Modal logic for philosophers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2006
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Table of contents only Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. ) and index |
| Physical Description: | XV, 455 S. |
| ISBN: | 9780521863674 9780521682299 0521863678 0521682290 |
Staff View
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| 245 | 1 | 0 | |a Modal logic for philosophers |c James W. Garson |
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| adam_text | Contents
Preface page xiii
Introduction: What Is Modal Logic? 1
1 The System K: A Foundation for Modal Logic 3
1.1 The Language of Propositional Modal Logic 3
1.2 Natural Deduction Rules for Propositional Logic: PL 5
1.3 Derivable Rules of PL 9
1.4 Natural Deduction Rules for System K 17
1.5 A Derivable Rule for O 20
1.6 Horizontal Notation for Natural Deduction Rules 27
1.7 Necessitation and Distribution 30
1.8 General Necessitation 32
1.9 Summary of the Rules of K 35
2 Extensions of K 38
2.1 Modal or Alethic Logic 38
2.2 Duals 44
2.3 Deontic Logic 45
2.4 The Good Samaritan Paradox 46
2.5 Conflicts of Obligation and the Axiom (D) 48
2.6 Iteration of Obligation 49
2.7 Tense Logic 50
2.8 Locative Logic 52
2.9 Logics of Belief 53
2.10 Provability Logic 54
3 Basic Concepts of Intensional Semantics 57
3.1 Worlds and Intensions 57
3.2 Truth Conditions and Diagrams for » and L 59
vii
viii Contents
3.3 Derived Truth Conditions and Diagrams for PL 61
3.4 Truth Conditions for D 63
3.5 Truth Conditions for O 66
3.6 Satisfiability, Counterexamples, and Validity 67
3.7 The Concepts of Soundness and Completeness 69
3.8 A Note on Intensions 70
4 Trees for K 72
4.1 Checking for K Validity with Trees 72
4.2 Showing K Invalidity with Trees 81
4.3 Summary of Tree Rules for K 91
5 The Accessibility Relation 93
5.1 Conditions Appropriate for Tense Logic 93
5.2 Semantics for Tense Logics 99
5.3 Semantics for Modal (Alethic) Logics 104
5.4 Semantics for Deontic Logics 108
5.5 Semantics for Locative Logics 111
5.6 Relevance Logics and Conditional Logics 112
5.7 Summary of Axioms and Their Conditions on Frames 115
6 Trees for Extensions of K 116
6.1 Trees for Reflexive Frames: M Trees 116
6.2 Trees for Transitive Frames: 4 Trees 121
6.3 Trees for Symmetrical Frames: B Trees 123
6.4 Trees for Euclidean Frames: 5 Trees 129
6.5 Trees for Serial Frames: D Trees 133
6.6 Trees for Unique Frames: CD Trees 135
7 Converting Trees to Proofs 136
7.1 Converting Trees to Proofs in K 136
7.2 Converting Trees that Contain Defined Notation into
Proofs 147
7.3 Converting M Trees into Proofs 149
7.4 Converting D Trees into Proofs 151
7.5 Converting 4 Trees into Proofs 152
7.6 Converting B Trees into Proofs 154
7.7 Converting 5 Trees into Proofs 159
7.8 Using Conversion Strategies to Find Difficult Proofs 163
7.9 Converting CD Trees into Proofs in CD and DCD 164
7.10 A Formal Proof that Trees Can Be Converted into
Proofs 165
8 Adequacy of Propositional Modal Logics 172
8.1 Soundness of K 172
8.2 Soundness of Systems Stronger than K 180
8.3 The Tree Model Theorem 182
Contents ix
8.4 Completeness of Many Modal Logics 188
8.5 Decision Procedures 189
8.6 Automatic Proofs 191
8.7 Adequacy of Trees 191
8.8 Properties of Frames that Correspond to No Axioms 192
9 Completeness Using Canonical Models 195
9.1 The Lindenbaum Lemma 195
9.2 The Canonical Model 198
9.3 The Completeness of Modal Logics Based on K 201
9.4 The Equivalence of PL+(GN) and K 210
