURS(S0 )))  . . . = λα∃H∀δ[H(δ) → ∃j∃k[DISCOVER(k)(tr)(j) ∧ |k| ≤ |tr| = 1 ∧ k = d(Ran(su)) ∧ μδ (d −1 (k)) = 3 ∧ k  j ∧ j  α] f. PAST(SYN(IMP(IN - THREE - HOURS(S0 ))))  . . . = ∃i ∃H∀δ[H(δ) → ∃j∃k[DISCOVER(k)(tr)(j) ∧ |k| ≤ |tr| = 1 ∧ k = d(Ran(su)) ∧ μδ (d −1 (k)) = 3 ∧ i < i ∧ i ◦ n]]

The last line of the derivation says that the length of the input Ran(su) to the function d equals the length of three hours. Recall that it is not necessary for the three hours to be connected in real time: the adverbial gives the sum total. Many scholars use the in-test as a way to make a distinction between Accomplishments and Achievements, as for instance Smith (1991:71) in (69). (69)

a. We built a sandcastle in an hour. (Acc.) b. He left in an hour. (Ach.)

I do not see any difference between the paraphrases ‘It took an hour for them to build a sandcastle’ and ‘It took an hour for him to leave’. In both cases, the preparations for getting a bounded eventuality are exactly the same. In building a sandcastle one may first spend time in order to find a sand scoop or strainer and to determine the right place. In a similar way, the verb leave includes considerations about packing the stuff that you take along, deciding on the clothes to wear, saying good bye, etc. Note also that in The six guests left the hotel in an hour the guests may have left all together at the same k or at different k’s, as discussed in Chapter 5. In all cases, the length of k1 ∪ . . . ∪ ki ∪ . . . ∪ kn with 1 ≤ i ≤ n, is equal to the length of an hour. Finally, the ungrammaticality of (55a) repeated here as (70a) can also be accounted for in a more general way. (70)

a. ∗ Mary walked in three hours. b. PAST(SYN(FOR - THREE - HOURS(IMP(S0 ))))  . . . = ∃i ∃j∃H∀δ[H(δ) → ∃k[WALK(k)(m) ∧ k = Ran(su) ∧ μδ (d −1 (k)) = 3 ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]

It is impossible for d −1 to find the function of which it is presumed to be the inverse.

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6.5.4 Further Escapes from the in/for-Test Dowty (1979) showed that the in/for-test fails in sentences like (71): the predications in (71a,b) should reject one of the adverbials in (71c) but they accept both. (71)

a. The spaghetti bowl became cool. b. The spaghetti bowl cooled. c. The spaghetti bowl became cool/cooled in ten minutes/for ten minutes.

The literature on verbs like fatten, cool, darken, melt, widen, etc., and on adjectives like cool, dark, dry, etc., is huge: Seuren (1973;1978), Declerck (1979), Abusch (1985), Tenny (1987), Bertinetto and Squartini (1995), Kennedy and McNally (1999), Rothstein (2004), Kennedy and Levin (2008), Husband (2012), Kennedy (2012), among others. The present analysis offers a binary alternative.17 In introductory books on formal semantics, the adjective cool is generally introduced as belonging to type e, t, just like nouns and intransitive verbs: all three lexical categories are supposed to denote sets. However, cool in (71a) is a predicative adjective expressing a relation to the eventuality index of the verb with which it occurs, in this case become. A proper variable for a predicative adjective is the variable X of type e, i, t. In (72a), the verb become informally expresses a three-place relation between the external argument s, the eventuality index k and the predicative adjective X as expressed in (71a), where X is replaced by the formula introduced in (72b). (72)

a. BECOME(αi )(X e,i,t )(se ) ∧ . . . b. cool  λxλβ[COOL(β)(x) ∧ β = Ran(id)]

The problem to be solved is that the verb become allows the su-clause α = Ran(su) as well as the d-clause α = d(Ran(su)) on the position of the dots in (72a) and that one does not know a priori which of the two should be chosen, there being no way for allowing the two clauses together. It is clear that the default use of become expresses discretization: there is a transitional point to a function expressing a state. Assuming that id is the function accounting for stativity, one may assume a transition from su to id at a point where su is made discrete because it is bounded. This is the second problem: how to connect the eventuality index α of become in (72a) to the eventuality index β in (72b). 17 Verbs like mow, push, paint, rub, beat, caress, etc. were brought forward by Tenny (1987;1994)

as problematic for the Plus-principle, that is, the thesis that non-stative verbs with an internal [+SQA]-argument always result in a terminative VP. For an extensive answer, see Verkuyl (1993:329–49). The present section does not repeat that answer because it does not belong in a section on adverbial modification.

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On page 138 in Chapter 5, both id and su were defined as y = ax + b with a = 1, there being no reason for having a different value for a as a constant. Therefore the graphs of the two functions show a parallelism illustrated in Figure 6.7 by the dashed lines starting in 0 and b. The constant a = 1-value for su

Figure 6.7 Non-stativity changing into stativity

provides the sense of continuity in a one-dimensional way. The copula become expresses, however, not only non-stativity but also the sense of discretization that it expresses by default in spite of allowing (71c).18 It is therefore arguable that become rather than running parallel to id, as in the cases discussed so far, is defined by the function su with a smaller slope than id, so that inevitably the two functions intersect. By having 0 < a < 1, the slope coefficient in y = ax + b is smaller than 1 so that the intersection of the su and id should take place at any point x  , y  , where x  = y  .19 The situation in Figure 6.7 is captured by (73). (73)

su(x) = ax + b, with 0 < a ≤ 1

The problem is now how to get the information in (73) into the lexical entry for become while escaping from “anything goes”. The first assumption is that become is a discretizing verb requiring α = d(Ran(su)) and that it also requires a second index β. Verbs requiring a second index may then be seen as requiring the possibility for intersection between α and β. At the point where Ran(su) ∩ Ran(id)  = ∅ holds (i.e. at the 18 Definitely not telicity or terminativity because Patients become ill in this hospital is durative. In

that sense become behaves like die or discover, but with the underspecification under discussion here. 19 The pair x  , y   in Figure 6.7 can be obtained with x  = 2 in su(x) = ax + b, with the (arbitrary chosen) values a = 0.75 and b = 0.5. The more general version of (73) is su(x) = y  −b y x + b, where a stands for the standard form x . x

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207

intersection x  , y  ), the function d, attributed lexically to become, automatically stops because its domain Ran(su) no longer provides images: α has obtained a value in N and its cardinality is and remains 1, because only id is available and d does not operate on id. This means that the information |α| = 1 provides two pieces of information: (a) d has applied and (b) a connection with the cool-index β is made. This is accounted for in (74a). Likewise, (74b) expresses continuation of the application of su in its construction of the eventuality index α. (74)

1. Ran(su α ) ∩ β = ∅ ⇔ |α| = 1 2. Ran(su α ) ∩ β = ∅ ⇔ |α| < 1

(d applied) (d not applied)

The situation obtained in (74a) implies that the lexical entry of become requires the clause α = d(Ran(su)) together with a clause obscuring whether or not α = d(Ran(su)) indeed obtains in sentences like (71). This leads to the lexical entry for become defined as a transitive verb in (75), where P is the variable replaced by the internal argument NP, which is of type e, i, t, i, t. (75)

become  λPλzλα(P(λvλα  [BECOME(α  )(v)(z) ∧ α  = d(Ran(su)) ∧ 0 < |α  | ≤ 1])(α))

This means that become is defined exactly as the verb lift in step 6 on page 161, apart from the extra clause 0 < |α  | ≤ 1. This clause accounts for the uncertainty of whether discretization has taken place in sentences like (71). The next step in the solution of the problem is a technical one: the predicate adjective cool in (72b) is of type e, i, t and that is not the type of the variable P. In Montague grammar it is near standard to interpret an adjective in predicative position as a full NP. Intuitively, this is a quite attractive idea: (71a) can be read as ‘The spaghetti bowl became a cool spaghetti bowl’. This also holds for sentences with the copula be: That dot is blue can be read as ‘That dot is a blue dot’ (or more generally: ‘That dot is a blue entity’). An extensional version of the grammar in Montague (1974c) makes it possible to assume a covert Lift operator ⇑ that allows an adjective of type e, t to be interpreted as belonging to type e, t, t, the type of NP. This operator is of type e, t, e, t, t: it takes something of type e, t to form something of type e, t, t. This happens to be the type of a determiner. In that sense, the drawback of having a covert operator is compensated for by the structural role it has to provide for NP-ness. This also holds for the lift of the predicative adjective cool to an NP, as made visible in (76).20 20 I thank Richard Moot (pers. comm.) whom I taught this type-logical procedure in a Montague

course in the nineties, for reassuring me that this has become a quite normal procedure in current categorial grammar and in the combinatorial logics employed in that framework.

208 (76)

Binary Tense Structure and Adverbial Modification a. ⇑  λY λX λα  ∃x∃β[X (x)(α  ) ∧ Y (x)(β)] b. ⇑ (cool)  . . . λX λα  ∃x∃β[X (x)(α  ) ∧ COOL(β)(x) ∧ β = Ran(id)]

The ⇑-operator is of type e, i, t, e, i, t, i, t and should be seen as tuning the copula and the adjective by giving cool the status of a predicate nominal much in the way of the intermediate -role between the verb lift and its internal argument, as accounted for in Chapter 5. This results in a meaning paraphrasable as ‘a cool something’ or ‘an x with (a certain degree of) coolness at β’. Note that cool expresses a state, also in (76b). At that point, (76) has the proper type for replacing the variable P in (75) and this brings (77) as the final representation. (77)

∃i ∃j∃k∃x∃β[BECOME(k)(x)(s) ∧ k = d(Ran(su)) ∧ 0 < |k| ≤ 1 ∧ COOL(β)(x) ∧ β = Ran(id) ∧ k  j ∧ j ≈ i ∧ i < i ∧ i ◦ n]

If |k| < 1, the function composition d ◦ su is blocked: su may go on unboundedly. If |k| = 1, the application of d does its job as expected on the basis of (72a) by mapping to 1. Adding a for-adverbial, as in (71c), evokes the continuity part of the meaning in (77) because due to |k| < 1 the application of su remains “undisturbed”. Adding an in-adverbial, as in (71c), yields the completion interpretation due to |k| = 1.21 Representation (77) is not intended as an elaborated contribution to work on degree adjectives. Rather it serves as signaling that not too much attention should be paid to the adjective cool of become cool at the cost of become. Moreover, the close relation between be and become as copulas of the same (linguistic) kind ignored in Dowty analysis of become based on Von Wright (1965) has now been restored, as will be confirmed in Section 7.1. There are some options with regard to the verb cool in (71b) The soup cooled. One is to represent (71b) as (77), with an underlying predicate BECOME . As shown in Kennedy and Levin (2008), this is in conflict with the fact that (71a) and (71b) are not interchangeable in all contexts. Another one is to regard - EN as an abstract morpheme creating verbhood. Combined with the adjective cool it yields the verb cool (= COOL+-EN) expressing a become-relation between the external argument denotation and a contextually determined degree of coolness of this denotation, along the lines of Svenonius 21 The argument the soup in (77) is simply represented by s. In some comments on earlier ver-

sions some doubt was raised about the need to represent the second argument of BECOME as COOL(β)(s) rather than as COOL(β). The former representation follows from (72b). The latter is acceptable so long as it expresses that s is the external argument of both become and cool.

6.6 Conclusion

209

and Kennedy (2006) and extended in Kennedy and Levin (2008).22 Translated into the present framework, this leads to the representation in (78). (78)

−EN(k)(COOL(β)(s))(s) ∧ k = d(Ran(su)) ∧ 0 < |k| ≤ 1 ∧ β = Ran(id) ∧ k  j ∧ j ≈ i ∧ i < i ∧ i ◦ n

Extending (71b) with the for-adverbial in (71c) leads to (79). (79)

a. The spaghetti bowl cooled for ten minutes. b. ∃i ∃j∃M10 ∀δ[M(δ) → ∃k∃β[- EN(k)((COOL)(β)(s))(s) ∧ k = d(Ran(su)) ∧ 0 < |k| ≤ 1 ∧ μδ (Ran(su)) = 10 ∧ β = Ran(id) ∧ k  j ∧ j ≈ i ∧ i < i ∧ i ◦ n]]

In this case, the clause 0 < |k| ≤ 1 must be interpreted as 0 < |k| < 1 blocking discretization because the measure function applies to Ran(su), as discussed in Section 6.5.3. The definition of in ten minutes requires the inverse d −1 . (80)

a. The spaghetti bowl cooled in ten minutes. b. ∃i ∃j∃M10 ∀δ[M(δ) → ∃k∃β[- EN(k)((COOL)(β)(s))(s) ∧ k = d(Ran(su)) ∧ 0 < |k| ≤ 1 ∧ νm (d −1 (k)) = 10 ∧ β = Ran(id) ∧ k  j ∧ j ≈ i ∧ i < i ∧ i ◦ n]]

This requires a |k| = 1-interpretation of 0 < |k| ≤ 1 because otherwise d −1 cannot do its job.

6.6

Conclusion

The present chapter aimed at showing how important adverbial modification is for the analysis of aspectual composition and for a better understanding of the role of indices introduced by the tense operators at three different levels of tense structure. It also shows that a binary approach is crucial for understanding the flexibility of interpretation by looking at the introduction of the clause O(α, δ) at different levels and by seeing it as requiring intersection rather than inclusion. In this way, non-deictic modification could be dealt with in accordance with the strict requirements of compositionality. The same holds for the analysis of frequency and habituality in compliance with the token-type distinction. The analysis of deictic modification followed the same line but it also showed that adverbials like last week and yesterday are semantically quite 22 The idea is to assume a measure function in - EN assigning a degree g of coolness to the soup

related to some standard. This idea is compatible with the idea of letting the context decide at which point of coolness between (0,1] the discretizing function d reaches a value at which the mapping can be seen as completed. The value 1 can be seen as representing the contextually determined degree g(s).

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complex because they hide the importance of the anteriority relation that is part of their definition. By identifying this relation in terms of the successor function, the first step could be made towards a structural solution of the Present Perfect puzzle. The second step consisted in indicating the degree of freedom to be attributed to binary oppositions permitting each language to make different choices. In the case of English, this has led to mainly using the Present Perfect as a report mode about i a , which is not the case with its counterparts in other languages. The analysis of adverbial modification made it possible to give a formal account of intervals that play a systematic role as index. Chapter 3 introduced the indices k, j, i, i  , j and n at each of the three levels of tense structure on which binary oppositions are operative, Chapter 5 accounted for the contribution of the eventuality index k as a member of an indexed family of sets by relating it to its arguments, and in the present chapter the analysis of modification showed firstly that modifiers can also be described in terms of indices and secondly that these – being part of the same index family of sets just mentioned – interact with them, all in a strictly compositional way. The chapter also shed light on the nature of the in/for-test and it explains why terminative sentences with a for-adverbial introduced at a higher level may be regarded as well-formed as opposed to those which are forced to be interpreted as pertaining to a token eventuality index k due to a lower position of the adverbial in phrase structure.

