One true logic: a monist manifesto
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford, United Kingdom
Oxford University Press
2022
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| Ausgabe: | First edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xxxi, 232 Seiten 24 cm |
| ISBN: | 9780198829713 |
Internformat
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Datensatz im Suchindex
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| adam_text | Contents xi xix Introduction Prologue PARTI. MONISM VS PLURALISM 1. Conceptions of Logical Consequence 1.1 Tarski on logical consequence 1.2 Accounts of logical consequence 1.3 Philonian consequence 1.4 The necessity of logic 1.5 The formality of logic 1.6 The intuitive concept of consequence’ З 2. What Is Monism? 2.1 Defining monism—a first pass 2.1.1 A scheme 2.1.2 Admissible formalizations 2.1.3 Admissible logics 2.1.4 A true logic 2.1.5 The one true logic 2.2 Epistemics Appendix: the least true logic 18 19 19 20 24 24 25 25 28 3. Against Pluralism 3.1 Extensionally divergent formalizations 3.2 Horses for courses: languages and domains 3.2.1 Horses for courses: interlinguistic 3.2.2 Horses for courses: intralinguistic 3.3 Pluralism proper 3.3.1 Beall and Restalľs modest pluralism 3.3.2 Shapiro’s eclectic pluralism 3.4 Beall and Restalľs modest pluralism 3.4.1 The‘settled core’of consequence 3.5 Shapiro’s eclectic pluralism 3.5.1 SIA as a test case for pluralism 3.6 Metalogical reasoning 3.7 Logical nihilism 3.8 A problem for logical pluralism 3.8.1 All true logics 3.8.2 The single correct metalogic 32 32 33 33 34 35 35 37 39 39 40 41 45 47 50 51 52 3 7 9 11 13 16
viii CONTENTS 3.8.3 Some arbitrary true logic 3.8.4 Each true logic 3.8.5 Summary 3.9 Two further issues 3.9.1 Non-deductive reasoning 3.9.2 A problem for monism? 3.10 Conclusion Appendix: metalogical meaning variance 53 54 55 55 56 57 58 58 PART II. THE L00G00S HYPOTHESIS 4. The L00G00S Hypothesis 4.1 Introduction 4.2 Type and sort 4.3 The L00G00S Hypothesis 4.4 Back to origins 4.5 Top-down and bottom-up arguments 4.6 Pure ПТЮ00 defined 4.7 Semantics for pure FTT^^ 4.8 What are the formulas of pure FTTœoo? 65 65 67 71 73 75 76 79 81 5. Beyond the Finitary 5.1 Generalized quantifiers 5.2 The concurrence argument for FOL 5.3 Beyond FOL: ‘there are infinitely many’ 5.3.1 Ihe finitude objection 5.3.2 Ihe mathematical validity objection 5.3.3 The finite-description objection 5.3.4 The indeterminacy objection 5.3.5 Diagnosis 5.4 Generalization: ‘there are к many’ 5.5 Beyond SOL: infinitary conjunction 5.5.1 Superhumans 5.5.2 Generalization 5.6 Beyond SOL: cardinality quantifiers 5.7 Conclusion Appendix: technical results 83 83 86 91 94 96 99 100 101 104 106 106 109 110 112 113 6. Isomorphism Invariance 6.1 Introduction 6.2 Form as schematic 6.2.1 MacFarlane on formality 6.2.2 Form as normative 6.2.3 Form as topic-neutral 6.2.4 Form as abstraction 117 117 118 119 119 121 123
CONTENTS ЕХ Permutation and isomorphism invariance A necessary condition on OTL Miscellaneous comments McGee’s Theorem 6.6.1 Isomorphism invariance 6.6.2 Relations 6.6.3 Caveats 6.6.4 Isomorphism-invariant relations 123 126 131 134 135 136 139 140 7. Towards the One True Logic 7.1 The logic’s type 7.2 Theory of models 7.3 Mathematical consequences? Appendix: the generalized quantifier ‘most’ 143 144 150 151 152 6.3 6.4 6.5 6.6 PARTIU. OBJECTIONS 8. The Heterogeneity Objection 8.1 Introduction 8.2 Uniform-isomorphism invariance 8.3 Feferman’s invariantism 8.4 Bonnay’s invariantism 8.5 Conclusion 157 157 158 163 168 171 9. The Overgeneration Objection 9.1 Introduction 9.2 Sensitivity 9.3 CH is logically true 9.4 CH is determinate 9.5 CH is epistemically determined 9.6 CH and neutrality 9.6.1 Dialectical neutrality 9.6.2 Informational neutrality 9.7 CH is logically expressible 9.8 Identity 9.9 Conclusion Appendix: logical notions 173 173 177 180 182 185 187 187 189 192 192 193 194 10. The Absoluteness Objection 10.1 The absoluteness objection 10.2 Meaning-theoretic motivations 10.3 Anti-realist motivations 10.4 Independence motivations 10.5 Conclusion 197 197 198 200 203 204