10 Axioms and Their Corresponding Conditions on R 211
10.1 The General Axiom (G) 211
10.2 Adequacy of Systems Based on (G) 215
11 Relations between the Modal Logics 221
11.1 Showing Systems Are Equivalent 222
11.2 Showing One System Is Weaker than Another 224
12 Systems for Quantified Modal Logic 228
12.1 Languages for Quantified Modal Logic 228
12.2 A Classical System for Quantifiers 231
12.3 Identity in Modal Logic 234
12.4 The Problem of Nondenoting Terms in Classical
Logic 239
12.5 FL: A System of Free Logic 242
12.6 fS: A Basic Quantified Modal Logic 245
12.7 The Barcan Formulas 248
12.8 Constant and Varying Domains of Quantification 250
12.9 A Classicist s Defense of Constant Domains 254
12.10 The Prospects for Classical Systems with Varying
Domains 256
12.11 Rigid and Nonrigid Terms 260
12.12 Eliminating the Existence Predicate 262
12.13 Summary of Systems, Axioms, and Rules 263
13 Semantics for Quantified Modal Logics 265
13.1 Truth Value Semantics with the Substitution
Interpretation 265
13.2 Semantics for Terms, Predicates, and Identity 268
13.3 Strong Versus Contingent Identity 270
13.4 Rigid and Nonrigid Terms 276
13.5 The Objectual Interpretation 278
13.6 Universal Instantiation on the Objectual
Interpretation 281
13.7 The Conceptual Interpretation 286
x Contents
13.8 The Intensional Interpretation 288
13.9 Strengthening Intensional Interpretation Models 293
13.10 Relationships with Systems in the Literature 294
13.11 Summary of Systems and Truth Conditions 300
14 Trees for Quantified Modal Logic 303
14.1 Tree Rules for Quantifiers 303
14.2 Tree Rules for Identity 307
14.3 Infinite Trees 309
14.4 Trees for Quantified Modal Logic 310
14.5 Converting Trees into Proofs 314
14.6 Trees for Systems that Include Domain Rules 319
14.7 Converting Trees into Proofs in Stronger Systems 320
14.8 Summary of the Tree Rules 321
15 The Adequacy of Quantified Modal Logics 323
15.1 Preliminaries: Some Replacement Theorems 324
15.2 Soundness for the Intensional Interpretation 326
15.3 Soundness for Systems with Domain Rules 329
15.4 Expanding Truth Value (tS) to Substitution (sS)
Models 332
15.5 Expanding Substitution (sS) to Intensional (iS)
Models 337
15.6 An Intensional Treatment of the Objectual
Interpretation 339
15.7 Transfer Theorems for Intensional and Substitution
Models 342
15.8 A Transfer Theorem for the Objectual Interpretation 347
15.9 Soundness for the Substitution Interpretation 348
15.10 Soundness for the Objectual Interpretation 349
15.11 Systems with Nonrigid Terms 350
15.12 Appendix: Proof of the Replacement Theorems 351
16 Completeness of Quantified Modal Logics Using Trees 356
16.1 The Quantified Tree Model Theorem 356
16.2 Completeness for Truth Value Models 361
16.3 Completeness for Intensional and Substitution
Models 361
16.4 Completeness for Objectual Models 362
16.5 The Adequacy of Trees 364
17 Completeness Using Canonical Models 365
17.1 How Quantifiers Complicate Completeness Proofs 365
17.2 Limitations on the Completeness Results 368
17.3 The Saturated Set Lemma 370
17.4 Completeness for Truth Value Models 373
Contents xi
17.5 Completeness for Systems with Rigid Constants 377
17.6 Completeness for Systems with Nonrigid Terms 379
17.7 Completeness for Intensional and Substitution
Models 382
17.8 Completeness for the Objectual Interpretation 383
18 Descriptions 385
18.1 Russell s Theory of Descriptions 385
18.2 Applying Russell s Method to Philosophical Puzzles 388
18.3 Scope in Russell s Theory of Descriptions 390