7 How to Deal Binarily with ...?

7.0

Introduction

The ellipsis in the title of the present chapter stands for domains of research on tense and aspect in which the compositional formal machinery presented in Chapters 5 and 6 should prove itself. There are three topics that are to be treated in order to make the picture complete. Firstly, the Progressive Form. This construction is typical of English but has obtained a central place in the formal semantic theory of tense and aspect, unjustifiedly in my view. Section 7.1 will give a detailed formal account of the huge difference between the semantics of the Progressive Form and the semantics of the tense operator IMP. It presents a theory of the Progressive Form in which the PROG operator is broken up and the modality inherent to those analyses is eliminated. Secondly, Slavic aspect. Verkuyl (2012) argued that compositionality opens the way for comparing the Slavic aspectual systems with non-Slavic systems. The binary approach formalized in the preceding chapters will be tested in Section 7.2 with respect to a comprehensive theory of Slavic aspect in order to see whether it can bridge the gap between Slavic and non-Slavic aspect. The aim is to show that this can be done and that this counters the need for a distinction between lexical aspect (Aktionsart) and grammatical aspect. Thirdly, the aorist. If the aorist does not fit in a binarily organized tense system, the importance of answering the question of where it should be positioned is self-evident. Section 7.3 accounts formally for the aorist in binary tense systems by making clear how aoristic forms differ from tense forms fitting in the system of the three binary oppositions. Georgian perhaps opens the way for assuming that speaker/hearer-oriented tense systems tend to replace tense systems in which tense is not speaker-oriented. 211

212 7.1

How to Deal Binarily with ...? The Semantics of the Progressive Form

7.1.0 Introduction The Progressive Form in (1a) poses a challenge to the present approach.1 (1)

a. The girl was lifting a table. b. λzλα∃Q[Q ⊆ TABLE ∧ |Q| = 1 ∧ ∀x[Q(x) → [LIFT(α)(x)(z) ∧ α = d(Ran(su)) ∧ |α| ≤ |Q|]]]

The formula in (1b) represents the terminative VP lift a table as treated in Chapter 5. The problem is to account for the fact that the Progressive Form requires continuity and unboundedness and for the fact that the for an hour-test leads to a clear difference between (2a) and (2b). (2)

a. For hours the girl was lifting tables. b. #For hours the girl was lifting a table.

Sentence (2b) is very close to expressing the forced repetition of #For hours the girl lifted a table, in particular when hours is replaced by minutes. At any rate, there is a clear difference between (2b) and For hours the girl was walking along the coast that should be accounted for. Due to Dowty (1977), one generally speaks about the problem as the imperfective paradox. Section 7.1.1 describes proposals for dealing with the Progressive Form by assuming a PROG operator building further on Dowty. Section 7.1.2 offers a binary account in which the operator PROG is broken up into two separate operators, the verb BE and the affix - ING taking the tenseless VP in (1b) as its input. 7.1.1 Attempts to Resolve the Alleged Imperfective Paradox Dowty (1977:46) asked: why is it that (3a) “entails that John was engaged in bringing-a-circle-into-existence activity but does not entail that he brought a circle into existence”? (3)

a. John was drawing a circle. b. John drew a circle. c. PROG(John draw a circle)

The difference between (3a) and (3b) is accounted for by assuming a PROG operator at the front of the logical form (3c) of (3a). Dowty (1977:57f.;1979:148f.) sees PROG as operating on a predication yielding a truth 1 Section 7.1 incorporates parts of a subsection of Verkuyl (2019a) which is chapter 14 of the OUP

Handbook of Event Structure, edited by Robert Truswell, who was so kind as to encourage the use of that material in the present setting. I have added insights not available at the time.

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definition of the form [[PROG(ϕ)]]i,w = 1 iff . . ., where i is an interval and w a possible world. The idea behind this is that (3a) is true in the actual world w if and only if there is an event e = ‘John-draw-a-circle’ not yet fully realized at the point of speech which under normal circumstances will be realized at a later time.2 The introduction of possible worlds in the analysis of (3a) is rather artificial, due to analyzing the Progressive as having an inherent telos. Dowty calls to draw a circle an Accomplishment verb (phrase) and appeals to Vendler for the decisive criteria for obtaining Accomplishments, namely [+Prog] and [+Def]. These criteria were discussed in Section 4.2.3 with the conclusion that Vendler’s continuous tense criterion is linguistically untenable.3 As sketched in Chapter 4, Vendler followed Aristotle by assigning a telos to the predicate draw a circle and then reasoned “downwards” by assuming that the activity leading to completion by reaching the inherent telos is best expressed by the Progressive Form. Thus he was forced to call draw a circle a verb, but he also falsely created what Dowty called a paradox, because essential to the Progressive is that it provides unbounded continuity rather than announcing a culmination point. In Mary was sleeping there is no goal at all. The same holds for Mary was reading a book and John was drawing quite at ease, with a smile on his face.4 Landman (1992) treats BE + ING as an operator on the VP. In his eventsemantic modal approach, the operator PROG is introduced in (4a) and its truth definition is given in (4b). (4)

a. BE + ING(VP)  λxλe.PROG(e, λe .VP(e ) ∧ Ag(e ) = x) b. [[PROG(e, λe [VP(e ) ∧ Ag(e ) = x]]]w = 1 if and only if there is an e which is completed in a world w  (closely resembling w) such that w  allows e to continue and not to be interrupted.

The intensionality of Dowty’s approach is reduced by the introduction of the notion of continuation branch (1992:26f.) which warrants that if one truthfully says (3a) at n, one is speaking at n about a stage e of a larger event e in 2 Bonomi (1997) points out that on Dowty’s approach John is not allowed to change his mind in

(3a) because it requires that there be a world in which John drew a circle. 3 The parentheses around phrase show that Dowty is aware of the fact that the term Accomplish-

ment verb is not correct but he does not draw the conclusion that he thereby suppresses the contribution of the verb to the compositionality involved in building an Accomplishment VP. Unfortunately, Dowty did not discuss John was drawing a line. 4 For a critical analysis of Dowty’s imperfective paradox, with respect to other features such as homogeneity, not discussed here, see Verkuyl (1993:206–9).

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which John actually completes the circle. Rothstein’s analysis of Progressive Achievements (2004:45ff) like (5) is based on Landman’s theory. (5)

Mary is arriving at the station.

Both Landman and Rothstein talk about the Progressive Form predominantly in terms of a continuation leading to a completed event, and in terms of the run time of the event actualized or not. Landman’s analysis of the Progressive Form as an operation on the VP improves on Dowty’s PROG(ϕ)-approach. However, (4) shows clearly that the PROG operator presumes BE + ING as a unit which prevents tense from being applied to BE alone in a natural way. It ignores the different role played by ING . Moreover, it appeals to possible worlds because a continuation branch is always in a possible world w. Positing a SHIFT operator on top of Landman’s PROG as done by Rothstein coerces an Achievement into an Accomplishment. Apart from reservations regarding coercion as an explanatory tool, this specific form is dependent on the problematic criterion [±Prog] separating the two Vendler classes. This makes a sharp distinction between the two aspectual classes impossible, as shown in Chapters 4 and 5, and coercion unnecessary. Chapter 4 also showed the systematic absence of an Accomplishment verb in a Vendlerian Accomplishment VP. Portner (1998) aims at improving on Dowty’s notion of inertia world in terms of a formal machinery based on Kratzer (1977;1981;1991b). Portner makes use of Kratzer’s distinction between two functions: M and L. The function M provides a set of worlds – called the modal base – which determines the interpretation of (3a). To this set belong propositions like John had the tools for drawing, John had begun with drawing, John used a ruler, etc. The function L rebaptized by Portner as O (for ordering source) provides a set of propositions ordered in terms of a scale from worse to better worlds. In the case of (3a), this set would contain propositions like John was not disturbed by a plane falling on his house, John had no mental blackout, John did not run out of ink, etc. Portner replaces Dowty’s inertia world by assuming a set of worlds in which John is not interrupted in reaching his goal. The tools provided by Kratzer are suitable for modal auxiliaries and adverbs but they do not make sense for the analysis of the Progressive Form. All proposals mentioned above suffer from pseudo-modality inherent to using telos as an aspectual notion: they ignore the fact that Dowty took an accusativus effectivus as prototypical for the Progressive Form at the expense of the accusativus affectivus in (1a), which does not require modality at all with respect to the existence of the table, as demonstrated in Section 7.1.2.

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An important improvement on the analyses discussed so far was made by Arche (2014) both for English and in particular for Spanish, which has a rich tense system including an aoristic tense form, the Indefinido also called Pretérito. I read its electronic edition of December 1913 after I had written Events and Temporality in a Binary Approach to Tense and Aspect in early 2014 as the first version of the later OUP chapter Verkuyl (2019a). That version proposed to break up the PROG operator into the copula be and a tenseless operator ING associated with -ing in order to assign tense to the copula only after the application of ING. The idea was and still is to assign to be its own lexical index α and to the main verb its own lexical index β. Arche’s proposal, based on Zagona, Stowell, Klein and Reichenbach, consists of inserting be and -ing at different places in the syntactic structure of the aspect phrase given in Figure 3.2 on page 53. Her informal proposal triggered me into formalizing the operators BE and - ING in the binary framework in order to see whether the two proposals to break up PROG would overlap. The result of this investigation appeared in a following version of the OUP chapter, now with the title Below the Radar of Event Structure: A Binary View on Tense and Aspect. That version was used in González and Verkuyl (2017) for comparing Arche’s main arguments with the binary approach as applied to the Spanish tense system. The conclusion of that joint paper was that the syntactic nodes of Figure 3.2 on page 53 do not suffice for a precise semantic characterization of the English Progressive Form and I still have that conviction. Therefore, Section 7.1.2 presents a formal binary account of the Progressive form paraphrasing and extending the final version of the OUP-chapter. The split of PROG into BE and ING leads to a quite different analysis of the progressive than possible for Arche in following the ternary Zagona-Stowell-Klein-Reichenbach line of thought. 7.1.2 A Binary and Compositional Analysis of the Progressive Form The critical analysis and rejection of Dowty’s proposal in Verkuyl (1993) did not focus on PROG as a sentential operator in (3c) but on the dubious status of [+Prog] as a criterion for obtaining Vendler classes. In the present section, I will argue that it is necessary to split up the PROG operator and that this follows from a strict compositional point of view. It is based on the observation that John was drawing a circle contains two verbs, be and draw – each having its own eventuality index obtained lexically – and that it is the stative copula be and not the non-stative draw that has a past tense form. Morphologically, one can analyze drawing in terms of an operator ING operating on the infinitival form draw so as to form drawing, as in Drawing a circle is quite easy

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with tikzpicture. The semantics of ING prevents the V draw and hence the VP draw a circle from expressing completion as long as the stativity expressed by be holds, sentences with plural or pluralized internal arguments such as (2) included. The relation between the two sentences in (3) can be elucidated with the help of Figure 7.1. In Figure 7.1a, the operator ING is positioned as taking a

Figure 7.1 The VP in (3a) versus the VP in (3b)

VP to form a nominal phrase, here written as NP. This makes it possible for the copula be to combine with the output of the ING-operation. The structure in Figure 7.1b is not suitable as input for BE. The ING-structure in Figure 7.1a also makes it possible to use the underlined NP in sentences like (6). (6)

Drawing a circle is hardly feasible without a pair of compasses.

Here again, the eventuality index β of draw is to be related to the eventuality index α of the main verb, in this case be, but turn out in the case of Drawing a circle turned out to be hardly feasible without a pair of compasses. The derivation for (3a) John was drawing a circle will be given on the basis of Figure 7.1a. Given the full-fledged derivation of Three girls lifted a table in Section 5.3.2, I will skip some of the steps in the derivation. Step 1 is made by introducing the VP draw a circle directly comparable to the representation of lift two tables in the last derivational line of step 7 on page 162. From here on, the steps below will be given in detail in the derivation (10) on page 298. 1. draw a circle  λzλα  ∃Q[Q ⊆ CIRCLE ∧ |Q| = 1∧ ∀y[Q(y) → [DRAW(α  )(y)(z) ∧ α  = d(Ran(su)) ∧ |α  | ≤ |Q|]]] At this point, the resulting VP has two ways to go in a compositional procedure. It either connects to an external argument in order to form a predication as in (3b) John drew a circle. Or it is going to be used nominally. In Figure 7.1a, the

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VP is combined with the operator ING which is responsible for the presence of the suffix -ing and for yielding an NP. This operator is introduced in step 2. 2. ING  λX λY λα∃x∃β[X (x)(β) ∧ Y (x)(α) ∧ | f A,α | = | f A,β |] The formula expresses a relation between two indices: α and β. The variable β is existentially bound by a quantifier and it will become an argument of the verb draw when the VP draw a circle substitutes for the λ-bound variable X . The index α will become an argument of the copula be and will eventually be replaced by the index k existentially introduced by IMP in this case or by PERF in the case of John has been drawing a circle. That ING follows the compositional path pictured in Figure 7.1a is due to its type-logical characterization: it is of type e, i, t, e, i, t, i, t. That is, ING receives a VP in order to construe an NP of type e, i, t, i, t. The crucial clause contributed by ING is: | f A,α | = | f A,β |. I will postpone treatment of that clause until after step 5 where it will be discussed in relation to the copula. First ING applies to the VP draw a circle of type e, i, t in step 3 as pictured in Figure 7.1b yielding an NP. 3. ING(DRAW- A - CIRCLE)  λX λY λα∃x∃β[X (x)(β) ∧ Y (x)(α) ∧ | f A,α | = | f A,β |](λzλα  ∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [DRAW(α  )(y)(z) ∧ α  = d(Ran(su)) ∧ |α  | ≤ |Q|]]]) ... = λY λα∃x∃β∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [DRAW(β)(y)(x) ∧ β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ Y (x)(β) ∧ | f A,α | = | f A,β |]]] The replacement of the variable X in the ING-formula by the formula for draw a circle as well as the replacement of the variable z by x and of the variable α  by β are represented by dots, as they follow the standard pattern. The final line introduces the two existential quantifiers contributed by ING. The first one introduces x, which is the external argument of DRAW, and the other one introduces β binding the eventuality index β of DRAW. In the final clause, the β-index of draw relates to the variable α of the copula be which at the level of IMP and PERF is to be replaced by k. The type of the last line is e, i, t, i, t. Step 4 is the introduction of the copula be. 4. be  λPλzλα(P(λyλγ [BE(γ )(y)(z) ∧ γ = Ran(id)])(α))

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I follow here the well-known analysis of be as a transitive verb, presented in Montague (1974c) as explained in detail in Partee (1975). Its type-logical structure is identical to the structure assigned to the copula become in Section 6.5.4 on page 207. The copula be is therefore of type e, i, t, i, t, e, i, t. This means that the resulting formula of step 3 can substitute for the λ-bound variable P in the formula for be in step 4, in the same way as the variable P of the verb lift on page 161 was replaced by its internal argument. That happens in step 5, resulting in a formula of type e, i, t. 5. BE(ING(draw a circle))  λPλzλα(P(λvλγ [BE(γ )(v)(z) ∧ γ = Ran(id)])(α)) (λY λα  ∃x∃β∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [DRAW(β)(y) (x) ∧ β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ Y (x)(α  ) ∧ | f A,α  | = | f A,β |]]]) ... = λzλα∃x∃β∃Q[Q ⊆ CIRCLE ∧|Q| = 1∧∀y[Q(y) → [BE(α)(x)(z) ∧ α = Ran(id) ∧ DRAW(β)(y)(x) ∧ β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ | f A,α | = | f A,β |]]] The last line of step 5 is typically the representation for a VP: being of type e, i, t, it expects a value of type e for the variable z contributed by the external argument in order to yield an expression of type i, t. Step 5 is the new part of the analysis and therefore some additional comment is needed. The index α of the copula be is Ran(id). A function with a domain and a co-domain can be seen as a set of pairs (x, y) with a value of x in the domain of the function and a value of y in its co-domain. Thus, id can be seen as a set of pairs (x, y) with id(x) = y and y = x. This set has a cardinality, which is the number of pairs in the set involved in the mapping. The clause | f A,α | = | f A,β | requires that the cardinality of the index β of draw does not exceed the cardinality of the index α of the copula be. In the case of (3a) John was drawing a circle, f A,α stands for the function id which defines the eventuality index α = Ran(id) of be whereas f A,β stands for the function su which is included in the index β = d(Ran(su)) of draw. In other words, | f A,α | = | f A,β | requires that the function su be applied as long as the function id of be is being applied. In this way, the function d cannot obtain cardinality 1 because it is not allowed to map to N and as long as the mapping to 1 keeps going on without yielding the value 1, there is no discretization. It follows that the actualization of the terminative predication John draw a circle cannot be fully obtained due to the stativity of the copula which requires unboundedness in R+ . This excludes modality as a feature of the analysis of a Progressive Form in English.

