Philosophical logic: a contemporary introduction
Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for...
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| Format: | Buch |
| Sprache: | English |
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New York, NY ; London
Routledge
2021
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| Schriftenreihe: | Routledge contemporary introductions to philosophy
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'--and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter |
| Beschreibung: | xviii, 238 Seiten Illustrationen 23 cm |
| ISBN: | 9781138737655 |
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| 520 | 3 | |a Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'--and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter | |
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Contents List of Exercises Preface XV Acknowledgements I Fundamentals l.l 1.2 I I I 1.1.2 Semantics 1.1.3 Proofs 1.1.4 Proof strategy 1.1.5 The relation of semantics and proofs Predicate logic Grammar 1.2.1 2 1.3 1.4 Grammar 1.3.1 1.3.2 Semantics Proofs 1.3.3 Use and mention 2 Quantifiers 2.2 xix Propositional logic l.l.ւ Grammar 1.2.2 Scope 1.2.3 Semantics 1.2.4 Proofs Identity 2.1 xii Beyond V and 3 2.1.1 What is a quantifier? 2.1.2 Semantics of binary quantifiers 2.1.3 Most: an essentially binary quantifier 2.1.4 Unary quantifiers beyond V and 3 2.1.5 Generalized quantifiers Definite descriptions 6 13 14 15 16 17 17 21 26 28 28 28 29 35 35 35 37 37 38 39 39
viii Contents Terms or quantifiers? Definite descriptions and scope 2.2.2 2.2.3 Russell’s theory of descriptions 2.2.4 Proofs Second-order quantifiers Standard semantics for monadic second-order logic 2.3.1 2.2.1 2.3 2.3.2 2.3.3 2.3.4 2.4 Expressive limitations of first-order logic Set theory in sheep’s clothing? Boolos’s plural interpretation 2.3.5 Beyond monadic second-order logic Substitutional quantifiers Objectual and substitutional quantification 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 Nonexistent objects Quantifying into attitude reports Sentence quantifiers Quantifying into quotes Defining truth Quantifying into quotes and paradox The circularity worry Modal Logic 3.1 3.2 3.3 Modal propositional logic Grammar 3.1.1 3.1.2 Semantics Modal logics from K to S5 3.1.3 41 43 44 46 47 50 52 54 57 57 58 59 60 61 61 62 64 67 67 67 3.1.4 68 70 74 The slingshot argument 3.3.1 Applications of slingshot arguments 80 80 81 82 83 85 87 Proofs Modal predicate logic 3.2.1 Opaque contexts 3.2.2 Opaque contexts and quantification 3.2.3 The number of planets argument 3.2.4 Smullyan's reply 3.3.2 3.3.3 3.4 39 41 The Gödel slingshot Critique of the slingshot Kripke’s defense of de re modality 3.4.1 Kripke’s strategy 3.4.2 The contingent a priori The necessary a posteriori 3.4.3 3.4.4 Epistemic and alethic modals 87 88 90 90 91 93 94
Contents 4 Conditionals 4.1 The material conditional 4.1.1 Indicative vs. counterfactual 4.1.2 4.2 4.3 4.4 Entailments between indicatives and material conditionals 5.2 5.3 97 97 99 100 101 4.2.1 4.2.2 4.2.3 Arguments for the material conditional analysis Arguments against the material conditional analysis Rejecting Or-to-if 102 102 104 4.2.4 4.2.5 Edgington’s positive view Against truth conditions 105 107 Stalnaker’s semantics and pragmatics 4.3.1 Propositions, assertion, and the common ground 109 109 4.3.2 110 Semantics 4.3.3 Reasonable but invalid inferences 4.3.4 Contraposition and Hypothetical Syllogism 4.3.5 The argument for fatalism Is Modus Ponens valid? 111 113 114 115 4.4.1 4.4.2 The intuitive counterexamples McGee’s counterexamples as seen by Edgington 116 117 4.4.3 4.4.4 McGee’s counterexamples as seen by Stalnaker Modus Ponens vs. Exportation 119 120 123 Informal characterizations of consequence 5.1.1 In terms of necessity 123 123 5.1.2 5.1.3 126 128 In terms of proof In terms of counterexamples Tarski’s account of logical consequence 5.2.1 Tarski’s aim 132 132 5.2.2 5.2.3 5.2.4 5.2.5 Why proof-based approaches won’t work Criteria of adequacy The insufficiency of (F) The semantic definition 132 135 136 137 5.2.6 Satisfying the criteria of adequacy 138 5.2.7 Logical constants 139 Interpretational and representationalsemantics 6 Logical Consequence via Proofs 6.1 97 4.1.3 Thomson against the “received opinion” No truth conditions? 5 Logical Consequence via Models 5.1 ix Introduction rules as self-justifying 140 145 145