18.4 Motives for an Alternative Treatment of Descriptions 392
18.5 Syntax for Modal Description Theory 394
18.6 Rules for Modal Description Theory: The System !S 396
18.7 Semantics for !S 400
18.8 Trees for !S 402
18.9 Adequacy of !S 403
18.10 How !S Resolves the Philosophical Puzzles 407
19 Lambda Abstraction 409
19.1 De Re and De Dicto 409
19.2 Identity and the De Re De Dicto Distinction 413
19.3 Principles for Abstraction: The System X.S 415
19.4 Syntax and Semantics for XS 416
19.5 The Adequacy of XS 422
19.6 Quantifying In 424
Answers to Selected Exercises 432
Bibliography of Works Cited 445
Index 449
|
| adam_txt |
Contents
Preface page xiii
Introduction: What Is Modal Logic? 1
1 The System K: A Foundation for Modal Logic 3
1.1 The Language of Propositional Modal Logic 3
1.2 Natural Deduction Rules for Propositional Logic: PL 5
1.3 Derivable Rules of PL 9
1.4 Natural Deduction Rules for System K 17
1.5 A Derivable Rule for O 20
1.6 Horizontal Notation for Natural Deduction Rules 27
1.7 Necessitation and Distribution 30
1.8 General Necessitation 32
1.9 Summary of the Rules of K 35
2 Extensions of K 38
2.1 Modal or Alethic Logic 38
2.2 Duals 44
2.3 Deontic Logic 45
2.4 The Good Samaritan Paradox 46
2.5 Conflicts of Obligation and the Axiom (D) 48
2.6 Iteration of Obligation 49
2.7 Tense Logic 50
2.8 Locative Logic 52
2.9 Logics of Belief 53
2.10 Provability Logic 54
3 Basic Concepts of Intensional Semantics 57
3.1 Worlds and Intensions 57
3.2 Truth Conditions and Diagrams for » and L 59
vii
viii Contents
3.3 Derived Truth Conditions and Diagrams for PL 61
3.4 Truth Conditions for D 63
3.5 Truth Conditions for O 66
3.6 Satisfiability, Counterexamples, and Validity 67
3.7 The Concepts of Soundness and Completeness 69
3.8 A Note on Intensions 70
4 Trees for K 72
4.1 Checking for K Validity with Trees 72
4.2 Showing K Invalidity with Trees 81
4.3 Summary of Tree Rules for K 91
5 The Accessibility Relation 93
5.1 Conditions Appropriate for Tense Logic 93
5.2 Semantics for Tense Logics 99
5.3 Semantics for Modal (Alethic) Logics 104
5.4 Semantics for Deontic Logics 108
5.5 Semantics for Locative Logics 111
5.6 Relevance Logics and Conditional Logics 112
5.7 Summary of Axioms and Their Conditions on Frames 115
6 Trees for Extensions of K 116
6.1 Trees for Reflexive Frames: M Trees 116
6.2 Trees for Transitive Frames: 4 Trees 121
6.3 Trees for Symmetrical Frames: B Trees 123
6.4 Trees for Euclidean Frames: 5 Trees 129
6.5 Trees for Serial Frames: D Trees 133
6.6 Trees for Unique Frames: CD Trees 135
7 Converting Trees to Proofs 136
7.1 Converting Trees to Proofs in K 136
7.2 Converting Trees that Contain Defined Notation into
Proofs 147
7.3 Converting M Trees into Proofs 149
7.4 Converting D Trees into Proofs 151
7.5 Converting 4 Trees into Proofs 152
7.6 Converting B Trees into Proofs 154
7.7 Converting 5 Trees into Proofs 159
7.8 Using Conversion Strategies to Find Difficult Proofs 163
7.9 Converting CD Trees into Proofs in CD and DCD 164
7.10 A Formal Proof that Trees Can Be Converted into
Proofs 165
8 Adequacy of Propositional Modal Logics 172
8.1 Soundness of K 172
8.2 Soundness of Systems Stronger than K 180
8.3 The Tree Model Theorem 182
Contents ix
8.4 Completeness of Many Modal Logics 188
8.5 Decision Procedures 189
8.6 Automatic Proofs 191
8.7 Adequacy of Trees 191
8.8 Properties of Frames that Correspond to No Axioms 192
9 Completeness Using Canonical Models 195
9.1 The Lindenbaum Lemma 195
9.2 The Canonical Model 198