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Step 6 involves applying the proper name John to the VP. For convenience, the quantified version of this external argument is written as λX λα[X (jo)(α)], which is of type e, i, t, i, t The resulting line of step 5 leads to the tenseless S0 which forms the input to IMP or PERF. 6. John be drawing a circle  λX λα[X (jo)(α)](λzλα  ∃x∃β∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [BE(α  )(x)(z) ∧ α  = Ran(id) ∧ DRAW(β)(y)(x) ∧ β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ | f A,α  | = | f A,β |]]]) ... = λα∃x∃β∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [BE(α)(x)(jo) ∧ α  = Ran(id) ∧ DRAW(β)(y)(x) ∧ β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ | f A,α | = | f A,β |]]] The final line says that the tenseless predication of type i, t looks for an index which can replace the variable α. This is the index k existentially introduced by IMP or PERF. The derivation for (3a) John was drawing a circle ends with step 7. 7. ∃i  ∃ j∃k∃x∃β∃Q[Q ⊆ CIRCLE ∧ |Q| = 1 ∧ ∀y[Q(y) → [BE(k)(x)(jo)∧k = Ran(id)∧ DRAW(β)(y)(x)∧β = d(Ran(su)) ∧ |β| ≤ |Q| ∧ | f A,k | = | f A,β | ∧ k  j ∧ j  i ∧ i < i ∧ i ◦ n]]] After the explanation of the preceding steps, this representation should be transparent. Crucial is that the interval k of be equals the interval Ran(su) of draw preventing the full application of d. An agreeable consequence is that no possible worlds are needed and that as a natural consequence of the analysis in the case of plural NPs some of the circles may already have been completed. (7)

a. John was drawing some circles. b. Three girls were drawing circles.

Sentence (7a) clearly allows for an interpretation in which some of the circles were already finished at the moment n  , that is, at the fleeting moment in the past when John is drawing some circles would have been appropriate. Sentence (7b) also shows what (3a) does not show, namely that a plural subject NP makes it possible to provide an interpretation in which one of the girls completed a circle whereas the other two were still busy. This interpretation is

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even more dominant when (7b) is continued with: I noticed that the youngest one had made Olympic circles, each with a different colour. The present analysis accounts in a natural way for the problem of comparing the sentences in (8), as done by Arche (2014) in the context of discussing proposals aiming at “detelicization” of terminative predicates, such as Bertinetto (1994b) and Borer (2005). (8)

a. Marta was swimming ⇒ Marta had swum. b. Marta was drawing a castle ⇒ Marta had drawn a castle.

Actually, I doubt very much the value of this test. After all Marta had swum means something different than intended by Arche, Bertinetto and Borer: it expresses that Marta had finished swimming.5 What clearly is intended by comparing (8a) with (8b) is based on the idea that if you were swimming at n  you must have swum before and adjacent to n  . That ‘ ⇒’ is the proper symbol for non-entailment in (8b), does not prove anything because Mary was drawing a castle is to be interpreted in terms of the structure in Figure 7.1a, whereas Marta had drawn a castle is interpreted on the basis of Figure 7.1b: there is no relation of consequence between the two phrase structures. Bertinetto (1994a) put question marks with respect to the position that progressives are stative. As shown in (8), Mary was drawing at n  entails that Mary had been drawing before n  and at n  . The present analysis reveals that this is due to the su-part of the eventuality index β assigned to draw as well as to the clause |id, k| = |su, β| which regulates the relation between two eventuality indices. This eliminates not only the need for detelicization but it also gives a more articulated answer to the question marks than was possible on the basis of just one PROG operator. Returning to Rothstein’s example, repeated here as (9a), one can easily see that this sentence is about an arrival going on and not yet completed. This is exactly what is expressed by (9a). (9)

a. Mary is arriving at the station. b. ∃j∃k∃x∃β[BE(k)(x)(m) ∧ ARRIVE - AT- STATION(β)(x) ∧ k = Ran(id) ∧ β = d(Ran(su)) ∧ |idk | = |su β | ∧ k  j ∧ j  i ∧ i◦n]

In that respect, there is no difference with John was drawing a circle. The present analysis also explains the difference between (10a) and (10b). (10)

a. Mary lives in London. b. ∃j∃k[LIVE - IN -L ONDON(k)(m) ∧ k = Ran(id) ∧ k  j ∧ j  i ∧ i ◦ n] c. Mary is living in London.

5 This explains why Marta was living in London does not entail Marta had lived in London which

immediately shows the weak basis for the test.

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d. ∃j∃k∃x∃β[BE(k)(x)(m) ∧ k = Ran(id) ∧ LIVE - IN -L ONDON(β)(x) ∧ β = Ran(id) ∧ |idk | = idβ | ∧ k  j ∧ j  i ∧ i ◦ i]

As well-known, (10a) says that London is the place where Mary lives permanently. This is accounted for by (10b). Sentence (10c) says that in the present period Mary lives in London on a temporary base. The clause |idk | = idβ | underscores the focus on the ongoing process going on at the fleeting point n.

7.2

Binary Indices, Compositionality and Slavic Aspect

7.2.0 Introduction There are quite divergent views on the relation between Slavic aspect and nonSlavic aspect. When I was working on my PhD thesis at the end of the sixties, the position of Slavicists was clearly the adoption of (11a), where PF is short for ‘perfective aspect’ and [+ T] short for ‘terminative aspect’ as defined in features in Chapter 4. In fact, (11a) stood for the firm conviction that aspect was a unique Slavic phenomenon. (11)

a. b.

PF PF

= [+ T] = [+ T]

c. d.

PF PF

= [+ T] + X = [+ T] – X

In the Slavistic literature, there is well-known distinction between Slavicstyle aspect and Romance-style aspect, discussed at some length in Kamphuis (2020:31–8). Dahl (1985) introduced the former term in order to mark the specific position of Slavic aspect. Tomerelli (2010) compared the former term to the latter and agrees with the distinction. I side with Lindstedt (1995) and Kamphuis (2020) in arguing that (11b) and (11c) are serious options deserving serious arguments before making a choice. To my knowledge, option (11d) has not received any support and it will be further ignored.6 The Plus-principle discussed in Section 4.3 opened the way for inspecting the possibility of (11b). This option has been investigated in detail by Schoorlemmer (1995) and by Borik (2006) in the generative framework. Schoorlemmer calls (11b) the null hypothesis with respect to option (11c) where perfectivity is seen as Aktionsart (= [+T]) plus something X. Both Schoorlemmer and Borik take into account the semantic differences between 6 Verkuyl (2012) suggests that X stands for temporal information needed to compensate for the

impoverishment of Slavic tense systems like Russian, Polish, etc. (but not Bulgarian as shown in Section 7.3.2). In the present book, this line has not been continued by relating PERF to the notion of full actualization.

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the perfective prefixes available in Russian before one can decide whether PF = [+ T ] or not. A similar conclusion can be found in work on the large variety of meanings expressed by perfective prefixes as reviewed in Fortuin and Kamphuis (2015). It provides a comprehensive survey of typological work done in this domain of research mainly in the framework of functionalism and cognitive linguistics. The authors present relevant data about the different ways of dealing with the perfective/imperfective distinction, in particular in contexts expressing habituality or general use and in narrative structure. The issue of the relation between [+T] and PF is also part of their analysis. All three sources just mentioned discuss this relation in terms of a comparison between tensed sentences. They all include temporal adverbials in the sentences expressing imperfective or perfective aspect. Their position will be sketched in Section 7.2.1, which brings them together as providing the relevant empirical information for deciding about the relation between PF and [+T]. The formal tools developed in the preceding chapters make it possible to give a more precise answer than they do, as will be argued in Section 7.2.2. This makes it possible to leave the feature-approach in (9) on page 123 in Chapter 4 behind. 7.2.1 PF vs [+ T ] and IPF vs [– T ] Schoorlemmer (1995:77–131) is a chapter testing the null hypothesis that terminative clauses are expressed with a perfective verb and durative ones with an imperfective verb. She treats some contexts in which this hypothesis cannot be maintained, for example in (12). (12)

Vasja cˇ erez mesjac pereˇcityvaet pis’ma byvšej podrugi. Vasja every month rereadsipf +3rd letters former girl-friend ‘Every month, Vasja rereads the letters of his former girl-friend.’

Sentence (12) as a whole is considered imperfective due to the fact that the (secondary) imperfectivizing infix -yva- is inserted in the verb form pereˇcitat’ which is perfective due to the prefix pere- meaning: ‘across, over, afresh’. In terms of features, one could see the imperfectivization by -yva- as changing the [+T VP ]-phrase pereˇcitat’ pis’ma ‘reread the letters’ into the [–T VP ]-phrase pereˇcityvat’ pis’ma ‘reread the letters’. Thus the sentence pertains to an unbounded sequence in N, that is, to a unbounded series of terminative eventuality indices k. This runs counter to the claim that IPF = [–T]. Another example is the question in (13) asked by a speaker assuming that the hearer knows that the room has been cleared before n.

7.2 Binary Indices, Compositionality and Slavic Aspect (13)

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Kto ubiral komnatu? who clearipf +3rdsg room ‘Who cleared/has been clearing the room?’

In that case, (13) can be understood as a question about who was responsible for the insufficient clearing. Schoorlemmer treats these two examples as standing for different things.7 An important ingredient of Schoorlemmer’s analysis is that two Russian verb classes are distinguished on the ground that “they are not sensitive to compositional aspectuality” (p. 98). She uses the lexical feature [+INH](erent) for these verbs. The first class contains phase aktionsart verbs. These focus on a certain stage of an eventuality; for example, verbs with za- indicating a start and verbs with ot- indicating an end. The second class consists of temporal aktionsart verbs. These are verbs occurring with the prefixes po- ‘a short while’ and pro- ‘a long while’. Examples of the two classes are given in (14). (14)

cˇ erez pjat’ minut/∗ cˇ as. a. Orkestr za-igraet val’s Orchestra PF-plays waltz-ACC in five minutes/ ∗ for-hour ‘In five minutes/∗ for an hour the orchestra will start to play a waltz.’ popisala pis’mo. b. Ol’ga cˇ as/∗ za cˇ as Olga hour/ ∗ in hour PF-wrote letter-acc ‘Olga wrote the letter for an hour/∗ in an hour.’ muzyku do utra. c. Vasja proslušal Vasja PF-listened-to music-ACC until morning ‘Vasja listened to (the) music until morning.’

The problem with these sentences is that their verbs do not meet the aspectual litmus test. It does not matter for za-igrat’ ‘play’ whether or not this PF-verb occurs with an internal argument (as it normally should do). In both cases, (14a) expresses perfectivity because the prefix za- contributes the sense of some sort of restriction independent of its internal argument. The same holds for (14b): it does not require that the letter be completed, but by the use of the prefix po- it pertains rather to the actualization of some part(s) of the unfinished letter. For (14c), the period of listening to music is much longer by the use of pro-. In terms of features: the [+ADDTO]-feature of the verb is immune to the [+SQA]-feature of the internal argument. In other words, there is no discretization of the whole denotation of the internal argument in (14). It is a sort of local use of the perfective prefixes as a lexical property of the verb involved. 7 Sentence (13) falls outside the scope of the present study but should not pose a problem for an

explanation in terms of focus on the verb at a level below its arguments.

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I do not see any problem for compositionality here. After all, in Dutch and English sentences like (15) show a parallel behaviour. (15)

a. Zij begon [∅ aan de boterhammen]. ‘She started with the sandwiches.’ b. Hij begon [opgewonden te discussiëren]. ‘He began to argue excitedly.’

In both (15a) and (15b), the aspectual litmus test shows that the sentences are terminative in spite of the possibility to interpret the complement of begon ‘began’ as expressing unboundedness. This is because they are not fulfilling the role of internal argument of the verb begin and hence do not receive the case marking of an internal argument formally defined in step 5 of the derivation given in Chapter 5 on page 161. This also holds for the complex verbs in (14): za- and pro- provide different roles for the complements of the verbs with which they occur. Note in passing that the PF-form of the Russian counterparts of unergative verbs like walk, lie, sleep, sit, run, etc. begins with the prefix po-. Borik (2006:94ff) agrees with Schoorlemmer’s analysis of a mismatch between [+T] and PF but rejects the idea of a lexically inherent [+T]specification for the two classes of Aktionsart verbs. I share Borik’s position but on different grounds, as will be made clear later on. As to compositionality, Borik opposes Schoorlemmer’s inclination to reduce the difference between [+T] and PF. Rather she follows the line of a strict separation between the [+T] in (11c) (in my terms: the S0 -domain) and X in which she locates viewpoint aspect at a higher level of phrase structure. I do not follow her at this point, the more so because her considerations are based on a ternary Reichenbachian treatment of tense. I endorse her plea for (11c) but for quite different reasons in view of a theory in which (11c) is a central building block. Fortuin and Kamphuis (2015) discuss this theory in their review of work done on what they call the East-West theory. This theory – also discussed in Kamphuis (2020) – partitions Slavic languages into Eastern (Russian, Belarusian, Ukrainian and Bulgarian) and Western (Czech, Slovak, Sorbian and Slovene). Transitional languages are Polish, Macedonian, Bosnian, Serbian and Croatian. The East-West theory aims at accounting for differences between Slavic languages in the use of morphemes marking imperfective or perfective aspect. Fortuin and Kamphuis treat the East-West theory as combining two aspectual theories that largely overlap. The first is what I will call the B-theory proposed in Barentsen (1985), a PhD thesis written in Dutch, and further developed in subsequent work mainly written in Russian. The second is what I will call the D-theory proposed in Dickey (2000) and applied in subsequent work

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including Dickey (2015). The B-theory belongs to functionalism; the D-theory to cognitive linguistics. Both are rather informal in the description of their key notions only using lines and circles to make them clearer.8 Fortuin and Kamphuis (2015) combine the B-theory and the D-theory into one BD-theory because the differences are so minimal, if not negligible in spite of the different frameworks in which they were developed. For the invariant meaning of perfective aspect, Barentsen distinguishes three different “layers” (1985:59–70): (16)

a. the “unit of action” is connected to the idea of a specific limitation which consists in transforming an existing situation into a new situation by “going through” this unit of action. This makes the predicate terminative (predel’nyj), written here as [+T];9 b. the unit of action is presented as one unit, a totality (celostnost’), written here as [+TOTAL]; c. the unit of action is seen as a link in a chain and therefore connected to following and/or preceding ones. This is called sequential connection, written here as [+SEQ].

