Comparative Quantifiers

M. Hackl, 2001

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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


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