X CONTENTS 11. The Intensional Objection 11.1 Unicorn negation 11.2 Modal responses 11.3 Biting the bullet 11.4 An open question 11.5 Conclusion 2θ5 20g 207 209 շ 13 216 Conclusion 217 Bibliography Index 219 229
О», с I rue I uçu Јч a nui, и , osii ribution to the philosophyof logic. It is the fit st nion graph елрііі i^y to articulate a version of logical monism. the view that duu ts.i »ingle correct foundational logic. Logical monism is opposed to logical pluralism, according to which there are mans՜ гімн·։ t logus. One True Logic provides a critical overvii w i ՛է tlie monism vs pluralism debate and argues for the former. It defends a particular monism,based on a highly infinitary logic. Breaking new ground on a number of fronts, it offers novel arguments for the genuine logicality of infinitary logic and unifies disparate discussions in the philosophical and logical literature.
|
| adam_txt |
Contents xi xix Introduction Prologue PARTI. MONISM VS PLURALISM 1. Conceptions of Logical Consequence 1.1 Tarski on logical consequence 1.2 Accounts of logical consequence 1.3 Philonian consequence 1.4 The necessity of logic 1.5 The formality of logic 1.6 'The intuitive concept of consequence’ З 2. What Is Monism? 2.1 Defining monism—a first pass 2.1.1 A scheme 2.1.2 Admissible formalizations 2.1.3 Admissible logics 2.1.4 A true logic 2.1.5 The one true logic 2.2 Epistemics Appendix: the least true logic 18 19 19 20 24 24 25 25 28 3. Against Pluralism 3.1 Extensionally divergent formalizations 3.2 Horses for courses: languages and domains 3.2.1 Horses for courses: interlinguistic 3.2.2 Horses for courses: intralinguistic 3.3 Pluralism proper 3.3.1 Beall and Restalľs modest pluralism 3.3.2 Shapiro’s eclectic pluralism 3.4 Beall and Restalľs modest pluralism 3.4.1 The‘settled core’of consequence 3.5 Shapiro’s eclectic pluralism 3.5.1 SIA as a test case for pluralism 3.6 Metalogical reasoning 3.7 Logical nihilism 3.8 A problem for logical pluralism 3.8.1 All true logics 3.8.2 The single correct metalogic 32 32 33 33 34 35 35 37 39 39 40 41 45 47 50 51 52 3 7 9 11 13 16
viii CONTENTS 3.8.3 Some arbitrary true logic 3.8.4 Each true logic 3.8.5 Summary 3.9 Two further issues 3.9.1 Non-deductive reasoning 3.9.2 A problem for monism? 3.10 Conclusion Appendix: metalogical meaning variance 53 54 55 55 56 57 58 58 PART II. THE L00G00S HYPOTHESIS 4. The L00G00S Hypothesis 4.1 Introduction 4.2 Type and sort 4.3 The L00G00S Hypothesis 4.4 Back to origins 4.5 Top-down and bottom-up arguments 4.6 Pure ПТЮ00 defined 4.7 Semantics for pure FTT^^ 4.8 What are the formulas of pure FTTœoo? 65 65 67 71 73 75 76 79 81 5. Beyond the Finitary 5.1 Generalized quantifiers 5.2 The concurrence argument for FOL 5.3 Beyond FOL: ‘there are infinitely many’ 5.3.1 Ihe finitude objection 5.3.2 Ihe mathematical validity objection 5.3.3 The finite-description objection 5.3.4 The indeterminacy objection 5.3.5 Diagnosis 5.4 Generalization: ‘there are к many’ 5.5 Beyond SOL: infinitary conjunction 5.5.1 Superhumans 5.5.2 Generalization 5.6 Beyond SOL: cardinality quantifiers 5.7 Conclusion Appendix: technical results 83 83 86 91 94 96 99 100 101 104 106 106 109 110 112 113 6. Isomorphism Invariance 6.1 Introduction 6.2 Form as schematic 6.2.1 MacFarlane on formality 6.2.2 Form as normative 6.2.3 Form as topic-neutral 6.2.4 Form as abstraction 117 117 118 119 119 121 123