Barentsen is more specific about the notion predel’nyj than Dickey, but Fortuin and Kamphuis treat the D-theory as similar to the B-theory with regard to (16a,b) and as slightly different as to what Barentsen calls sequential connection and Dickey temporal definiteness. An eventuality is temporally definite when it is uniquely located given a certain context. By interpreting Barentsen’s sequential connection in terms of identifying a uniquely located eventuality in a chain, Fortuin and Kamphuis (2015) obtain the BD-theory with regard to PF: it captures the set of three elements that are involved in perfective aspect as: PF = {[+ T ], [+ TOTAL ], [+ TDEF ]}. Thus the BD-theory is an explicit form of choosing for option (11c), where X consists of the two “layers” b and c in (16). As to imperfective aspect, there is even less difference between the B- and D-theory. The BD-theory amounts here to the following characterization of IPF . (17)

a. an IPF-predication pertains to a non-terminative eventuality in the sense that there is no situational change as is the case with [+T] in (16a). This amounts to saying that there is no boundary playing a role in the interpretation. Notation: [–T]; b. an IPF-predication does neither express totality nor completion. Notation: [–TOTAL];

8 Apart from the dissertation Barentsen (1985) written in Dutch, the references to Barentsen’s

work in Fortuin and Kamphuis (2015) are papers written in Russian. 9 Barentsen uses the term terminative in order to escape from the term telic: for him prefixes like

po- ‘for a while’ and pro- ‘through’ are difficult to connect with the notion of telos.

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How to Deal Binarily with ...? c. an IPF-predication may express completion and termination but only if there is no temporal definiteness involved relative to other states of affairs. Notation: [–TDEF].

One minus value suffices for obtaining IPF. Thus one can write IPF = {[±T], [±TOTAL], [±TDEF]} with the condition that at least one of the elements of the set IPF has a minus value. An hierarchical condition comparable with the Plus-Principle is that IPF may not contain the subsets {[–T],[+TOTAL]} or {[–TOTAL],[+TDEF]}. The aforementioned characterizations of the BD-theory form the basis on which Fortuin and Kamphuis (2015) proceed in comparing the different uses of the imperfective and perfective aspect in various Slavic languages as signaled in the literature, mainly by Slavicists. According to them, the differences between the various Slavic languages with respect to PF and IPF concern mainly (16c) and (17c). A closer look at Barentsen (1985) – and at what Fortuin and Kamphuis (2015) says about Barentsen’s later work – and a closer look at Dickey (2015) combined with what Fortuin and Kamphuis (2015) says about Dickey’s earlier work, can only lead to the conclusion that its informal approach prevents the explanatory power of the BD-theory from transcending that of the feature approach of (18a) and (19a) below. In Section 6.5, that approach was shown to be inadequate when it comes to accounting for compositionality. This means that when accepting (16) and (17) as valid claims about the differences between perfective and imperfective aspect, there is much room for translating them into the formal language developed so far in the preceding chapters. The claims in (16) and (17) for Slavic languages fully describe the claims made in Verkuyl (1972a) and Verkuyl (1993) about the opposition between terminative and durative in non-Slavic languages. If the formal machinery presented in the present book is an extension of my earlier work, then it should be able to deal with the Slavic data as theoretically captured by (16) and (17). 7.2.2 Dividing PF and IPF between Three Levels In order to establish whether the features [+T] or [−T] in the English sentences (18a) and (19a) could be seen as “theoretically equivalent” with the features PF and IPF assigned to the Russian (18b) and (19b), respectively, we will give a formal analysis of the latter two. (18)

a. [S Olga [VP wrote the letter]] [+T S [+SQA][+T VP [+ADDTO] [+SQA]]] ⇒ terminative b. [S Ol’ga [VP napisalapf pis’mo]] ⇒ terminative

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c. λzλα∃Q[Q ⊆ PIS ’ MO ∧ |Q| = 1 ∧ ∀y[Q(y) → [NAPISAT ’(α)(y)(z) ∧ α = d(Ran(su)) ∧ |α| ≤ |Q|]]] d. int  λQλY λα∃Q[Q(Y )(α)(Q) ∧ |α| ≤ |Q|] (19)

a. [S Olga [VP wrote/was writing (a) letter]] [−T S [+SQA][−T VP [+ADDTO][−SQA]]] ⇒ durative b. [S Ol’ga [VP pisalaipf pis’mo]] ⇒ durative c. λzλα∃Q[Q ⊆ PIS ’ MO ∧ |Q| = 1 ∧ ∀y[Q(y) → [PISAT ’(α)(y)(z) ∧ α = Ran(su) ∧ |α| ≤ |Q|]]]

An important difference between English and Russian is that Russian has no overt article, so that the determiner DET of an NP is empty. Yet the NP immediately dominating DET and N expresses cardinality information in (18b). This is represented as |.| in Figure 7.2a and made precise in (18c). The

Figure 7.2 Structuring perfective and imperfective aspect in Russian

arrows in Figure 7.2a illustrate the formal connection between the two clauses α = d(Ran(su)) and |α| ≤ |Q| in (18c): the lower arrow makes the perfective prefix na- responsible for requiring (or implementing) the [+SQA]-cardinality information of the NP and the higher one illustrates the connection between the information expressed by DET and by int defined in (18d). The Russian NP pis’mo in (18b) corresponds with the English NP the letter in contextually identifying a specific letter. In (19b), pis’mo is stripped off its referential force: Olga is ‘letter-writing’, so to say, although Olga may be working on a specific letter identified earlier in the discourse. Ignoring the role of the [+SQA]-NP Ol’ga, we focus here on what happens if one translates the feature representation in (18a) into a formula of the kind occurring in the twelve steps of the derivation of the terminative sentence Three girls lifted two tables in Section 5.3. Apart from the lexical items, formula (18c) is structurally identical to the last line of step 7 in the derivation of the VP lift two tables on page 162. As shown in the formal account of compositional derivation, the

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contribution of the thematic function int defined in step 4 on page 161 and repeated here as (18d) is to make a match between the eventuality index α and the internal argument as expressed by the clauses α = d(Ran(su)) and |α| ≤ |Q|. In (19b), the story is different: the absence of the perfective prefix naprevents a connection with the cardinality information of the NP pis’mo and this blocking information is transferred to int . However, the combination of the two clauses α = Ran(su) and |α| ≤ |Q| in (19c) does not lead to discretization (i.e. to mapping into N): the eventuality index α remains in R+ itself and can only be understood as a closed interval by contextual information or due to the anteriority expressed by PAST. The clause |α| ≤ |Q| attributed by int turns out to be superfluous and can be ignored because |α| is not available.10 The analysis of the difference between the Russian sentences (18b) and (19b) shows that it makes sense to assign the feature [+T] both to them and to their English counterparts in (18a) and (19a). However, this analysis covers only a small part of the phrase structure that should be taken into account. Given option (11c), that is, PF = [+T] + X, one may expect the X pertains to information above the level of S0 . In terms of the BD-theory, it means for Figure 7.2a that (the still tenseless) S0 harbours the predel’nyj-part of PF, its [+T]-part, according to (16a). Likewise, Figure 7.2b represents [–T]. By using the presence or absence of the discretizing function d as characteristic for the opposition between Figures 7.2a and 7.2b, it follows that the source of the criterial oppositions between (16b,c) and (17b,c) should be found elsewhere in the tree. It will be argued that this is at levels above S0 . This follows from the assumption that both PF and IPF are complex notions to be broken apart. Focussing therefore on the feature [±TOTAL] standing for the opposition between (16b) and (17b), a natural step is to associate this feature with the third opposition of binary tense structure, that is, with the opposition between IMP and PERF as understood in the preceding chapters. After all, k ≺ j expresses that k should be seen as fully actualized in j (as a totality), whereas k  j can be understood as not providing sufficient information about whether k is completed in j. Figure 7.3a covers the configuration + + + with respect to the three BD-criteria by connecting the compositional steps to the three elements of PF in (16). The [+ T]-index α = d(Ran(su)) at the level of S0 in Figure 7.3a 10 There is an alternative analysis available: to define a  for perfective verbs and a  for int int

imperfective verbs, where the latter is (18d) minus the clause |α| ≤ |Q|. I will not make a choice between the two.

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Figure 7.3 Sorting out the three layers of the Barentsen-Dickey theory

is replaced by the bound variable k which is identified as [+TOTAL] (in the BD-sense) by the clause k ≺ j introduced by PERF. The Russian tense system does not have a separate tense form for the perfect, so that [+TOTAL] can be seen as the Russian concretization of PERF. Figure 7.3b accounts for the configuration + – –. The structure in Figure 7.3b is available in the case of secondary imperfectivization discussed in (12) and in other pairs treated in Schoorlemmer (2004), as given in (20). (20)

a. pisat’: perepisat’ – perepisyvat’ b. pisat’: vypisat’ – vypisyvat’.

In (20a), the perfective prefix pere- changes the meaning of pisat’ ‘write’ into ‘copy’ and as such the perfective perepisat’ can be imperfectivized by the infix -yva-. In (20b), the perfective prefix vy- changes the meaning of pisat’ into ‘subscribe to’ and so the perfective vypisat’ pairs with the secondary imperfective form vypisyvat’. There are two ways of relating -yva- to perein (21). (21)

a. Ol’ga perepisyvala pis’mo. ‘Olga was copying the letter.’ b. PAST ( SYN ( IMP(Ol’ga(( YVA(perepisat’))(pis’mo))))) c. PAST ( SYN ( YVA(Ol’ga(perepisat’(pis’mo)))))

The first is to locate -yva- in the domain of the VP, say as in (21b), and leave it to morphological theory to account for the insertion of -yva- in perepisat’. In that case, the presence of -yva- sends a [–TOTAL]-arrow to IMP k  j. The second is to locate it above S0 as the overt representation of IMP as in (21c). In both cases, the sentence may be interpreted both at the micro-level by

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pertaining to just one k and at the macro-level by expressing unboundedness due to the plurality of k, as discussed in Mønnesland (1984) and in Stunova (1993). A choice between these options falls outside the scope of the present analysis. The two structures in Figure 7.3 can be formalized as given in (22) following the first steps of Chapter 5 until SYN or POST applies. (22)

a. λα∃k∃Q[Q ⊆ PIS ’ MO ∧ |Q| = 1 ∧ ∀y[Q(y) → [NAPISAT ’(k)(y)(o) ∧ k = d(Ran(su)) ∧ |k| ≤ |Q| ∧ k ≺ α]]] b. λα∃k∃Q[Q ⊆ PIS ’ MO ∧ |Q| = 1 ∧ ∀y[Q(y) → [PEREPISAT ’(k)(y)(o) ∧ k = d(Ran(su)) ∧ |k| ≤ |Q| ∧ k  α]]]

Representation (22a) accounts more formally for the PF-interpretation of (18b). The clause k = d(Ran(su)) contributes the predel’nyj-part of PF, the PERFclause k ≺ α in combination with the discretizing d-information contributed by na- for the [+TOTAL]-part. The token [+SEQ]-feature of the predication will be contributed at a later stage by the application of PRES or PAST. Representation (22b) retains the terminative character of the predication but the IMP -clause k  α prevents it from being applied by the infix -yva-. Without making any claim about the cognitive processing involved in compositionality, one may say that the two tenseless S0 structures given in Figure 7.3 have two options with respect to the IMP / PERF -opposition on its way to the top of the tense structure: the first adds [+TOTAL] to [+T] and then faces a choice between opting for an operator providing a type-option or opting for a token-option. In the latter case, it ends up as PF = {[+T], [+TOTAL], [+SEQ]} via SYN and PAST or PRES. This option is provided by Figure 7.3a and it accounts for sentence (18b) Ol’ga napisala pis’mo interpreted as pertaining to a unique (B-sequentially connected, D-temporally definite) eventuality k distinguished as having occurred in a unique chain of events. The other option is [–TOTAL] in Figure 7.3b, with the possibility of having the Russian alternative for the English Progressive Form by getting into a terminative structure and preventing a mapping into N. So far the formalization of the BD-theory has been applied to Russian. Fortuin and Kamphuis (2015) discusses at length that in this respect Western Slavic languages behave differently from Eastern ones. In past tense habitual sentences in Russian, IPF is required whereas Western languages allow for PF as shown in Mønnesland (1984) and Dickey (2000). (23)

a. Každyj den’ Ol’ga vypivaetipf /∗ vyp’etpf rjumku vodki. (Ru.) a glass of vodka Every day Olga drinks ‘Olga drinks a glass of vodka every day.’

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b. Ol’ga vypijepf jednu skleniˇcku vodky dennˇe. (Cz.) Olga drinks a glass vodka daily ‘Olga drinks a glass of wodka every day.’ c. Dennˇe dostávámipf nˇekolik dopis˙u. (Cz.) some letters Daily I receive ‘I receive some letters every day.’

The Eastern languages may only use imperfective forms as shown in (23a). A Western language like Czech may (but need not) use the perfective aspect. A binary explanation of this difference can be founded on the assumption that the Russian requirement on the function d – to provide cardinality information of the internal argument – leaves no way for multiplying the information provided by the DET of the internal argument: d requires a token interpretation. This explanation receives support from the analysis of prefixes like po‘for a while, a little’ and pro- ‘through’ in taking them as restricting prefixes not requiring the application of the function d. This means that they do not discretize in N: they react to the aspectual litmus test differently from other aspectual prefixes. In My poigrali ‘We played for a while’ the perfective affix po- restricts the duration of our playing whereas the IPF verb form igrali does not. The sentences in (24) are discussed in Borik (2006) as an example in which the perfectivizing contribution of pro- is minimal, so that there is no or hardly any difference between the interpretation with pro- and the one without pro-. (24)

v tjur’me pjat’ let. a. Petja sidel Petja IPF-sit-past in prison five years ‘Petja was in prison for five years.’ b. Petja prosidel v tjur’me pjat’ let. Petja PF-sit-past in prison five years ‘Petja was in prison for five years.’

Yet Borik observes that (24b) with prosidel is ungrammatical without the durational adverbial, but that (24a) with sidel remains grammatical in that case. In my view, this can be accounted for by assuming that PERF+id in (24b) can be seen as expressing completion in R+ due to the presence of pro-, which requires an overt measurement. If Figure 7.4a illustrates the configuration for the imperfective sentence (24a) without the adverbial, then Figure 7.4b accounts for the structure of its perfective counterpart in (24b). The basic idea is here that in (24a) the absence of a perfectivizing prefix restricts the domain of [–T] to the VP without involving its internal argument. Since IMP requires the absence of the feature [+TOTAL], the resulting structure is open to a token interpretation or to a type interpretation in the form of iteration or habituality as in (25).

