Comparative Quantifiers
M. Hackl, 2001
The main goal of the thesis is to present a novel analysis of comparative quantifiers such as more than three students. The prevalent view on such expressions advocated in Generalized Quantifier Theory is that they denoted generalized quantifiers ranging over individuals – entirely on par with expressions like every student, some student(s), etc. According to this view, more than three is a determiner (like every) that is, even though morpho-syntactically complex, semantically a simplex expression that can – in terms of its interactions with the syntactic environment it appears in – be viewed as denoting simply a relation between sets of individuals.
The proposal that will be developed in this thesis maintains on the other hand that expression like more than three are also semantically complex. More specifically, an analysis off comparative quantifiers will be given that is fully compositional down to level of the formation of comparative determiners. The proposal is based on concepts that are independently needed to analyze comparative constructions. Three main pieces will be argued to form the semantic and syntactic core of comparative quantifiers: a degree function expressed by MANY, a degree description given by the numeral and the comparative relation expressed by the comparative morpheme –er. Importantly, each of the three pieces can be empirically shown to interact in predictably and (partially) independent ways with elements inside the quantifier as well as with elements in the matrix clause. These interactions are unexpected unless comparative quantifiers are built in the syntax. Giving a fully compositional analysis is therefore not just conceptually appealing but also required to explain new empirical generalizations. The more general enterprise that this thesis hopes pave the way is giving a uniform and fully compositional analysis of comparative quantificational structures that does not exist so far.
Thesis Supervisor: Irene Heim
Title: Professor of Linguistics
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Table of Contents
Chapter 1 Amount Comparison and Quantification: Basic Questions
1.1 Introduction 8
1.2 Background assumptions and notational conventions 14
1.3 Comparative quantifiers in generalized quantifier theory 19
1.3.1 Some properties of comparative quantification 26
1.3.2 Extension to 3- and 4-place comparative quantifiers 39
1.4 Comparative quantifiers as comparative constructions 43
1.4.1 The basic elements of comparative constructions 44
1.4.2 Amount comparatives and comparative quantifiers 52
1.5 Three empirical questions 55
1.5.1 Detecting the degree quantifier 56
1.5.2 Detecting the degree function 58
1.5.3 Detecting the measure phrase 59
Chapter 2 A Comparative Syntax for Comparative Quantifiers
2.1 Introduction 61
2.2 The minimal number of participants generalization with
comparative quantifiers 62
2.3 The idea in a nutshell 75
2.4 MANY as parameterized determiner 78
2.4.1 Bresnan (1973) 78
2.4.2 d-MANY 82
2.4.3 Measure phrase comparatives 87
2.4.4 Summary 94
2.5 Predicative uses of MANY – are there any? 96
2.6 Intensionalizing Maximality 103
2.6.1 Two problems getting the truth-conditions right 103
2.6.2 Diagnosing the source of the problems 106
2.6.3 The remedy: intensional maximality 107
2.6.4 Semantic correlates 114
2.6.5 Syntactic correlates 119
2.7 Simple extensions: at least, at most, between n and m 126
2.8 Summary 129
2.9 Appendix: A GQT-analysis of the MNPG 136
2.8.1 Multiply-headed noun phrases 136
2.8.2 Getting the truth-conditions right 139
2.8.3 Some critical remarks 141
Chapter 3 Scope Splitting with Comparative Quantifiers
3.1 Introduction 146
3.2 Scope splitting with comparative quantifiers 148
3.2.1 Limitations for degree operator scope 150
3.2.2 Scope splitting over intensional operators 155
3.2.3 A note on van Benthem’s problem 160
3.3 A note on the scope of comparative quantifiers 170
3.4 Summary 179
Chapter 4 Amoun Comparatives and Plural Predication
4.1 Introduction 180
4.2 Gradable predicates express measure functions 182
4.3 Measuring cardinality 191
4.3.1 Numerous 191
4.3.2 Excursus: The semantics of plural predicates 194
4.3.3 Many 199
4.4 Some applications and amendments 200
4.4.1 Plural morphology on nominal predicates 200
4.4.2 Genuine collective nouns 203
4.4.3 Essentially plural nouns 206
1st ammendment: counting atomic parts 212
2nd ammendment: units of measurement 217
4.5 Genuine collective VPs and comparative quantifiers 221
4.5.1 Morphological and semantic number 222
4.5.2 The Dowty-Winter generalization 226
4.5.3 A proposal for comparative quantifiers 233
4.5.4 Appendix: Winter (1998) 239
4.6 Summary 244