The many and the one: a philosophical study of plural logic
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford, United Kingdom
Oxford University Press
2021
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Volltext Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | xii, 314 Seiten |
| ISBN: | 9780198791522 |
| DOI: | 10.1093/oso/9780198791522.001.0001 |
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Contents Preface Ackn owledgments xi xiii 1. Introduction 1 I. PRIMITIVE PLURALS 2. Taking Plurals at Face Value 2.1 Some prominent views of plural sentences 2.2 Taking plurals at face value 2.3 The language of plural logic 2.4 The traditional theory of plural logic 2.5 The philosophical significance of plural logic 2.6 Applications of plural logic 2.7 Our methodology 9 9 14 15 19 20 24 29 3. The Refutation of Singularism? 3.1 Regimentation and singularism 3.2 Substitution argument 3.3 Incorrect existential consequences 3.4 The paradox of plurality 3.5 Plural Cantor: its significance 3.6 Plural Cantor: its statement and proof 3.7 Conclusion 3.A Alternative formulations of Plural Cantor 31 31 34 36 38 41 42 45 47 II. COMPARISONS 4. Plurals and Set Theory 4.1 A simple two-sorted set theory 4.2 Plural logic and the simple set theory compared 4.3 Plural logic vs. set theory: classifying the options 4.4 Against the elimination of pluralities in favor of sets 4.5 Against the elimination of sets in favor of pluralities 4.6 The iterative conception of set 4.7 Zermelo-Fraenkel set theory 55 55 57 59 60 64 66 68
viii CONTENTS 4.8 4.9 4.A 4.B Proper classes as pluralities Are two applications of plural logic compatible? Defining the translations Defining the interpretation 70 72 73 74 5. Plurals and Mereology 5.1 Mereology 5.2 Can mereology represent the plural? 5.3 One- sorted plural logic 5.4 Classifying some ways to talk about the many 5.5 Mereological singularism in linguistic semantics 5.6 Assessment of singularism in linguistic semantics 5.7 The elimination of mereology in favor of plural logic 5.8 Keeping both plural logic and mereology 5.A Partial orders and principles of decomposition 5.B Some notions of sum 5.C Atomicity 5.D One- and two-sorted plural logic compared 76 76 77 81 83 85 88 90 92 96 98 101 102 6. Plurals and Second-Order Logic 6.1 Second-order logic 6.2 Plural logic and second-order logic compared 6.3 The elimination of pluralities in favor of concepts 6.4 The elimination of concepts in favor of pluralities 6.5 Conclusion 104 104 107 109 П6 118 III. PLURALS AND SEMANTICS 7. The Semantics of Plurals 7.1 Regimentation vs. semantics 7.2 Set-based model theory 7.3 Plurality-based model theory 7.4 Criticisms of the set-based model theory 7.5 The semantics of plural predication 7.6 The problem of choice 7.7 Absolute generality as a constraint 7.8 Parity constraints 7.9 Conclusion 123 124 126 130 135 139 144 146 147 150 8. On the Innocence and Determinacy of Plural Quantification 8.1 Introduction 8.2 A plurality-based Henkin semantics 8.3 The legitimacy of ascending one order 151 151 154 155
CONTENTS 8.4 8.5 8.6 8.7 8.8 8. A 8.В Does ontological innocence ensure determinacy? The semantic determinacy of plural quantification The metaphysical determinacy of plural quantification A generalized notion of ontological commitment Applications reconsidered Henkin semantics Completeness of the Henkin semantics 9. Superplurals 9.1 Introduction 9.2 What superplural reference would be 9.3 Grades of superplural involvement 9.4 Possible examples from natural language 9.5 The possible examples scrutinized 9.6 The multigrade analysis 9.7 Covers 9.8 Mixed-level predications 9.9 Mixed-level terms, order, and repetition 9.10 Conclusion 9.A The notion of upwards closure ІХ 157 160 