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Figure 7.4 The BD-theory applied to the absence of pro- and its presence in

Russian

(25)

a. Neodnokratno Petja sidel v tjur’me v tot period. Repeatedly Petja was in prison in that period ‘Repeatedly Petja was in prison in that period.’ b. Beskoneˇcno Ol’ga pisala pis’ma svoemu drugu. Endlessly Olga wrote letters to her friend ‘Endlessly Olga wrote letters to her friend.’

This is what should be expected, the more so because the difference between the token interpretation and the type interpretation is decided on the highest level when the choice between (16c) and (17c) has to be made. In Figure 7.4b, things are more complex. The lexical meaning of pro- is too weak to require the function d (which is not allowed by the function id). Yet pro- expresses a bounded measurement. Phrased in terms of the formulas of Chapter 6: a pro-verb cannot “see” cardinality information about the internal argument of the verb because its k is either Ran(su) or Ran(id). But this does not prevent PERF from being applied and so the [+TOTAL] can be seen as requiring k to be fully actualized in j because the length of k is bounded by a value m in R+ , as explained in Section 6.5. 7.2.3 Temporal Definiteness and Indefiniteness As said, the third criterion of for defining perfectivity has been called sequential connection by Barentsen and temporal definiteness by Dickey. Barentsen underscores the importance of contrast between the eventuality and its “surroundings” (1985:60), whereas Dickey underscores the unique location given a certain context (2000:27). I think that these two contrasts are captured

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by the notion of discretization actualized in the real time of the domain of interpretation. The set Ad at the top of Figure 5.3 repeated here as Figure 7.5 is a set of discretely organized eventualities each of which is contrasted to other eventualities by their isolated nature. The instruction to a Russian verb to express

Figure 7.5 Token and type in different number systems

perfectivity can be understood as providing uniqueness, that is, as the instruction to reduce Ad to a unique singleton a1 . If Ad has more members, each of them is unique in its location and with respect to other eventualites in the context. This type-interpretation is problematic for Russian, not for some other Slavic languages as discussed. The set Ac in Figure 7.5 is also relevant. If a Russian verb is marked as imperfective, it may express habituality assuming the indexed family of sets Ac to have a cardinality greater than or equal to 2. As argued, this habituality can be invoked by prefixes like po- and pro- which remain vague about the length of the interval(s) to which they pertain. In terms of the binary tense structure in Figure 7.6 this means that after the point at which SYN or POST

Figure 7.6 Token and type interpretation of na-

has applied – the boldface S – there are two options for going on: 1. the token option in Figure 7.6a leading to a1 in Ac or Ad ;

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The simplest way is to assume that if no frequency adverbial is in sight at the level of the boldface S, the step from S to S can be taken directly, in which case the token interpretation of k in Figure 7.6a prevails. This is the case in the Russian sentence (18b) Ol’ga napisala pis’mo and also when the adverbial utrom ‘in the morning’ is located lower down as in (26b), as was the case in the derivation (15) of Ron saw Mary in the morning on page 179. (26)

a. Ol’ga napisala pis’mo utrom. Olga AFFd -write letter in the morning ‘Olga wrote a letter in the morning.’ b. PAST ( SYN ( PERF ( UTROM(S0 ))))  . . . c. ∃i ∃j∃k∃δ[NAPISAT ’(k)(pis’mo)(o) ∧ k = d(Ran(su)) ∧ k  j ∧ U(δ) ∧ O(k, δ) ∧ j  i ∧ i < i ∧ i ◦ n]

The resulting formula is (26c). This says that there is a past domain i  where δ is a contextually unique identifiable morning in i  , and the terminative eventuality k is uniquely actualized and located in δ. One can now account for the data in (23): Russian restricts adverbials like utrom ‘in the morning’ to the position when (k, δ) is required for verbs with prefixes like na-, whereas adverbials in the Western group do not have that restriction. They may occur at a higher position allowing for (δ, i  ) or (δ, i). The situation in Figure 7.6b is exactly the one in which an adverbial operates on j as shown in the representation (25) of the adverbial every morning in Chapter 6 on page 183 and applied here as in (27a). (27)

a. Ol’ga pisala pis’mo každoe utro. Olga ∅-write letter every morning ‘Olga wrote a letter every morning.’ b. PAST(TADV(SYN(IMP(S0 ))))  ∃i ∃U∀δ[U(δ) → ∃j∃k[∅- PISAT ’(k)(p)(o) ∧ k  j ∧ j  i ∧ O(δ, i ) ∧ i < i ∧ i ◦ n]

In this case, the adverbial is located as in Figure 7.6b which yields the interpretation that for all mornings in a series of mornings there is a k and a j such that the three underlined clauses are true. In this case, the use of the PF-form napisat’ is not allowed, as was shown in (23b). As demonstrated in Fortuin and

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Kamphuis (2015), this restriction holds only for the Eastern group of Slavic languages, not for the Western group: (28)

a. Každý den vypijupf sklenku vodky. (Czech) b. Svaki dan pijemipf /popijempf cˇ ašu votke. (Serbian) ‘Every day I drink a glass of vodka.’

Sentence (28a) shows that Czech is insensitive for the restriction of the perfective affix in Russian to appear only in a formula with the clause O(k, δ), as in (26), and not in the case of clauses like O(k, j) and O(δ, i  ). That the Serbian imperfective form may appear in (28b) can be explained in terms of (27). 7.2.4 Lexical and Grammatical Aspect Summarizing, I think that the formalized binary account of Slavic aspect presented here comes close to what the Barendsen-Dickey theory says more informally. In my view, the formalization provides a bridge between Slavic and non-Slavic aspectuality. An important conclusion to be drawn is that it does not make much sense to distinguish between grammatical aspect and lexical aspect as two different theoretical notions. Of course, one may distinguish between S0 as the domain of lexical aspect marked by [±T] and the next level as the domain of grammatical aspect marked by [±TOTAL] and for the Eastern group [±SEQ], but theoretically it does not make sense to distinguish two sorts of aspect when [±T] and [±TOTAL] are just two interrelated steps in a larger process for aspect formation called PF; interrelated, due to variables inserted lexically and obtaining their final values at the top. What does the term grammatical aspect account for halfway? A perspective introduced at the level of IMP (S0 ) or PERF (S0 )? The answer is negative because in a cognitive approach as the present one, choices made by a speaker in constructing a sentence are dependent on perspective at the top, that is, on perspective on how to present information. In that sense, the decision to add a (covert) [+ DEF]-determiner to the noun pis’mo ‘letter’ so as to form the noun phrase pis’mo ‘the letter’ in order to make [±T], is not lexical aspectual at all. It is as phrasal as the choice in English for using an auxiliary for expressing PERF. The three-step construal of PF or IPF makes it unnecessary to make a distinction between lexical information and phrasal information: aspectuality is essentially a matter of phrasal structure. 7.3

The Position of the Aorist in a Binary System

7.3.0 Introduction The aorist indicative form egrapsa in Ancient Greek is generally translated into English by ‘I wrote/have written/had written’. It is neither a Simple Past

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nor a Present Perfect nor a Pluperfect; rather something in between. As noted in Chapter 2 on page 22, CGCG characterizes the Greek aorist as “used to present the occurrence of an action in the past as a single uninterrupted whole”. According to Humbert (1945:120): “The [Greek] aorist is effectively that which is stripped of subjective values of duration and completion as expressed by present and perfect”.11 This sort of characterization of a tense form taking an eventuality as a whole can also be found in grammars of languages with aoristic forms such as French and Spanish. For example, the authoritative French grammar Grevisse says: “the Passé Simple (Definite Past) expresses a fact actualized completely at a determinate moment in the past, without taking into account the contact that this fact, in itself or by its consequences, may have with the present”.12 One can even find this sort of description in languages which had an aorist but have lost it, such as Russian: Timberlake (1985:159), for example, uses the term aorist perfective for the actual realization of a token eventuality denoted by a [+T]-predication. The present section has two goals. The first is to argue that ‘to present as a whole’ as characteristic for an aorist tense form cannot be seen in terms of applying the discretizing function d as defined in Chapter 5. CGCG 33.30 gives a sentence from Herodotus in which two aorist tense forms of stative verbs appear: emeinan ‘they stayed’ from the verb menô and (ii) eudaimonêsan ‘they prospered’ from the verb eudaimoneô ‘to be prosperous, to be well’. The discretizing function d does not apply to the function id restricted as d is to the output of the non-stative function su at a level below S0 . This has as an immediate consequence that whatever the aorist presents as a whole is to be located above S0 : the aorist may occur with durative and terminative tenseless predications in order to form a tensed S in a way comparable to IMP or PERF. The second goal is to argue that in languages which have aoristic tense forms, the position of these forms is outside the binary system presented here because all tense forms in binarily organized tense systems relate the index pair k and j to the speaker and hearer in their present domain i. That does not hold for the aorist forms in rich tense systems.

11 In his own wording: “L’Aoriste est effectivement ce qui est dépouillé des valeurs subjectives

de durée ou d’achèvement qu’expriment présent et parfait”. [translation in text mine] 12 “Le Passé Simple (passé defini) exprime un fait complètement achevé à un moment déterminé

du passé, sans considération du contact que ce fait, en lui-même ou par ses consequences, peut avoir avec le présent.” Grevisse (1964:654) [translation mine]

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Verkuyl (2008) discussed three sorts of tense systems: poor (less than eight tense forms: Russian, Chinese), medium (eight tense forms: Germanic languages like English and Dutch) and rich (more than eight forms: French, Bulgarian, Georgian). In González and Verkuyl (2017) a fourth rich system was explored: Spanish. All four have an aorist (Bulgarian, Georgian) or aoristic tense forms (French, Spanish). I will not repeat here what was discussed at length in 2008 and 2017 about the aoristic forms in rich systems. On the other hand, some of the formal tools applied in Chapter 5 and in the present chapter were not available at the time. So I will restrict myself here to clarifying issues connected with the compositional machinery presented so far. Section 7.3.1 analyzes the French Passé Simple in a discussion with De Swart (1998), which uses coercion as a way to account for the position of the Passé Simple in the French tense system and with Lefeuvre (2014), a formal semantic proposal in the binary framework. Section 7.3.2 offers a more precise analysis of Bulgarian data than was possible in Verkuyl (2008:231–52) so that the Bulgarian aorist can be compared in Section 7.3.3 with the French Passé Simple. Section 7.3.4 aims at trying to understand the role of the aorist in rich tense systems from a historical point of view but also aims at determining aoristic traces in medium and poor tense systems. This should make it possible to reach the two goals of the present section. 7.3.1 The French Passé Simple In dealing with the French tense system in order to account for the position of the Passé Simple and the Passé Antérieur in a binary reorganization, it is perhaps helpful to make use of Table 7.1, which appears in Verkuyl (2008:222).13 This table provides a reshuffle of the French tense forms in a binary set up. The two upper rows fall under the heading of IMP, the three bottom rows under the heading of PERF. Thus the richness of the French system can be understood in terms of the availability of tense forms in the bottom row 5 and of the two tense forms not captured by the three binary oppositions: the Passé Simple and the Passé Antérieur. Binarily seen, they are not allowed to appear in Table 7.1. Chapter 1 sketched the Babylonian confusion about terms. Table 7.1 illustrates that we are in the heart of it. The term Passé occurs both in the PRES -column (3a,5a) and in the PAST -column (4b), as does the term Présent (1a,2b). With regard to cell 3a, one may assume that it is the semantic sense of 13 The formulas are updated, the repetition of PERF in the cells 5 follows from the fact that the

tense forms makes use of the Present Perfect and Past Perfect forms of the auxiliary avoir ‘have’.

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Table 7.1 French tense forms defined by the binary operators PRES

PAST

1a. Elle écrit She writes Présent: PRES(SYN)(IMP) kj∧ji∧i◦n

1b. Elle écrivait She wrote Imparfait: PAST(SYN)(IMP) k  j ∧ j  i  ∧ i < i ∧ i ◦ n

2a. Elle écrira She will write Futur Simple: PRES(POST)(IMP) k  j ∧ j  i♦ ∧ i ◦ n

2b. Elle écrirait She would write Présent Conditionnel: PAST(POST)(IMP) k  j ∧ j  i♦ ∧ i < i ∧ i ◦ n

3a. Elle a écrit She has written Passé Composé: PRES(SYN)(PERF) k≺j∧ji∧i◦n

3b. Elle avait écrit She had written Plus-que-Parfait: PAST(SYN)(PERF) k ≺ j ∧ j  i ∧ i  < i ∧ i ◦ n

4a. Elle aura écrit She will have written Futur antérieur: PRES(POST)(PERF) k ≺ j ∧ j  i♦ ∧ i ◦ n

4b. Elle aurait écrit She would have written Passé Conditionnel: PAST(POST)(PERF) k ≺ j ∧ j  i♦ ∧ i < i ∧ i ◦ n

5a. Elle a eu écrit

5b. Elle avait eu écrit

lit: She has had written Passé Surcomposé: PRES ( SYN )( PERF )( PERF ) k ≺ k ∧ k ≺ j ∧ j  i ∧ i ◦ n

lit: She had had written Plus-que-Parfait Surcomposé: PAST ( SYN )( PERF )( PERF ) k ≺ k ∧ k  ≺ j ∧ j  i  ∧ i  < i ∧ i ◦ n

anteriority that must have led to the term Passé in Passé Composé and not the tense carrier a itself. As argued in the preceding chapters, the sense of anteriority is wrongly attributed to the Passé Composé and it has been replaced by the sense of full actualization expressed by the PERF-clause k ≺ j. Let me first give the two tense forms that do not fit in Table 7.1: the Passé Simple in (29a) and the Passé Antérieur in (29b). (29)

a. Jeanne écrivit une lettre. Jeanne write-PS a letter ‘Jeanne wrote/has written a letter.’ écrit une lettre. b. Jeanne eut Jeanne have-PS written a letter ‘Jeanne had written a letter.’

The complex tense form eut écrit in (29b) is not the past of écrivit in the same sense in which the Plus-que-Parfait avait écrit is the past of the Passé Composé a écrit: the form eut is the Passé Simple of avoir ‘have’. In this way, the Passé Antérieur is the Passé Simple of a Passé Composé. This deviates from the

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pattern in Table 7.1 so that it is impossible to extend the table with a row 6 in which the Passé Simple would be located in 6a and Passé Antérieur in 6b. Clearly both tense forms in (29) belong to a system different from the one regulating the relation between the a-forms and the corresponding b-forms in Table 7.1. So the question is: how to explain the peripheral and marginal position of the two missing forms in terms of their belonging to a different system that has been replaced by the reshuffle illustrated in Table 7.1? In a ternary approach to tense, De Swart (1998) opts for appealing to aspectual classes available at S0 .14 In other words, De Swart makes the proper application of the PS dependent on the terminative marking of S0 : the PS is for her a tense form allowing only for a terminative predication and the Imparfait is marked by requiring a durative one. This means that two coercive operations are necessary for obtaining the right result: one for the PS in (30) and one for the Imparfait in (31). (30)

a. Jeanne écrivit une lettre. (= (29a)) ‘Jeanne wrote/has written a letter.’ du piano (lors d’une réunion). b. Jeanne joua (...) Jeanne play-PS piano ‘Jeanne played/has played the piano (during a gathering).’ PAST (Cdur→term (Jeanne play the piano))

(31)

une lettre. a. Jeanne écrivait Jeanne write-IMPF a letter ‘Jeanne wrote/was writing a letter.’ PAST (Cterm→dur (Jeanne write a letter)) du piano (lors d’une réunion). b. Jeanne jouait Jeanne play-IMPF the piano (during a gathering) ‘Jeanne was playing/played the piano (during a gathering).’