9.3 The Completeness of Modal Logics Based on K 201
9.4 The Equivalence of PL+(GN) and K 210
10 Axioms and Their Corresponding Conditions on R 211
10.1 The General Axiom (G) 211
10.2 Adequacy of Systems Based on (G) 215
11 Relations between the Modal Logics 221
11.1 Showing Systems Are Equivalent 222
11.2 Showing One System Is Weaker than Another 224
12 Systems for Quantified Modal Logic 228
12.1 Languages for Quantified Modal Logic 228
12.2 A Classical System for Quantifiers 231
12.3 Identity in Modal Logic 234
12.4 The Problem of Nondenoting Terms in Classical
Logic 239
12.5 FL: A System of Free Logic 242
12.6 fS: A Basic Quantified Modal Logic 245
12.7 The Barcan Formulas 248
12.8 Constant and Varying Domains of Quantification 250
12.9 A Classicist's Defense of Constant Domains 254
12.10 The Prospects for Classical Systems with Varying
Domains 256
12.11 Rigid and Nonrigid Terms 260
12.12 Eliminating the Existence Predicate 262
12.13 Summary of Systems, Axioms, and Rules 263
13 Semantics for Quantified Modal Logics 265
13.1 Truth Value Semantics with the Substitution
Interpretation 265
13.2 Semantics for Terms, Predicates, and Identity 268
13.3 Strong Versus Contingent Identity 270
13.4 Rigid and Nonrigid Terms 276
13.5 The Objectual Interpretation 278
13.6 Universal Instantiation on the Objectual
Interpretation 281
13.7 The Conceptual Interpretation 286
x Contents
13.8 The Intensional Interpretation 288
13.9 Strengthening Intensional Interpretation Models 293
13.10 Relationships with Systems in the Literature 294
13.11 Summary of Systems and Truth Conditions 300
14 Trees for Quantified Modal Logic 303
14.1 Tree Rules for Quantifiers 303
14.2 Tree Rules for Identity 307
14.3 Infinite Trees 309
14.4 Trees for Quantified Modal Logic 310
14.5 Converting Trees into Proofs 314
14.6 Trees for Systems that Include Domain Rules 319
14.7 Converting Trees into Proofs in Stronger Systems 320
14.8 Summary of the Tree Rules 321
15 The Adequacy of Quantified Modal Logics 323
15.1 Preliminaries: Some Replacement Theorems 324
15.2 Soundness for the Intensional Interpretation 326
15.3 Soundness for Systems with Domain Rules 329
15.4 Expanding Truth Value (tS) to Substitution (sS)
Models 332
15.5 Expanding Substitution (sS) to Intensional (iS)
Models 337
15.6 An Intensional Treatment of the Objectual
Interpretation 339
15.7 Transfer Theorems for Intensional and Substitution
Models 342
15.8 A Transfer Theorem for the Objectual Interpretation 347
15.9 Soundness for the Substitution Interpretation 348
15.10 Soundness for the Objectual Interpretation 349
15.11 Systems with Nonrigid Terms 350
15.12 Appendix: Proof of the Replacement Theorems 351
16 Completeness of Quantified Modal Logics Using Trees 356
16.1 The Quantified Tree Model Theorem 356
16.2 Completeness for Truth Value Models 361
16.3 Completeness for Intensional and Substitution
Models 361
16.4 Completeness for Objectual Models 362
16.5 The Adequacy of Trees 364
17 Completeness Using Canonical Models 365
17.1 How Quantifiers Complicate Completeness Proofs 365
17.2 Limitations on the Completeness Results 368
17.3 The Saturated Set Lemma 370
17.4 Completeness for Truth Value Models 373
Contents xi
17.5 Completeness for Systems with Rigid Constants 377
17.6 Completeness for Systems with Nonrigid Terms 379
17.7 Completeness for Intensional and Substitution
Models 382
17.8 Completeness for the Objectual Interpretation 383
18 Descriptions 385
18.1 Russell's Theory of Descriptions 385