x Contents 6.2 6.1.1 Carnap’s Copernican turn 146 6.1.2 Prior’s article 146 6.1.3 Stevenson’s response 147 6.1.4 Belnap’s Response 148 6.1.5 Prawitz’s Response 150 Prawitz’s proof-theoretic account of consequence 151 6.2.1 Arguments 152 6.2.2 Validity 152 6.2.3 Λ Intro and Elim 153 6.2.4 V Intro and Elim 154 6.2.5 Philosophical reflections 155 6.3 Intuitionistic logic 156 6.4 Kripke semantics for intuitionistic logic 159 6.5 Fundamental logical disagreement 162 6.5.1 163 Changing the subject? 6.5.2 Interpreting classical logic in intuitionistic logic 164 6.5.3 Interpreting intuitionistic logic in classical logic 166 6.5.4 Logical pluralism 167 7 Relevance, Logic, and Reasoning 7.1 7.2 7.3 Motivations for relevance logic 169 170 The Lewis Argument 171 7.2.1 Rejecting Disjunctive Weakening 172 7.2.2 Rejecting transitivity 173 7.2.3 Rejecting Disjunctive Syllogism 175 First-degree entailment 176 7.3.1 A syntactic procedure 176 7.3.2 The four-valued truth tables 180 7.4 Logic and reasoning 181 7.5 Uses for relevance logic 185 7.5.1 186 Dialetheism 7.5.2 The moderate approach 187 7.5.3 Truth in a corpus 188 8 Vagueness and the Sorites Paradox 191 8.1 What is vagueness? 191 8.2 Three-valued logics 194 8.2.1 194 Semantics for connectives 8.2.2 Defining validity in multivalued logics 196 8.2.3 Application to the sorites 196
Contents 8.3 8.4 8.5 Fuzzy logics xi 198 8.3.1 Semantics 199 8.3.2 Application to the sorites 199 8.3.3 Can we make sense of degrees of truth? 200 8.3.4 Troubles with degree-functionality 202 Supervaluations 203 8.4.1 Application to sorites 206 8.4.2 Higher-order vagueness 207 8.4.3 The logic of definiteness Vagueness in the world? 208 209 8.5.1 Evans on vague identity 210 8.5.2 Evans and Quine 212 Appendix A Greek Letters 215 Appendix В Set-Theoretic Notation 217 Appendix C Proving Unrepresentability 219 References 223 Index 231 |
| adam_txt |
Contents List of Exercises Preface XV Acknowledgements I Fundamentals l.l 1.2 I I I 1.1.2 Semantics 1.1.3 Proofs 1.1.4 Proof strategy 1.1.5 The relation of semantics and proofs Predicate logic Grammar 1.2.1 2 1.3 1.4 Grammar 1.3.1 1.3.2 Semantics Proofs 1.3.3 Use and mention 2 Quantifiers 2.2 xix Propositional logic l.l.ւ Grammar 1.2.2 Scope 1.2.3 Semantics 1.2.4 Proofs Identity 2.1 xii Beyond V and 3 2.1.1 What is a quantifier? 2.1.2 Semantics of binary quantifiers 2.1.3 Most: an essentially binary quantifier 2.1.4 Unary quantifiers beyond V and 3 2.1.5 Generalized quantifiers Definite descriptions 6 13 14 15 16 17 17 21 26 28 28 28 29 35 35 35 37 37 38 39 39
viii Contents Terms or quantifiers? Definite descriptions and scope 2.2.2 2.2.3 Russell’s theory of descriptions 2.2.4 Proofs Second-order quantifiers Standard semantics for monadic second-order logic 2.3.1 2.2.1 2.3 2.3.2 2.3.3 2.3.4 2.4 Expressive limitations of first-order logic Set theory in sheep’s clothing? Boolos’s plural interpretation 2.3.5 Beyond monadic second-order logic Substitutional quantifiers Objectual and substitutional quantification 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 Nonexistent objects Quantifying into attitude reports Sentence quantifiers Quantifying into quotes Defining truth Quantifying into quotes and paradox The circularity worry Modal Logic 3.1 3.2 3.3 Modal propositional logic Grammar 3.1.1 3.1.2 Semantics Modal logics from K to S5 3.1.3 41 43 44 46 47 50 52 54 57 57 58 59 60 61 61 62 64 67 67 67 3.1.4 68 70 74 The slingshot argument 3.3.1 Applications of slingshot arguments 80 80 81 82 83 85 87 Proofs Modal predicate logic 3.2.1 Opaque contexts 3.2.2 Opaque contexts and quantification 3.2.3 The number of planets argument 3.2.4 Smullyan's reply 3.3.2 3.3.3 3.4 39 41 The Gödel slingshot Critique of the slingshot Kripke’s defense of de re modality 3.4.1 Kripke’s strategy 3.4.2 The contingent a priori The necessary a posteriori 3.4.3 3.4.4 Epistemic and alethic modals 87 88 90 90 91 93 94