CONTENTS ЕХ Permutation and isomorphism invariance A necessary condition on OTL Miscellaneous comments McGee’s Theorem 6.6.1 Isomorphism invariance 6.6.2 Relations 6.6.3 Caveats 6.6.4 Isomorphism-invariant relations 123 126 131 134 135 136 139 140 7. Towards the One True Logic 7.1 The logic’s type 7.2 Theory of models 7.3 Mathematical consequences? Appendix: the generalized quantifier ‘most’ 143 144 150 151 152 6.3 6.4 6.5 6.6 PARTIU. OBJECTIONS 8. The Heterogeneity Objection 8.1 Introduction 8.2 Uniform-isomorphism invariance 8.3 Feferman’s invariantism 8.4 Bonnay’s invariantism 8.5 Conclusion 157 157 158 163 168 171 9. The Overgeneration Objection 9.1 Introduction 9.2 Sensitivity 9.3 CH is logically true 9.4 CH is determinate 9.5 CH is epistemically determined 9.6 CH and neutrality 9.6.1 Dialectical neutrality 9.6.2 Informational neutrality 9.7 CH is logically expressible 9.8 Identity 9.9 Conclusion Appendix: logical notions 173 173 177 180 182 185 187 187 189 192 192 193 194 10. The Absoluteness Objection 10.1 The absoluteness objection 10.2 Meaning-theoretic motivations 10.3 Anti-realist motivations 10.4 Independence motivations 10.5 Conclusion 197 197 198 200 203 204
X CONTENTS 11. The Intensional Objection 11.1 Unicorn negation 11.2 Modal responses 11.3 Biting the bullet 11.4 An open question 11.5 Conclusion 2θ5 20g 207 209 շ 13 216 Conclusion 217 Bibliography Index 219 229
О», с I rue I uçu Јч a nui, и , osii ribution to the philosophyof logic. It is the fit st nion graph елрііі i^y to articulate a version of logical monism. the view that duu ts.i »ingle correct foundational logic. Logical monism is opposed to logical pluralism, according to which there are mans՜ гімн·։ t logus. One True Logic provides a critical overvii w i ՛է tlie monism vs pluralism debate and argues for the former. It defends a particular monism,based on a highly infinitary logic. Breaking new ground on a number of fronts, it offers novel arguments for the genuine logicality of infinitary logic and unifies disparate discussions in the philosophical and logical literature. |
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| author | Griffiths, Owen Paseau, Alexander 1974- |
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| spelling | Griffiths, Owen Verfasser (DE-588)127031954X aut One true logic a monist manifesto Owen Griffiths and A.C. Paseau First edition Oxford, United Kingdom Oxford University Press 2022 xxxi, 232 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Logik (DE-588)4036202-4 gnd rswk-swf Monismus (DE-588)4170453-8 gnd rswk-swf Logic Monism Logik (DE-588)4036202-4 s Monismus (DE-588)4170453-8 s DE-604 Paseau, Alexander 1974- Verfasser (DE-588)1127559281 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033925148&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033925148&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Griffiths, Owen Paseau, Alexander 1974- One true logic a monist manifesto Logik (DE-588)4036202-4 gnd Monismus (DE-588)4170453-8 gnd |
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| title | One true logic a monist manifesto |
| title_auth | One true logic a monist manifesto |
| title_exact_search | One true logic a monist manifesto |
| title_exact_search_txtP | One true logic a monist manifesto |
| title_full | One true logic a monist manifesto Owen Griffiths and A.C. Paseau |
| title_fullStr | One true logic a monist manifesto Owen Griffiths and A.C. Paseau |
| title_full_unstemmed | One true logic a monist manifesto Owen Griffiths and A.C. Paseau |
| title_short | One true logic |
| title_sort | one true logic a monist manifesto |
| title_sub | a monist manifesto |
| topic | Logik (DE-588)4036202-4 gnd Monismus (DE-588)4170453-8 gnd |
| topic_facet | Logik Monismus |
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