18.2 Applying Russell's Method to Philosophical Puzzles 388
18.3 Scope in Russell's Theory of Descriptions 390
18.4 Motives for an Alternative Treatment of Descriptions 392
18.5 Syntax for Modal Description Theory 394
18.6 Rules for Modal Description Theory: The System !S 396
18.7 Semantics for !S 400
18.8 Trees for !S 402
18.9 Adequacy of !S 403
18.10 How !S Resolves the Philosophical Puzzles 407
19 Lambda Abstraction 409
19.1 De Re and De Dicto 409
19.2 Identity and the De Re De Dicto Distinction 413
19.3 Principles for Abstraction: The System X.S 415
19.4 Syntax and Semantics for XS 416
19.5 The Adequacy of XS 422
19.6 Quantifying In 424
Answers to Selected Exercises 432
Bibliography of Works Cited 445
Index 449 |
| any_adam_object | 1 |
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| author | Garson, James W. |
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| callnumber-subject | BC - Logic |
| classification_rvk | CC 2400 SK 130 |
| ctrlnum | (OCoLC)63164861 (DE-599)BVBBV021770308 |
| dewey-full | 160 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 160 - Philosophical logic |
| dewey-raw | 160 |
| dewey-search | 160 |
| dewey-sort | 3160 |
| dewey-tens | 160 - Philosophical logic |
| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV021770308 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:38:09Z |
| indexdate | 2024-07-09T20:43:40Z |
| institution | BVB |
| isbn | 9780521863674 9780521682299 0521863678 0521682290 |
| language | English |
| lccn | 2006001152 |
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| physical | XV, 455 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Garson, James W. Verfasser aut Modal logic for philosophers James W. Garson 1. publ. Cambridge [u.a.] Cambridge University Press 2006 XV, 455 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. ) and index Modalité (Logique) - Manuels d'enseignement supérieur Modality (Logic) Textbooks Modallogik (DE-588)4074914-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Modallogik (DE-588)4074914-9 s DE-604 http://www.loc.gov/catdir/toc/ecip066/2006001152.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0633/2006001152-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014983241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garson, James W. Modal logic for philosophers Modalité (Logique) - Manuels d'enseignement supérieur Modality (Logic) Textbooks Modallogik (DE-588)4074914-9 gnd |
| subject_GND | (DE-588)4074914-9 (DE-588)4123623-3 |
| title | Modal logic for philosophers |
| title_auth | Modal logic for philosophers |
| title_exact_search | Modal logic for philosophers |
| title_exact_search_txtP | Modal logic for philosophers |
| title_full | Modal logic for philosophers James W. Garson |
| title_fullStr | Modal logic for philosophers James W. Garson |
| title_full_unstemmed | Modal logic for philosophers James W. Garson |
| title_short | Modal logic for philosophers |
| title_sort | modal logic for philosophers |
| topic | Modalité (Logique) - Manuels d'enseignement supérieur Modality (Logic) Textbooks Modallogik (DE-588)4074914-9 gnd |
| topic_facet | Modalité (Logique) - Manuels d'enseignement supérieur Modality (Logic) Textbooks Modallogik Lehrbuch |
| url | http://www.loc.gov/catdir/toc/ecip066/2006001152.html http://www.loc.gov/catdir/enhancements/fy0633/2006001152-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014983241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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