4. Quantifiers
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Edward Keenan
Abstract
The presentation distinguishes broadly between Determiner (D-) Quantification and Adverbial (A-) Quantification, with the former being much better studied and understood than the latter. We present D-quantification first and use it to study novel types of quantification such as polyadic quantification and mass term quantification. Then we extend the concepts developed to A-quantification. We characterize semantically over 20 types of Determiner quantification in natural language, focusing on questions of logical expressive power-what we can say and what constraints there are on what we can say. We do not focus on the formalization of syntactic representations, though we do show that there are quantifiers denotable by syntactically complex Determiners that are not denotable by syntactically simple Determiners. We do this within the broad framework of Generalized Quantifier Theory. In terms of the semantic categories of analysis developed we offer several non-obvious semantic generalizations which hold for well studied languages and which we think may hold more generally. In two cases we explicitly suggest that the properties are language universal.
Abstract
The presentation distinguishes broadly between Determiner (D-) Quantification and Adverbial (A-) Quantification, with the former being much better studied and understood than the latter. We present D-quantification first and use it to study novel types of quantification such as polyadic quantification and mass term quantification. Then we extend the concepts developed to A-quantification. We characterize semantically over 20 types of Determiner quantification in natural language, focusing on questions of logical expressive power-what we can say and what constraints there are on what we can say. We do not focus on the formalization of syntactic representations, though we do show that there are quantifiers denotable by syntactically complex Determiners that are not denotable by syntactically simple Determiners. We do this within the broad framework of Generalized Quantifier Theory. In terms of the semantic categories of analysis developed we offer several non-obvious semantic generalizations which hold for well studied languages and which we think may hold more generally. In two cases we explicitly suggest that the properties are language universal.
Chapters in this book
- Frontmatter I
- Contents V
- 1. Pronouns 1
- 2. Definiteness and indefiniteness 33
- 3. Specificity 70
- 4. Quantifiers 112
- 5. Bare noun phrases 149
- 6. Possessives and relational nouns 177
- 7. Mass nouns and plurals 204
- 8. Genericity 232
- 9. Aspectual class and Aktionsart 274
- 10. Perfect and progressive 313
- 11. Verbal mood 369
- 12. Deverbal nominalization 407
- 13. Tense 436
- 14. Modality 463
- 15. Conditionals 503
- 16. Propositional attitudes 532
- 17. Indexicality and De Se reports 562
- Index 619
Chapters in this book
- Frontmatter I
- Contents V
- 1. Pronouns 1
- 2. Definiteness and indefiniteness 33
- 3. Specificity 70
- 4. Quantifiers 112
- 5. Bare noun phrases 149
- 6. Possessives and relational nouns 177
- 7. Mass nouns and plurals 204
- 8. Genericity 232
- 9. Aspectual class and Aktionsart 274
- 10. Perfect and progressive 313
- 11. Verbal mood 369
- 12. Deverbal nominalization 407
- 13. Tense 436
- 14. Modality 463
- 15. Conditionals 503
- 16. Propositional attitudes 532
- 17. Indexicality and De Se reports 562
- Index 619