162 163 168 170 172 174 174 174 178 179 182 185 188 193 195 198 200 IV. THE LOGIC AND METAPHYSICS OF PLURALS 10. Plurals and Modals 10.1 Introduction 10.2 Why plural rigidity matters 10.3 Challenges to plural rigidity 10.4 An argument for the rigidity of sets 10.5 An argument for plural rigidity 10.6 Towards formal arguments for plural rigidity 10.7 The argument from uniform adjunction 10.8 The argument from partial rigidification 10.9 The argument from uniform traversability 10.10 Pluralities as extensionally definite 10.11 The status of plural comprehension 10.A Traversability and quasi-combinatorial reasoning 10.B Proofs 205 205 207 208 210 216 219 221 223 224 226 229 231 232 11. Absolute Generality and Singularization 11.1 Absolute generality 11.2 A challenge to absolute generality 11.3 A trilemma 11.4 Relativism and inexpressibility 240 240 241 244 246
X CONTENTS 11.5 11.6 11.7 11. A Traditional absolutism and ascent Ascent and inexpressibility Lifting the veil of type distinctions The Ascent Theorem 249 253 256 262 12. Critical Plural Logic 12.1 Introduction 12.2 The extendability argument 12.3 Our Uberal view of definitions 12.4 Why plural comprehension has to be restricted 12.5 The principles of critical plural logic 12.6 Extensions of critical plural logic 12.7 Critical plural logic and set theory 12.8 GeneraUzed semantics without a universal plurality? 12.9 What we have learnt 268 268 269 272 276 278 284 286 290 293 References Index 297 307 |
| adam_txt |
Contents Preface Ackn owledgments xi xiii 1. Introduction 1 I. PRIMITIVE PLURALS 2. Taking Plurals at Face Value 2.1 Some prominent views of plural sentences 2.2 Taking plurals at face value 2.3 The language of plural logic 2.4 The traditional theory of plural logic 2.5 The philosophical significance of plural logic 2.6 Applications of plural logic 2.7 Our methodology 9 9 14 15 19 20 24 29 3. The Refutation of Singularism? 3.1 Regimentation and singularism 3.2 Substitution argument 3.3 Incorrect existential consequences 3.4 The paradox of plurality 3.5 Plural Cantor: its significance 3.6 Plural Cantor: its statement and proof 3.7 Conclusion 3.A Alternative formulations of Plural Cantor 31 31 34 36 38 41 42 45 47 II. COMPARISONS 4. Plurals and Set Theory 4.1 A simple two-sorted set theory 4.2 Plural logic and the simple set theory compared 4.3 Plural logic vs. set theory: classifying the options 4.4 Against the elimination of pluralities in favor of sets 4.5 Against the elimination of sets in favor of pluralities 4.6 The iterative conception of set 4.7 Zermelo-Fraenkel set theory 55 55 57 59 60 64 66 68
viii CONTENTS 4.8 4.9 4.A 4.B Proper classes as pluralities Are two applications of plural logic compatible? Defining the translations Defining the interpretation 70 72 73 74 5. Plurals and Mereology 5.1 Mereology 5.2 Can mereology represent the plural? 5.3 One- sorted plural logic 5.4 Classifying some ways to talk about the many 5.5 Mereological singularism in linguistic semantics 5.6 Assessment of singularism in linguistic semantics 5.7 The elimination of mereology in favor of plural logic 5.8 Keeping both plural logic and mereology 5.A Partial orders and principles of decomposition 5.B Some notions of sum 5.C Atomicity 5.D One- and two-sorted plural logic compared 76 76 77 81 83 85 88 90 92 96 98 101 102 6. Plurals and Second-Order Logic 6.1 Second-order logic 6.2 Plural logic and second-order logic compared 6.3 The elimination of pluralities in favor of concepts 6.4 The elimination of concepts in favor of pluralities 6.5 Conclusion 104 104 107 109 П6 118 III. PLURALS AND SEMANTICS 7. The Semantics of Plurals 7.1 Regimentation vs. semantics 7.2 Set-based model theory 7.3 Plurality-based model theory 7.4 Criticisms of the set-based model theory 7.5 The semantics of plural predication 7.6 The problem of choice 7.7 Absolute generality as a constraint 7.8 Parity constraints 7.9 Conclusion 123 124 126 130 135 139 144 146 147 150 8. On the Innocence and Determinacy of Plural Quantification 8.1 Introduction 8.2 A plurality-based Henkin semantics 8.3 The legitimacy of ascending one order 151 151 154 155