In (30b) the operator Cdur→term must upgrade the “aspectually weak” predication to a level at which it expresses terminativity; in (31a) the operator Cterm→dur must switch off the terminative force of a predication in order to make it durative. This analysis of the Passé Simple is incompatible with the compositional approach in the preceding chapters. In my view, coercion may be only used as a last resort but apart from that, there is a binary resort available. As argued, the aspectual information contributed by the internal and/or external arguments below the node S0 is connected to the verbal index α and this information as a whole is bound by the existential quantifier ∃k introduced by IMP or PERF. Compositionally this means that the clause k  j for IMP and the clause k ≺ j 14 I am using the terms dur(ative) rather than h(omogeneous) and term(inative) rather than

e(vent). De Swart’s position in 1998 is also part of Molendijk et al. (2004).

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for PERF are neutral as to aspectual information in the sense that they do not change the S0 -information about k but give it a place with respect to factors belonging to higher levels of tense structure and not to S0 . When speakers use the IMP-form, they express indeterminacy about k but they do not change k and the same holds for PERF: this operator requires full actualization independent of whether the eventuality index k is [–T] or [+T]. Definition (32) appears in Verkuyl (2008:226) as a characterization of the French Passé Simple. (32)

PS

:= λϕ∃k[ϕ[k] ∧ k < a]

The idea behind this was to provide an anchor point a somewhere in the past contextually identified in the preceding discourse to which k is to be directly related, doing justice to what Grevisse observed about the Passé Simple as quoted in footnote 12 on page 236. Of course, there is a difference in interpretation between (30a) and (30b) when they occur in a discourse, say as part of a story, but this difference is simply due to the fact that a speaker chooses the words to faithfully report what happened. If Jeanne had done otherwise than just writing one letter, the speaker should have continued with Jeanne écrivit des lettres ‘Jeanne wrote/has/had written letters’ which is durative but reported in the PS. There is no need to coerce because taking the writing of one letter or the writing of more letters as a complete whole is the essence of the PS and given (32) that is done by anteriority between k and a. The anteriority relation provides for the sense of complete termination independent of the terminative or durative nature of k. In both (30a) and (30b), k is not related to the present domain of speaker and hearer i either directly or indirectly, although one may not exclude that a happens to be located in i a itself. The direct orientation of k on a rather than on an anchor directly related to i ◦ n, however, remains the essential ingredient causing the interpretation of presenting k as a whole. Definition (32) does not account for the fact that in Paul knocked on the door. He entered the room, Paul’s entering the room follows his knocking on the door. Such an account is to be given at the level of discourse organization and the study of discourse has shown that this account requires specific discourse operators. There are adverbials available for identifying a, for example puis ‘then’ or un peu plus tard ‘a bit later’, as discussed extensively in Bras et al. (2001) and Borillo et al. (2004). Given the scope of the present study, it is not necessary to relate the aorist to these operators any further. Definition (32) is also compatible with a definition which makes the French Passé Simple into a tense essentially expressing what the Greek aorist

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Indicative expresses, as underscored by CGCG in their characterization (6) on page 22 of Chapter 2. In (32), the tense structure construed and required by the opposition between PRES and PAST is absent, from which it follows that PS is to be located outside the binary system. This means that there is no connective for relating a to a fleeting point n  in the past, because this point is not made available in the system of which PS takes part. A proposal to encapsulate the Passé Simple in the binary tense system is Lefeuvre (2014). This proposal assumes the binary organization as given in Table 7.1 but considers the aorist an “objectifying” function which allows for presenting the eventuality as a block, without a preparatory phase, internal or consecutive phase.15 She rejects definition (32) in favour of (33). (33)

PS

:= λϕ∃i ∃j∃k[ϕ[k] ∧ k = j ∧ j  i ∧ i < n]

Crucial in (33) is that it is based on a ternary partition of the third opposition into k  j vs k ≺ j vs k = j, as shown in Table 7.2.16 It is obtained by Table 7.2 Lefeuvre’s proposal for harbouring the aorist in a binary system Operator

Lefeuvre

Binary Tense

IMP

k j k< j k= j

k j k≺ j k t and |=t  p). d. Gp: it will always be the case that p. That is: |=t Gp iff ∀t  ( t  > t and |=t  p).

The past operator P existentially introduces a time t  before the anchor point t at which p is true whereas the past operator H says that for all t  before t the proposition p is true. These operators are temporal in the sense that they are defined as operating on actualized temporal units t  positioned before n. The other two tense operators mirror modal logical operators: F p is the tenselogical translation of ♦ p and Gp the temporal counterpart of  p. In this way,

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it has become possible to render Aristotle’s problem into a temporal one and to deal with the sea-battle problem in terms of (alleged) temporal operators. In the philosophical literature, one can find formulas in which the tense operators are combined with modal operators, as, for example, in P p ⇒ P p, the axiom discussed previously founding the notion of settledness and F p ⇒ F p (if it will be the case that p occurs, it is necessary that it will be the case that p occurs). Prior accepted this axiom in adopting the Peircian position. As said, the philosophical discussion about future contingencies and, more generally, about the relation between modality and time, is primarily based on the ternary division of time into Past-Present-Future, as should be clear from the title of Prior (1967). This raises the question of how to deal with the opposition between the two positions with regard to future contingencies discussed in a binary framework. The only proper answer to this question is to compare Prior’s ternary tense logic and its operators P and F to the operators of the binary tense system in a strictly compositional linguistic-semantic approach. This can be done with the help of Table 8.2 used earlier in Verkuyl (2008) in a section in which Te Winkel’s binary approach is compared to Prior’s ternary approach (2008:47–50). Prior’s tripartition is made visible in the left column. Table 8.2 Prior and Te Winkel Prior

Tense forms

Pϕ P Fϕ P Pϕ P F Pϕ

Mary wrote the letter Mary would write the letter Mary had written the letter Mary would have written the letter

ϕ Fϕ Pϕ F Pϕ

Mary writes the letter Mary will write the letter Mary has written the letter Mary will have written the letter

Te Winkel PAST (ϕ) PAST ( POST )(ϕ) PAST ( PERF )(ϕ) PAST ( POST )( PERF )(ϕ) PRES (ϕ) PRES ( POST )(ϕ) PRES ( PERF )(ϕ) PRES ( POST )( PERF )(ϕ)

It does not include an operator for the present tensed sentence ϕ standing for Mary writes the letter. Assuming that Prior’s ϕ at the left-hand side stands for the tensed sentence Mary writes the letter, F Pϕ should be read as ‘It will be the case at some time t (t > n) that it was the case at t  (n < t  < t) that ϕ (= Mary writes the letter) was true’. Note that, for English, this requires that ϕ be interpreted as ‘Mary is writing the letter’ and that this requirement is exactly what led to a discomfort among linguists focussed on tense and aspect in the early seventies with respect to evaluation at a point of time debouching in interval semantics and event semantics.

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Actually, the same worry should apply to the operators P and F in the formulas in the left column of Table 8.2: it is not clear how a tense form of a sentence is accounted for. Of course, one should not expect such a thing from philosophers, but linguists have the task of accounting for modality in natural language sentences. Therefore it is necessary to point out that Table 8.2 shows that Te Winkel’s binary proposal presents Prior’s system in a linguistically more appropriate form by providing a present tense operator PRES introducing a present tense form expressed by a verb and a past tense operator PAST doing the same for a past tense form and by setting the Priorean P and F free from their task to stand for a tense form. In other words, the ϕ following the operators PAST and PRES should be seen as tenseless propositions as opposed to Prior’s ϕ which is supposed to express tense. More differences are made clear in the quote taken from Verkuyl (2008:47f.), all to Prior’s disadvantage. At first sight, the upper part of Table 8.2 suggests that Prior and Te Winkel have developed the same sort of machinery for the Past tense forms. However, the suggestion raised by P = PAST, F = POST and P = PERF is misleading. In the Te Winkelian binary system sketched above PAST has a different status from POST and PERF: it is always in front position and its type-logical status differs from the other two operators. In sentences like Mary had written the letter the tense form had is to be analyzed as PAST +have. For Prior this translates as PP, for Te Winkel as PAST ( PERF ). Te Winkel is more adequate in differentiating between the two operators. Prior’s system turns out to be misleading, in the sense that P does not pertain to a constant value. Table 8.2 also shows that where Prior has the problem of analyzing both Simple Past and Present Perfect as P, the binary system yields a proper distinction between the Imperfect form, which is a PAST(IMP(ϕ))-configuration, and the Present Perfect form which is a PRES(PERF)(ϕ)-configuration.

To this it should be added that SYN and IMP as operators are left out in the right-hand column to make the comparison between the first and third column more direct. The binary approach explains the present tense forms in the PRES part of the table and it treats ϕ as the tenseless S0 -predication which ϕ factually is in Prior’s system under the guise of being presented as a tensed proposition. I have repeated Table 8.2 here because it shows exactly the difference between a ternary tense system with operators and a binary one. In my view, to the profit of the binary one when it comes to accounting for interpretation of sentences in natural language. This is may be felt differently in, say, computer science and in other domains where branching structure is to be checked or investigated. Looking at a straight line drawn on a paper with a dot marked A on the left-hand side and a dot marked B on the right-hand side, we allow ourselves to say metaphorically

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that B comes later than A and that by following the line we are not yet at B and that B lies in the future of A. This also holds for Figure 8.1, where we can easily say that w1 is later than n. The only thing we have to do is to imagine ourselves moving forward on the line and knowing that there is a final point w1 on the line from n to w1 . In fact, we operate then on a metalinguistic level by loading atemporal representations with temporality. The linguistic reality, however, is that binarily ♦ is more appropriate as a modal operator in an unactualized present or past domain expressing a ‘perhaps’ caveat because in using natural language sentences there is no separate (already) temporal domain for talking about the future. Logicians using Prior’s system have quite different goals in mind from linguists who aim at accounting for interpretations of natural language sentences used in a discourse, where natural language is the object language. In other words, in dealing with a compositional account of tense, mood and aspect, the representations in the three bottom lines in the right-hand column of Table 8.2 should be used instead of their counterparts F and P at the left-hand side. 8.2.3 Modal Base and Accessibility The notion of modal base is rooted in the assumption that a proposition can be defined as a set of possible worlds in which this proposition is true. (18)

a. Mischa may play KV 467 in William’s church on Sunday afternoon. b. M(w) = {Mischa has properly prepared his part, Mischa is physically in a good condition, The orchestra is well prepared, Mischa has played successfully before with the orchestra, . . . } c. O(w) = {Mischa is not ill on Sunday, The piano is in a sufficiently good condition, The conductor has sufficiently rehearsed, No airport strike in China will prevent Mischa from flying back, . . . }

The basic idea is that someone who says (18a) must have previous knowledge in the form of propositions concerning Mischa, churches in their current use, Mozart, etc., organized in some form available to the speaker of (18a). M(w) in (18b) is the modal base, that is, the set of facts in a given world w relevant to the interpretation of (18a). M can be seen as a function from the set W of possible worlds mapping to 1 those propositions which are considered true by the speaker s based on the available knowledge of s, and mapping to 0 those which are considered false.9 9 I am here following Portner (1998) in giving a concrete example of a sentence in natural lan-

guage in order to explain the notion of modal base developed in Kratzer (1981;1991b). It is natural to speak about M and M(w) as sets.

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As to O(w) in (18c), this parameter accounts for outside factors that need to go right before Mischa played KV 467 in William’s Church on Sunday afternoon can be said true after the actual performance. The set O(w) is ordered by the relation < O,w , where O is the ordering source for M. O is a function from W to sets of propositions ranking the propositions in a scale with the best worlds in the top of the ranking dependent on M. The expression w  < O,w w  means that w is ranked as a better world than w with respect to the facts accessible from w. Table 8.3 is given in Kaufmann et al. (2006). It shows how properties of a modal base and ordering source can be expressed in terms of accessibility relations between worlds. The latter have been extensively studied in the formal Table 8.3 Modal base and accessibility relations Modal Base

Accessibility relation

consistency M(w) = ∅ realism w ∈ M(w) total realism M(w) = {w} positive introspection w  ∈ M(w) ⇒ (M(w ) ⊆ M(w)) negative introspection w  ∈ M(w) ⇒ (M(w) ⊆ M(w  ))

seriality ∀w∃w (w Rw  ) reflexivity ∀w(w Rw) identity ∀w(w Rw  ⇔ w = w ) transivity ∀ww  w ((w Rw  ∧ w  Rw  ) → w Rw  ) euclidity ∀ww w ((w Rw  ∧ w  Rw  ) ⇒ w  Rw  )

Axiom ϕ ⇒ ♦ϕ ϕ ⇒ ϕ ϕ ⇔ ϕ ϕ ⇒ ϕ ♦ϕ ⇒ ♦ϕ

logical literature on modality and have led to different systems of accessibility by combining different conditions: different combinations of accessibility relations lead to a different sort of a modal base. I will follow Kaufmann et al. (2006) in looking at possible restrictions on the interpretation of SYN and POST. A favorite combination of accessibility relations in the domain of epistemic modality is the one in (19). (19)

a. R is transitive: if wRw  and w  Rw  , then wRw  b. R is euclidean: if wRw  and wRw  , then w  Rw  c. R is self-reflexive: if wRw , then w Rw  if and only if wRw 

This has to do with the fact discussed in Geurts (2005:388f.) that knowledge has not only the property of Positive Introspection as expressed by (19a): if  p, then  p (‘if you know something you know that you know that’).

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Knowledge also has (not uncontroversially, but it is generally accepted) the Euclidean property of Negative Introspection: if ¬ p, then ¬ p (‘if there is something you do not know (for certain), then you know that’). Self-reflexivity follows from (19a) and (19b). It is up to the theorist to decide which set of accessibility relations accounts properly for the empirical facts. Table 8.3 is interesting in the present context because it gives two conditions that contain the term realism. This is so close to the linguistic term realis that one cannot escape from comparing the two notions. To avoid the danger of drowning in the vast literature on philosophical realism, I will make use of Miller (2019) which provides a workable characterization: Generic Realism: a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H -ness is . . . independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on.