Contents 4 Conditionals 4.1 The material conditional 4.1.1 Indicative vs. counterfactual 4.1.2 4.2 4.3 4.4 Entailments between indicatives and material conditionals 5.2 5.3 97 97 99 100 101 4.2.1 4.2.2 4.2.3 Arguments for the material conditional analysis Arguments against the material conditional analysis Rejecting Or-to-if 102 102 104 4.2.4 4.2.5 Edgington’s positive view Against truth conditions 105 107 Stalnaker’s semantics and pragmatics 4.3.1 Propositions, assertion, and the common ground 109 109 4.3.2 110 Semantics 4.3.3 Reasonable but invalid inferences 4.3.4 Contraposition and Hypothetical Syllogism 4.3.5 The argument for fatalism Is Modus Ponens valid? 111 113 114 115 4.4.1 4.4.2 The intuitive counterexamples McGee’s counterexamples as seen by Edgington 116 117 4.4.3 4.4.4 McGee’s counterexamples as seen by Stalnaker Modus Ponens vs. Exportation 119 120 123 Informal characterizations of consequence 5.1.1 In terms of necessity 123 123 5.1.2 5.1.3 126 128 In terms of proof In terms of counterexamples Tarski’s account of logical consequence 5.2.1 Tarski’s aim 132 132 5.2.2 5.2.3 5.2.4 5.2.5 Why proof-based approaches won’t work Criteria of adequacy The insufficiency of (F) The semantic definition 132 135 136 137 5.2.6 Satisfying the criteria of adequacy 138 5.2.7 Logical constants 139 Interpretational and representationalsemantics 6 Logical Consequence via Proofs 6.1 97 4.1.3 Thomson against the “received opinion” No truth conditions? 5 Logical Consequence via Models 5.1 ix Introduction rules as self-justifying 140 145 145
x Contents 6.2 6.1.1 Carnap’s Copernican turn 146 6.1.2 Prior’s article 146 6.1.3 Stevenson’s response 147 6.1.4 Belnap’s Response 148 6.1.5 Prawitz’s Response 150 Prawitz’s proof-theoretic account of consequence 151 6.2.1 Arguments 152 6.2.2 Validity 152 6.2.3 Λ Intro and Elim 153 6.2.4 V Intro and Elim 154 6.2.5 Philosophical reflections 155 6.3 Intuitionistic logic 156 6.4 Kripke semantics for intuitionistic logic 159 6.5 Fundamental logical disagreement 162 6.5.1 163 Changing the subject? 6.5.2 Interpreting classical logic in intuitionistic logic 164 6.5.3 Interpreting intuitionistic logic in classical logic 166 6.5.4 Logical pluralism 167 7 Relevance, Logic, and Reasoning 7.1 7.2 7.3 Motivations for relevance logic 169 170 The Lewis Argument 171 7.2.1 Rejecting Disjunctive Weakening 172 7.2.2 Rejecting transitivity 173 7.2.3 Rejecting Disjunctive Syllogism 175 First-degree entailment 176 7.3.1 A syntactic procedure 176 7.3.2 The four-valued truth tables 180 7.4 Logic and reasoning 181 7.5 Uses for relevance logic 185 7.5.1 186 Dialetheism 7.5.2 The moderate approach 187 7.5.3 Truth in a corpus 188 8 Vagueness and the Sorites Paradox 191 8.1 What is vagueness? 191 8.2 Three-valued logics 194 8.2.1 194 Semantics for connectives 8.2.2 Defining validity in multivalued logics 196 8.2.3 Application to the sorites 196
Contents 8.3 8.4 8.5 Fuzzy logics xi 198 8.3.1 Semantics 199 8.3.2 Application to the sorites 199 8.3.3 Can we make sense of degrees of truth? 200 8.3.4 Troubles with degree-functionality 202 Supervaluations 203 8.4.1 Application to sorites 206 8.4.2 Higher-order vagueness 207 8.4.3 The logic of definiteness Vagueness in the world? 208 209 8.5.1 Evans on vague identity 210 8.5.2 Evans and Quine 212 Appendix A Greek Letters 215 Appendix В Set-Theoretic Notation 217 Appendix C Proving Unrepresentability 219 References 223 Index 231 |
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| spelling | MacFarlane, John Verfasser (DE-588)133884023 aut Philosophical logic a contemporary introduction John MacFarlane New York, NY ; London Routledge 2021 xviii, 238 Seiten Illustrationen 23 cm txt rdacontent n rdamedia nc rdacarrier Routledge contemporary introductions to philosophy Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'--and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter Logik (DE-588)4036202-4 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Logic Logik (DE-588)4036202-4 s Philosophie (DE-588)4045791-6 s DE-604 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032657484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title_short | Philosophical logic |
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| topic | Logik (DE-588)4036202-4 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Logik Philosophie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032657484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT macfarlanejohn philosophicallogicacontemporaryintroduction |