CONTENTS 8.4 8.5 8.6 8.7 8.8 8. A 8.В Does ontological innocence ensure determinacy? The semantic determinacy of plural quantification The metaphysical determinacy of plural quantification A generalized notion of ontological commitment Applications reconsidered Henkin semantics Completeness of the Henkin semantics 9. Superplurals 9.1 Introduction 9.2 What superplural reference would be 9.3 Grades of superplural involvement 9.4 Possible examples from natural language 9.5 The possible examples scrutinized 9.6 The multigrade analysis 9.7 Covers 9.8 Mixed-level predications 9.9 Mixed-level terms, order, and repetition 9.10 Conclusion 9.A The notion of upwards closure ІХ 157 160 162 163 168 170 172 174 174 174 178 179 182 185 188 193 195 198 200 IV. THE LOGIC AND METAPHYSICS OF PLURALS 10. Plurals and Modals 10.1 Introduction 10.2 Why plural rigidity matters 10.3 Challenges to plural rigidity 10.4 An argument for the rigidity of sets 10.5 An argument for plural rigidity 10.6 Towards formal arguments for plural rigidity 10.7 The argument from uniform adjunction 10.8 The argument from partial rigidification 10.9 The argument from uniform traversability 10.10 Pluralities as extensionally definite 10.11 The status of plural comprehension 10.A Traversability and quasi-combinatorial reasoning 10.B Proofs 205 205 207 208 210 216 219 221 223 224 226 229 231 232 11. Absolute Generality and Singularization 11.1 Absolute generality 11.2 A challenge to absolute generality 11.3 A trilemma 11.4 Relativism and inexpressibility 240 240 241 244 246
X CONTENTS 11.5 11.6 11.7 11. A Traditional absolutism and ascent Ascent and inexpressibility Lifting the veil of type distinctions The Ascent Theorem 249 253 256 262 12. Critical Plural Logic 12.1 Introduction 12.2 The extendability argument 12.3 Our Uberal view of definitions 12.4 Why plural comprehension has to be restricted 12.5 The principles of critical plural logic 12.6 Extensions of critical plural logic 12.7 Critical plural logic and set theory 12.8 GeneraUzed semantics without a universal plurality? 12.9 What we have learnt 268 268 269 272 276 278 284 286 290 293 References Index 297 307 |
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| spellingShingle | Florio, Salvatore Linnebo, Øystein The many and the one a philosophical study of plural logic Logik (DE-588)4036202-4 gnd |
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| title | The many and the one a philosophical study of plural logic |
| title_auth | The many and the one a philosophical study of plural logic |
| title_exact_search | The many and the one a philosophical study of plural logic |
| title_exact_search_txtP | The many and the one a philosophical study of plural logic |
| title_full | The many and the one a philosophical study of plural logic Salvatore Florio and Øystein Linnebo |
| title_fullStr | The many and the one a philosophical study of plural logic Salvatore Florio and Øystein Linnebo |
| title_full_unstemmed | The many and the one a philosophical study of plural logic Salvatore Florio and Øystein Linnebo |
| title_short | The many and the one |
| title_sort | the many and the one a philosophical study of plural logic |
| title_sub | a philosophical study of plural logic |
| topic | Logik (DE-588)4036202-4 gnd |
| topic_facet | Logik |
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