This statement is compatible with the mentalistic framework of the present binary approach because it does not (seem to) require that the properties of F, G and H are fixed once and for all. It allows for seeing the mental lexicon of an individual speaker or hearer as a knowledge base in which the names F, G and H are theoretical terms of a theory about the world, as proposed in Verkuyl (1972b;1978a) and extended in Verkuyl (2000;2013). That is, a property F can be seen as independent of an individual speaker using the word/term F even though the meaning assigned to F may change due to new insights into how the property F should be understood. The independence consists of seeing F as a set “out there” to which a, b and c belong at a certain time t, but it allows for different extensions (and hence intensions) due to changes in the knowledge base so that, say, b  ∈ F at a later time t  . This mentalistic interpretation of General Realism allows for accounting for communication between speakers with different levels of knowledge (causing a lot of trouble), for updating our knowledge in a discourse by new information, etc. It also accounts for the depth of the controversies between supporters and opponents of Donald Trump. An utterance at n is to the best of the knowledge of a speaker s. If not, Grice manages to remind s of this obligation. What we do not change as a speaker is an n-place predicate into an n − 1or n + 2-predicate in order to prevent obscuring the relational character of a verb for the hearer. This does not only hold for verbs but also for prepositions and in fact for all words expressing a relation. These n-place relations are too important for the consistency of the lexical knowledge that we use while talking, to allow for changes in the degree of n-hood. This strengthens the idea

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that we need an actual world as a solid base for realism. Our excursions to other worlds are on the basis of what we have learnt so far and what is stored in our mental lexicon. Fictitious excursions to possible worlds in which elephants may speak, rocks may open and princesses may sleep for years without bedsores, require epistemically minor monadic operations on existing knowledge: either we mark the noun elephant lexically as [–HUMAN] and this means that we know that it follows that elephants and rocks cannot speak, or we mark the verb speak as [+HUMAN] by restricting the domain of entities which may be the external argument so as to exclude elephants and rocks. So one has only to change a minus-feature into a plus-feature or vice versa and one has already entered a possible world deviating from the one that counts as actual. With respect to excursions into the future (i.e. the set of possibilities available at n), Table 8.3 contains two interesting conditions, one under the heading of realism which requires by w ∈ M(w) that w be a member of the modal base M(w) having access to itself. However, there is also a stronger form of realism, total realism, which demands that all worlds w in M(w) are w itself. This says that the modal base M(w) has only a singleton member, say w0 , which is the actual world. This means that the truth of an indicative sentence is relative to the possible world w0 in which the valuation of such a sentence takes place, (i.e. in i a ), not depending on other possible worlds. In this way, the strict separation between indicative/realis and subjunctive/potentialis-irrealis is formally accounted for as far as the actualized part of the domain i  or i  is concerned. It provides a solid ground for the distinction between the actualized and non-actualized part of these domains. The restriction of the modal base to just the actual world w0 is in line with what many logicians assume in the Priorean form P p ⇒ P p which says that something occurring in the past is necessarily (known to be) in the past. This comes close to “the unalterability of whatever has already happened” which makes the truth-value of all statements about the past “ineluctably settled, though we may not know in which way”, as Ackrill (1965:122 and 139) formulated.10 8.2.4 Adapting the Connectives Introduced by SYN and POST What does it say for two worlds w and w  to be historically equivalent at a certain time t? In tense logic, it means that w is just like w at all times t  10 A problem with the formulation of this axiom in Prior’s framework is that it cannot be used in

the binary framework because the Prior operator P is intended to cover past (and not present perfect) sentences, whereas the axiom should also hold in the present domain i restricted to i a as well as to i  restricted to i a .

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preceding and including t but it allows w and w to be different at a time later than t. Due to the fact that worlds and indices are already connected before PRES and PAST apply, it is necessary to define historical equivalence of possible worlds in terms of the points defined in Chapter 6 as the leftmost point (a) or the rightmost point r (a) of an index a. This is done in (20).11 (20)

a. b. c. d.

∀ ∀w w ∼ w (reflexivity) ∀ ∀w∀w (w ∼ w → w ∼ w) (symmetry) ∀ ∀w∀w  ∀w ((w ∼ w ∧ w  ∼ w ) → w ∼ w ) (transitivity) ∀ ∀  ∀w∀w ((  < ∧ w ∼ w ) → w ∼  w )

The expression w ∼ w  says that w and w  are historically equivalent at . The axioms (20a) – (20c) warrant that ∼ is an equivalence relation. Axiom (20d) says: if w and w  are historically equivalent at , then they are so at (an earlier)  . The conditions in (20) ensure that all worlds in an ∼ -relation are indiscernible from each other from the first point up to and including the last point . In this way, the conditions in (20) account for the restriction of j to i a in the case of SYN. To connect worlds w to indices and points in indices, it is useful to define a function w :  −→ W , that is, a function from indices to worlds. This makes w of type i, s. In other words, w(a) is the world w of a (i.e. the world w in which index a occurs), written as wa . It means for k that wk (i.e. the world in which k occurs), is of type s. Given this, the definition of the ∼ -relation can be expanded as: (21) a1 ∼ a2 := (a1 ) = (a2 ) ∧ r (a1 ) = r (a2 ) ∧ wa1 ∼ wa2

This says that the ∼ -ordering between the indices a1 and a2 ensures that the indices have the same length and that the world in which a1 occurs respects the linearity imposed by ∼ in the same way as the world in which a2 occurs. This provides the historical equivalence of wa1 and wa2 for the indices a1 and a2 . It is now possible to redefine the connectives defined for PERF and IMP in earlier chapters at a more finegrained level, as in (22): (22)

PERF : k ≺ α := (α) ≤ (k) ∧ r (k) < r (α) ∧ wk ∼r (k) wα replaces (5a) on p. 56. b. IMP: k  α := (α) ≤ (k) ∧ r (k) ≤ r (α) ∧ wk ∼r (k) wα replaces (5b) on p. 56.

a.

11 The formalism used in the present section is due to Reinhard Muskens (pers. comm., on top of

the use of his NASSLLI-course on Multi-Modal Logic in 2016 which treated and simplified the formalism used by Kaufmann et al. for sharpening the notion of settledness). The formalism of the 2016 course has been adapted so as to meet the demands of a binary tense approach without a future tense operator.

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This warrants that k and j in the clauses k ≺ j and k  j have the same image under the function w. Note that possible worlds enter the picture as soon as composition proceeds on the basis of IMP(S0 ) or PERF(S0 ): it is necessary to connect the introduction of the index k directly to the world(s) in which k occurs. It should be emphasized that the underinformation attributed to the connective ‘’ remains an essential ingredient of the aspectual definition of IMP . The next step after (22) is to redefine the connective ‘’ introduced by the SYN operator in (23a). (23)

a. SYN  λϕλα∃j[ϕ[j] ∧ j  αa ] replaces (6) on p. 57 b. j  αa := j ∼r (j) αa by (21) c. j ∼r (j) αa ≡ (j) = (αa ) ∧ r (j) =r (αa ) ∧ wj ∼r (j) wαa

This redefinition ensures is that the worlds of j and αa are equivalent up to and including their end point.12 It also ensures that the present domain j of k is restricted to αa . With the IMP-clause k  j as its input, the result of applying SYN is made visible in (24). (24)

a. SYN(IMP(S0 ))  . . . k  j ∧ j  αa . . . b. ( j) ≤ (k) ∧ r (k) ≤ r ( j) ∧ wk ∼r (k) w j ∧    ( j) = (αa ) ∧ r ( j) = r (αa ) ∧ w j ∼r (j) wαa   

The introduction of the two clauses in (24a) is now materialized in (24b) by combining (22b) with (23b). It is not necessary to include (24b) in a representation itself because the definitions (23b) and (21) warrant that the information in (24b) is available. As to the introduction of POST, the division of the present domain i into i a and i ♦ is based on the following structural order: (25) (ia ) = (i) ∧ r (ia ) = (i♦ ) ∧ r (i♦ ) = r (i)

This defines the fleeting point n as uniting the last actualized point i a with the first unactualized point of i ♦ . The operator POST covers a variety of modal operators as discussed in Section 8.1.1. Some of them, for example, must, require inspection of all possible worlds and therefore it will be necessary to make the universal quantifier part of the definition as in (26a) where POST is subscripted with a . 12 More generally, one may require the axiom schema (i) ∀αβ(α  β → (A[α] ↔ A[β])). This

warrants that when α and β speak about the same index and their worlds are equivalent for that whole interval, they make the same atomic statements A true.

8.3 The Proof of the Modal Pudding . . . (26)

279

a. POST  λϕλα∀j(j ∼ = α♦ → ϕ[j]) b. POST∃  λϕλα∃j[ϕ[j] ∧ j ∼ = α♦ ] c. j ∼ = α♦ ≡ j ∼( j) α♦ d. a1 ∼(j) α♦ := (j) = (α♦ ) ∧ r (j) =r (α♦ ) ∧ wj ∼(j) wα♦

However, there are more “modest” forms of modality and in those cases, for example, may and can, the POST∃ -operator introduces two conjuncts in (26b). The different uses of POST will be illustrated in Section 8.3. At this point, the clause (26c) needs to be explained. A POST operator requires a different equivalence relation from the one in SYN. Therefore both versions of POST are defined by the connective ‘∼ =’ which differs from the -connective introduced by SYN by positioning j in α♦ as made clear by (26d). The definition of the connective in (26c) ensures that the relation expressed by POST looks at the first point of j, which is the final point of i a by (21) as defined in (26d): after the application of PRES or PAST, j and α♦ are (left-)equivalent from the left-most point ( j) to the endpoint r (α♦ ). With IMP as input again, the result of applying POST∃ is demonstrated in (27b). (27)

a. POST∃ (IMP(S0 ))  . . . k  j ∧ j ∼ = α♦ . . . b. (j) ≤ (k) ∧ r (k) ≤ r (j) ∧ wk ∼r (k) wj ∧    (j) = (α♦ ) ∧ r (j) ≤ r (α♦ ) ∧ wj ∼(j) wα♦   

The clause r (i a ) = (i ♦ ) in (25) is crucial for interpreting the clause ( j) = (α♦ ) in (27b): it offers the possibility for the operator to include the moment of speech in the range of worlds to be inspected. This will play a role in the analysis of the operators to be discussed in the following section. 8.3

The Proof of the Modal Pudding . . .

The first check will be done with respect to (2a) which reappears here as (28a). (28)

a. b. c. d. e. f.

Olga is thuis. (= (2a)) Olga is at home. PRES ( SYN ( IMP (S0 ))) ∃j∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ j  ia ∧ i ◦ n] PRES ( POST ( IMP (S0 ))) ∀j[j ∼ = i♦ → ∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ i ◦ n]]

Representation (28d) accounts for the realis-interpretation of (28a,b). As defined in (23b), the clause j  i a ensures that the worlds of j and i a are equivalent up to and including the endpoint r (i a ). This means that the existential

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introduction of j is reduced to just one j. Representation (28f) accounts for the irrealis-interpretations of positive sentences in the Simple Present expressing maximal modal force in the sense of ‘Olga must be at home, it cannot be otherwise’. It also accounts for the Dutch habit of using the Simple Present for projecting forward as in Morgen ben ik thuis ‘lit: Tomorrow I am home’. The difference between the representations in (29) and (3) is more complex because both require a doubling of the SYN- and POST-representations. (29)

a. Olga is niet thuis. (= (3a)) b. Olga is not at home. c. PRES(SYN(¬(IMP(BE - AT- HOME(k)(o) ∧ k = Ran(id)))))  . . . ∃j¬∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ j  ia ∧ i ◦ n] d. PRES(¬(SYN(IMP(BE - AT- HOME(k)(o) ∧ k = Ran(id)))))  . . . ¬∃j∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ j  ia ∧ i ◦ n] e. PRES(POST(¬(IMP(BE - AT- HOME(k)(o) ∧ k = Ran(id)))))  . . . ∀j[j ∼ = i♦ → ¬∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j]] f. PRES(¬(POST(IMP(BE - AT- HOME(k)(o) ∧ k = Ran(id)))))  . . . ¬∀j[j ∼ = i♦ → ∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j]]

Representation (29c) expresses that, according to the speaker, Olga is not at home, because the worlds of k, j and i a are all equivalent. This brings the speaker s into a position of seeing just one actualized j at n. Representation (29d) accounts for the interpretation in which s concludes that Olga cannot be at home by expressing ‘I do not see a j in which Olga is at home’. This is a natural interpretation in a situation in which we just rang the doorbell and the door remains closed and (29a) is said by a speaker who knows that Olga always opens the door when someone rings the bell. Apart from the difference concerning SYN, there is a difference concerning POST . The POST  -interpretation of the Dutch (29a) expressed by (29e) is that for all I know (in all worlds accessible to me in i♦ ) there is no k in which Olga is at home at k. This is the strong modal interpretation of (29a). The weaker interpretation, accounted for in (29f), is that the speaker cannot warrant that Olga is at home at k because it is not the case in all accessible worlds w Olga is at home at k. The weaker interpretation has another version made available by definition (26b) with existential quantification: ∃ j¬∃k. For English, the modal use of the present tense is much more restricted, as discussed in earlier chapters. The lexical definition of must in (30d) is the same as the one for POST . In my view, this is justified by the fact that POST and MUST are to be interpreted here as epistemic operators not as operators expressing metaphysical modality.

8.3 The Proof of the Modal Pudding . . . (30)

a. b. c. d. e.

281

Olga moet thuis zijn. (= (9a)) Olga must be at home. PRES ( MUST ( IMP (S0 ))) must  λϕλα∀j[j ∼ = α♦ → ϕ[j]] ∀j[j ∼ = i♦ → ∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ i ◦ n]]

The definition of must makes the strength of the claim that Olga is at home dependent on the number of ( j, wj )-pairs accessible to the speaker. The representations of (9a) and (30a) are the same except for replacing j  i♦ by j ∼ = i♦ . Where POST is the covert operator, MUST is the overt one.13 Kaufmann et al. (2006) observe that with a universal quantifier as assumed for must in (35d) a sentence like (31a) entails (31b). (31)

a. It must have rained overnight. b. It rained overnight. c. No, it didn’t rain, ten minutes ago they flushed the street.

According to them, this is not permitted: the water perceived may be due to another source and universal quantification overlooks relevant possible worlds without any rain, among which the one evoked in (31c). From a mentalistic point of view, Kaufmann et al. (2006) miss the need to see (31c) as a correction on the use of the universal quantifier invoked by must: the speaker of (31a) has simply chosen the wrong modal auxiliary for modifying S0 and should have used a modal auxiliary with less modal force than must, for example, may. The lexical definition in (32c) treats may as a POST operator with an existential quantifier. (32)

a. b. c. d. e.

Olga kan thuis zijn. (= (5a)) Olga may be at home. may  λϕλα∃j[ϕ[j] ∧ j ∼ = α♦ ] PRES ( MAY ( IMP (S0 ))) ∃j∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k  j ∧ j ∼ = i♦ ∧ i ◦ n]

Due to the clause r (i a ) = (α♦ ) in (25) and (26d), there is a range from n (= r (i a ) to r (i ♦ ) to which (32a,b) may apply. That is, Olga may be at home now, but the sentence may also pertain to i ♦ , the unactualized part of the present domain. This is in line with what was said about the interpretations of may in (5), but in a more precise way. Condoravdi (2002) analyzes terminative predications occurring with may or might and combined with the auxiliary have, as in (33). 13 If MUST is stronger than POST, this is most probably due to the fact that must is much closer

to a fully metaphysical interpretation than an epistemical one because it appeals to settled knowledge shared in a community.

