Quantification

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ISBN: 9780521887960 | 0521887968
Cover: Hardcover
Copyright: 1/17/2011

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Quantification forms a significant aspect of cross-linguistic research into both sentence structure and meaning. This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behaviour in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A unique feature of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, covering French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu) and points to formal semantic literature involving quantification in around thirty languages.

List of figures	p. ix
List of tables	p. x
Acknowledgements	p. xi
What this book is about and how to use it	p. 1
The proper treatment of quantification in ordinary Human	p. 1
How to use this book	p. 3
Notation and terminology	p. 4
Generalized quantifiers and their elements: operators and their scopes	p. 5
Generalized quantifiers - heroes or old fogeys?	p. 5
Generalized quantifiers and their elements: operators and their scopes	p. 6
Scope and constituent structure	p. 11
The basic idea	p. 11
The (first) proper treatment of quantification: Montague	p. 12
Interlude: quantifier phrases do not directly bind pronouns	p. 14
Quantifier Raising: May	p. 16
All the scopes, but a simple syntax: Hendriks	p. 19
Continuations and scope: Barker and Shan	p. 23
Summary and Direct Compositionality	p. 32
Generalized quantifiers in non-nominal domains	p. 33
Domains of quantification	p. 33
Raising verbs as quantifiers	p. 36
Some empirically significant properties of quantifiers and determiners	p. 45
Quantifiers	p. 46
Boolean compounds	p. 46
Monotonicity: increasing, decreasing, and non-monotonic quantifiers	p. 50
Witnesses: the sets quantifiers contribute to interpretation	p. 55
Monotonicity and existential quantification over sets	p. 56
Determiner denotations	p. 60
Determiners as relations or two-place functions	p. 60
The determiner's restriction	p. 62
Summary	p. 70
Potential challenges for generalized quantifiers	p. 71
Referential indefinites	p. 71
Collective readings	p. 72
Type multiplicity	p. 73
Presuppositions and the weak/strong distinction	p. 75
Implicatures	p. 76
Comparative and superlative determiners vis-à-vis compositionality	p. 77
De re vs. de dicto, local vs. global	p. 80
Cross-linguistic variation	p. 82
Interim summary	p. 82
Scope is not uniform and not a primitive	p. 83
Different quantifiers, different scopes	p. 83
Quantifiers or referring expressions?	p. 86
How to obtain reliable scope data	p. 87
Existential scope versus distributive scope	p. 91
Indefinites	p. 91
No such thing as "the scope" of an indefinite	p. 91
Existential closure of a choice function variable	p. 93
Skolemized choice functions	p. 96
Universals of the every NP-type	p. 102
Existential vs. distributive scope in universals	p. 102
Inducing and exhibiting referential variation	p. 103
Indefinites and universals unified?	p. 104
Do all "quantifier phrases" have the same dual scope behavior?	p. 106
Summary	p. 108
Distributivity and scope	p. 109
Background notions: sorting keys, distributed shares, and events	p. 109
Distributive readings with plural (in) definites	p. 113
Distributivity and cumulativity	p. 113
All, both, stressed AND, and some cross-linguistic counterparts	p. 117
Distributive singular quantifiers	p. 121
Floating quantifiers, anti-quantifiers, and dependent plurals	p. 129
Floating quantifiers: an overview	p. 129
Binominal each and other anti-quantifiers	p. 130
Plurals - dependent plurals among them	p. 133
Numeral reduplication as NumP pluralization	p. 135
All NP/NumP pluralization is event-key distribution	p. 137
Referential dependency: event semantics vis-à-vis Skolemization	p. 139
Bare numeral indefinites	p. 141
The flexible DP hypothesis	p. 141
How many is two?	p. 144
Cardinal vs. individual readings of numeral indefinites	p. 151
Numeral interpretation, agreement, and the split-DP hypothesis	p. 153
Summary	p. 160
Modified numerals	p. 161
The absence of scalar implicatures in modified numerals	p. 161
The non-synonymy of comparative and superlative modifiers	p. 166
The split-scope analysis of comparative quantifiers	p. 167
More than half, most of the, and the most	p. 169
Counting quantifiers	p. 171
Summary and experimental evidence	p. 175
Clause-internal scopal diversity	p. 177
The basic facts	p. 177
The basic approaches	p. 179
Scope as a by-product of feature checking	p. 180
Scope restrictions, internal structure, economy	p. 185
Cross-linguistic hypotheses	p. 187
Towards a compositional semantics of quantifier words	p. 189
Is there interesting syntax in and around universal quantifiers?	p. 190
The view from Lillooet: quantifier words operate on DP	p. 191
A closer look at determiners: Mandarin, Modern Greek, and Hungarian	p. 194
And finally, the deep end: diving into quantifier words in German	p. 198
Word-internal compositionality? Cross-linguistic isomorphy?	p. 202
Notes	p. 206
Bibliography	p. 222
Index	p. 248
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Quantification

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