282 (33)

Tense, Mood and Aspect a. b. c. d. e. f.

That house at the corner may collapse. Dat huis op de hoek kan instorten. ∃j∃k[COLLAPSE(k)(h) ∧ k = d(Ran(su)) ∧ k  j ∧ j ∼ = i♦ ∧ i ◦ n] That house at the corner might have collapsed. Dat huis op de hoek zou kunnen zijn ingestort. ∃i ∃j∃k[COLLAPSE(k)(h) ∧ k = d(Ran(su)) ∧ k ≺ j ∧ j ∼ = i♦ ∧  i < i ∧ i ◦ n]

Condoravdi says that the possibility expressed by may in (33a) is unambiguously from the perspective of the present about the future and the modality can be either epistemic of metaphysical. Epistemic modality has to do with knowledge or information of agents. Metaphysical modality has to do with how the world may turn out, or might have turned out. (2002:61)

I disagree with two important ingredients attributed to modality in this quotation. The first is that modality is not a perspective about the (temporal) future but rather about the unactualized i ♦ part of the present domain i. The operator MAY in MAY(ϕ) prevents ϕ from being considered fully actualized at n by the speaker due to the fact that the clause k  j in (33c) and the clause k ≺ j in (33f) are connected to i ♦ preventing (33a,b) from pertaining to an actual collapse at n. In my view, epistemic modality concerns the degree of certainty about the truth of the formula ∃ j∃k . . . expressed by the speaker. The second disagreement concerns the idea that sentences like (33a) may express metaphysical modality. In a discourse, there is no room for both a human and a godlike perspective in one sentence. A speaker saying (33) may be simply wrong and may be corrected by the hearer who has better information available. Or the speaker may not be convinced by the reaction of the hearer even when an appeal to objective truth has been made by the latter. Given these considerations, I think that the representation in (33c) correctly represents the meaning of (33a,b). What should be added to (33f) is the idea that the use of might have instead of may in (33f) brings the speaker back to an earlier time at which several options were discussed about what could happen with the house at the corner. Representation (33f) says that in the past domain i  there is a then-present domain j of k located in i♦ , no information being available about the factual actualization of k itself. In the case of an extension, for example by adding an adverbial as in . . . might have collapsed then, the hearer cannot even determine whether the house has since collapsed: the sentence is about a possibility at n  then available as That house at the corner may collapse. In general, a sentence offering a branching structure in the past at n  can never express its later actualization on one of the branches itself.

8.3 The Proof of the Modal Pudding . . .

283

A final remark on may and must and metaphysical modality is relevant here in view of what I said earlier about the lexicon as structuring our modal base as a theory about the actual world. It is easy to see 1 + 1 = 2 as expressing a universal truth but modal auxiliaries restrict truth to certain knowledge domains. (34)

a. Here it reads 1 + 1 = 1. That must be 2, of course. b. No, no, 1 + 1 may also be 1; in Boolean algebra it even must be 1.

In (34a), speaker s1 appeals to metaphysical modality (in the sense of suggesting an established objective truth) and so the universal quantifier for must is appropriate for expressing certainty. Yet the hearer of (34a) uses may as the speaker s2 of (34b) introducing a world in which 1 + 1 = 1 counts as true. In this way, s2 relativizes the appeal by s1 to metaphysics by pointing out that not all possible worlds are captured by must. The set M(w) of possible worlds w in (34a) is restricted to a domain different from the one assumed in (34b). Broekhuis and Verkuyl (2014) argues that the auxiliaries zullen in Dutch and their English counterparts will and shall are to be dealt with as strictly modal auxiliaries, defined as in (35d).14 (35)

a. b. c. d. e.

Olga zal thuis zijn. Olga will be at home. will  λϕλα Q ≈1 j[j ∼ = α♦ → ϕ[j]] PRES ( WILL ( IMP (S0 ))) Q ≈1 j∃k[j ∼ = i♦ → BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k ≺ j ∧ i ◦ n]

In the present context, the generalized quantifier Q ≈1 j is taken to mean ‘practically all’ and it is given the structure of the POST -operator defined in (26a) with a universal quantifier by defining will as in (35c), articulating the sense that comes close to expressing universal quantification over worlds. The strong conviction on the side of the speaker is that Olga will be at home (now or in the future): (35e) is then due to not including worlds that are not welcome, appealing to a mechanism described in detail in Verkuyl (2000;2013) In fact, this comes down to using the generalized quantifier as a universal one 14 That definition restricted the number of worlds in the modal base to a certain percentage of

all the worlds accessible. In other words, the idea was that between ∃w and ∀w there is room for some value ‘≈ 1’ bringing the quantifier Q≈ ‘nearly all’ close to ∀. That idea makes use of the theory of generalized quantification that has established itself in formal semantics. The symbol Q≈1 abbreviates the representation used in Broekhuis and Verkuyl (2014). Due to now having two connectives available in the clauses involving j and i, I will propose an alternative in which one can do without generalized quantifiers in the representation itself. I will not repeat the arguments supporting the ‘only modal’-claim of Broekhuis and Verkuyl (2014) here and refer to that paper.

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analogously to interpreting Politicians are unreliable stereotypically as ‘all politicians are unreliable’. In the case of (35a,b) it means that the speaker does not see (or wants to ignore) any world in which Olga is not at home. The difference between ∀ j and Q ≈1 is captured by the phrase deo volente in the Dutch counterpart of sentences like I will be in New York tomorrow. As discussed in Chapter 3, Dutch allows for more bluntness at this point by saying Morgen zit ik in New York ‘lit: tomorrow I sit in NY’, in which case the speaker prefers to quantify universally over possible worlds skipping worlds with plane crashes or COVID-19 restrictions. However, there is another interpretation of (35a) in which zullen ‘will’ approaches the meaning of may as given in (32c). That is also the case in the Dutch negative sentence (36a) and its English equivalent (36b): they have two interpretations, a strong modal one in (36d) and a weak one in (36f). Both in (35a) and in (36a) this has the effect of suggesting a possibility. (36)

a. Olga zal niet thuis zijn. b. Olga will not be at home. c. PRES(WILL(¬(IMP(S0 )))) d. Q ≈1 j[j ∼ = i♦ → ¬∃k[BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k ≺ j ∧ i ◦ n]] e. PRES(¬(WILL(IMP(S0 )))) f. ∃j∃k[[j ∼ = i♦ ∧ BE - AT- HOME(k)(o) ∧ k = Ran(id) ∧ k ≺ j ∧ i ◦ n]]

Representation (36d) expresses that the speaker does not (want to) see a k in which Olga is at home: (36a,b) counts as true for a speaker who acts to the best of his or her knowledge (i.e. without consciously ignoring relevant worlds). The interpretation represented in (36f) leaves open a j in which Olga is at home and can be seen as suggesting a possibility. At this point, it is time to do what was promised on page 268 in the discussion of Aristotle’s sea battle argumentation: to give a representation of the sentences in (14). (37)

a. Tomorrow there will be a sea-battle. b. PRES(TOMORROW(WILL(IMP(S0 )))) c. ∃γ ∃δ Q ≈1 j[j ∼ = i♦ ∧ D(γ ) ∧ D(δ) ∧ δ = s(γ ) ∧ O(i, γ ) → ∃k∃x[SB(x) ∧ BE(k)(x) ∧ k = Ran(id) ∧ |k| ≤ |SB| ∧ k ≺ j ∧ γ ◦ n ∧ i ◦ n]] d. ∃j∃k∃γ ∃δ∃x[D(γ ) ∧ D(δ) ∧ δ = s(γ ) ∧ O(i, γ ) ∧ SB(x) ∧ BE(k)(x) ∧ k = Ran(id) ∧ |k| ≤ | SB| ∧ k ≺ j ∧ j ∼ = i♦ ∧ γ ◦ n ∧ i ◦ n]] e. ∃j∃k∃γ ∃δ¬∃x[D(γ ) ∧ D(δ) ∧ δ = s(γ ) ∧ O(i, γ ) ∧ SB(x) ∧ BE(k)(x) ∧ k = Ran(id) ∧ |k| ≤ | SB| ∧ k ≺ j ∧ j ∼ = i♦ ∧ γ ◦ n ∧ i ◦ n]] f. ∃γ ∃δ∀j[j ∼ = i♦ ∧ D(γ ) ∧ D(δ) ∧ δ = s(γ ) ∧ O(i, γ ) → ∃k∃x[SB(x) ∧ BE(k)(x) ∧ k = Ran(id) ∧ |k| ≤ |SB| ∧ k ≺ j ∧ γ ◦ n ∧ i ◦ n] ∨ ¬∃k∃x[SB(x) ∧ BE(k)(x) ∧ k = Ran(id) ∧ |k| ≤ |SB| ∧ k ≺ j ∧ γ ◦ n ∧ i ◦ n]]

8.3 The Proof of the Modal Pudding . . .

285

Some remarks are in place here. Firstly, the strong modal interpretation of (14a) is given in (37c), the weak one in (37d). The negative sentence (14b) is represented as (37e). The representations are restricted to the interpretation based on the overlap O(i, γ ). As shown in Chapter 6, interpretations with the clause O(i, k) or O(i, j) are also available. Secondly, the verb be is analyzed here as an unergative verb along the line followed in Section 5.3.3. Syntactically there are other options as pointed out in, for example, Hoekstra and Mulder (1990), Moro (1997) and Broekhuis and Corver (2016). And finally, strengthening the modal operator to having universal force, one can see (37f) as an instance of the modal logical law expressed in (15a), without the oddity of (16a), due to tense. As mentioned in footnote 11 on page 60, Verkuyl (2008) argued that the correction of Kamp (1971) on Prior’s tense logic by the introduction of a Now operator is superfluous in a binary tense system. In the present context of analyzing will, Kamp’s (38a) will be given an updated representation in the form of (38b).15 (38)

a. A child was born that will rule the world. b. ∃i  ∃j∃k[BE - BORN(k)(c) ∧ k = d(Ran(su) ∧ k  j ∧ j  ia ∧ i < i ∧ ∀j[j ∼ = i♦ → ∃k [RW(k )(c) ∧ k = Ran(id)) ∧ k  j ∧ i ◦ n]]] c. A child was born that would rule the world. d. ∃i  ∃j∃k[BE - BORN(k)(c) ∧ k = d(Ran(su) ∧ k  j ∧ j  ia ∧ ∀j [j ∼ = i♦ → ∃k [RW(k )(c) ∧ k = Ran(id)) ∧ k  j ∧ i < i ∧ i ◦ n]]]

Sentence (38a) falls apart into two predications connected anaphorically: it means that the child c introduced in the past domain of the main sentence also occurs as c in the present domain of speaker and hearer.16 Representation (38b) shows that the predication located in the past tense domain has a tense structure involving k  , j  and i  , whereas the embedded clause involves the indices k, j, i and n. As expected. Apart from the connection made by the double occurrence of c, the two tense domains are connected by the clauses i < i and i ◦ n. It is quite natural to treat the English auxiliary can on a par with may rather than with will. However, there are some interesting sentences like 15 Some simplifications are helpful for understanding the real point at issue. Thus a child is simply

notated as c both as antecedent and as an anaphoric pronoun. Rather than having become ruler of the world I have opted for rule the world. These simplifications have no bearing on the status of the Now operator in Kamp’s analysis. 16 For a detailed analysis of the direct access of a speaker to the temporal structure of the subordinate clause, see De Jong and Verkuyl (1982).

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(39a) discussed in Janssen (1997) as a possible counterexample against compositionality due to what Partee (1984b:289) calls “sentence-internal context-sensitivity”. (39)

a. Chris can win any match. b. ∃j∃k¬∃x[MATCH(x) ∧ ¬WIN(k)(x)(c) ∧ k = d(Ran(su)) ∧ kj∧j∼ = i♦ ∧ i ◦ n]]

They are interesting because the auxiliary can is a modest one by definition assuming existential quantification as in (26b), but in (39a) it seems to behave more like requiring inspection of all accessible worlds. In my view, this is due to the specific form of quantification expressed by the determiner any: (39b) represents the so-called free-choice interpretation of any paraphrased as ‘there is no match which Chris does not win’. This interpretation is, I think, adequately accounted for by the negation sign in front of the quantifier ∃x and the negation sign in front of the WIN-proposition leading to the paraphrase ‘there is no match that Chris will not win’. Janssen (1997) considers the negation of (39a) in (40a) in conflict with the principle of compositionality because of the “impact of an existential quantification” expressed by (40a), given the paraphrase ‘there is a match that Chris cannot win’. (40)

a. Chris cannot win any match. b. ∃j∃k∃x[MATCH(x) ∧ ¬WIN(k)(x)(c) ∧ k = d(Ran(su)) ∧ kj∧j∼ = i♦ ∧ i ◦ n]] c. ∃j¬∃k¬∃x[MATCH(x) ∧ ¬WIN(k)(x)(c) ∧ k = d(Ran(su)) ∧ kj∧j∼ = i♦ ∧ i ◦ n]] d. ¬∃j∃k¬∃x[MATCH(x) ∧ ¬WIN(k)(x)(c) ∧ k = d(Ran(su)) ∧ kj∧j∼ = i♦ ∧ i ◦ n]]

The present approach shows that the problem raised by Janssen disappears because the existential interpretation is just what should be expected on the basis of any having just one meaning, the one expressed by ¬∃x[. . . ¬ϕ . . .] in (39b). Applying a negation sign to S0 leads to ¬¬∃x[. . . ¬ϕ . . .] which means that the two negation signs are cancelled leaving only ∃x: (40b) is therefore to be understood as expressing that the speaker sees a k in i♦ at which Chris cannot win a match. Representation (40c) introduces the negation of cannot at a higher level: ¬(IMP(ϕ)). It says that there is near-certainty that for all indices k there is a match that Chris cannot win, due to the equivalence: ¬∃k¬ϕ ⇔ ∀kϕ. The third interpretation of (40a) based on ¬(SYN(IMP(¬ϕ))) in (40d) excludes a j

8.4 Reaching the Top: Temporalization by PRES and PAST

287

in which Chris wins all matches.17 I do not want to burden the present analysis with further references to the vast literature on any later than 1997. Here it suffices to show that the split between S0 and the three upper levels of tense structure has the advantage of being able to have one lexical meaning for any which works out differently with negation dependent on the level of insertion in compliance with the principle of compositionality.

8.4

Reaching the Top: Temporalization by PRES and PAST

The formal machinery developed for the account of the aspectual composition from the bottom of phrase structure to the top just below the level of PRES and PAST, makes it possible to have a very small top. The crucial connection between atemporal and temporal structure is located in a clause which occurs in the definition of both operators: i ◦ n. This is understandable because the speaker and hearer experience real time in their discourse interaction, n being identified as the fleeting point of time during this interaction. From its introduction in Chapter 3 up to this point, the clause i ◦ n, though intuitively quite perspicuous, has remained underdefined, doing its job as marking the present domain by the occurrence of n. In the present section, it will be finally given the precise definition it deserves. The introduction of a temporal unit t in a binary tense system presumes the structure attributed to the time axis T based on the point structure T ,