Philosophical Logic: A Contemporary Introduction / Edition 1 available in Hardcover, Paperback, eBook
Philosophical Logic: A Contemporary Introduction / Edition 1
- ISBN-10:
- 1138737658
- ISBN-13:
- 9781138737655
- Pub. Date:
- 11/30/2020
- Publisher:
- Taylor & Francis
- ISBN-10:
- 1138737658
- ISBN-13:
- 9781138737655
- Pub. Date:
- 11/30/2020
- Publisher:
- Taylor & Francis
Philosophical Logic: A Contemporary Introduction / Edition 1
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$48.99Overview
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
Product Details
| ISBN-13: | 9781138737655 |
|---|---|
| Publisher: | Taylor & Francis |
| Publication date: | 11/30/2020 |
| Series: | Routledge Contemporary Introductions to Philosophy |
| Pages: | 258 |
| Sales rank: | 1,031,943 |
| Product dimensions: | 6.00(w) x 9.00(h) x (d) |
About the Author
John MacFarlane is Professor of Philosophy and a member of the Group in Logic and the Methodology of Science at the University of California, Berkeley. He is the author of Assessment Sensitivity: Relative Truth and Its Applications (2014).
Table of Contents
List of Exercises xii
Preface xv
Acknowledgements xix
1 Fundamentals 1
1.1 Propositional logic 1
1.1.1 Grammar 1
1.1.2 Semantics 2
1.1.3 Proofs 6
1.1.4 Proof Strategy 13
1.1.5 The relation of semantics and proofs 14
1.2 Predicate logic 15
1.2.1 Grammar 16
1.2.2 Scope 17
1.2.3 Semantics 17
1.2.4 Proofs 21
1.3 Identity 26
1.3.1 Grammar 28
1.3.2 Semantics 28
1.3.3 Proofs 28
1.4 Use and mention 29
2 Quantifiers 35
2.1 Beyond ∀ and &exists; 35
2.1.1 What is a quantifier? 35
2.1.2 Semantics of binary quantifiers 37
2.1.3 Most: an essentially binary-quantifier 37
2.1.4 Unary quantifiers beyond ∀ and &exists; 38
2.1.5 Generalized quantifiers 39
2.2 Definite descriptions 39
2.2.1 Terms or quantifiers? 39
2.2.2 Definite descriptions and scope 41
2.2.3 Russell's theory of descriptions 41
2.2.4 Proofs 43
2.3 Second-order quantifiers 44
2.3.1 Standard semantics for monadic second-order logic 46
2.3.2 Expressive limitations of first-order logic 47
2 3.3 Set theory in sheep's clothing? 50
2.3.4 Boolos's plural interpretation 52
2.3.5 Beyond monadic second-order logic 54
2.4 Substitutional quantifiers 57
2.4.1 Objectual and substitutional quantification 57
2.4.2 Nonexistent objects 58
2.4.3 Quantifying into attitude reports 59
2.4.4 Sentence quantifiers 60
2.4.5 Quantifying into quotes 61
2.4.6 Defining truth 61
2.4.7 Quantifying into quotes and paradox 62
2.4.8 The circularity worry 64
3 Modal Logic 67
3.1 Modal propositional logic 67
3.1.1 Grammar 67
3.1.2 Semantics 68
3.1.3 Modal logics from K to S5 70
3.1.4 Proofs 74
3.2 Modal predicate logic 80
3.2.1 Opaque contexts 80
3.2.2 Opaque contexts and quantification 81
3.2.3 The number of planets argument 82
3.2.4 Smullyan's reply 83
3.3 The slingshot argument 85
3.3.1 Applications of slingshot arguments 87
3.3.2 The gödel slingshot 87
3.3.3 Critique of the slingshot 88
3.4 Kripke's defense of de re modality 90
3.4.1 Kripke's strategy 90
3.4.2 The contingent a priori 91
3.4.3 The necessary a posteriori 93
3.4.4 Epistemic and alethic modals 94
4 Conditionals 97
4.1 The material conditional 97
4.1.1 Indicative vs. counterfactual 97
4.1.2 Entailments between indicatives and material conditionals 99
4.1.3 Thomson against the "received opinion" 100
4.2 No truth conditions? 101
4.2.1 Arguments for the material conditional analysis 102
4.2.2 Arguments against the material conditional analysis 102
4.2.3 Rejecting Or-to-if 104
4.2.4 Edgington's positive view 105
4.2.5 Against truth conditions 107
4.3 Stalnaker's semantics and pragmatics 109
4.3.1 Propositions, assertion, and the common ground 109
4.3.2 Semantics 110
4.3.3 Reasonable but invalid inferences 111
4.3.4 Contraposition and Hypothetical Syllogism 113
4.3.5 The argument for fatalism 114
4.4 Is Modus Ponens valid? 115
4.4.1 The intuitive counterexamples 116
4.4.2 McGee's counterexamples as seen by Edgington 117
4.4.3 McGee's counterexamples as seen by Stalnaker 119
4.4.4 Modus Ponens vs. Exportation 120
5 Logical Consequence via Models 123
5.1 Informal characterizations of consequence 123
5.1.1 In terms of necessity 123
5.1.2 In terms of proof 126
5.1.3 In terms of counterexamples 128
5.2 Tarski's account of logical consequence 132
5.2.1 Tarski's aim 132
5.2.2 Why proof-based approaches won't work 132
5.2.3 Criteria of adequacy 135
5.2.4 The insufficiency of (F) 136
5.2.5 The semantic definition 137
5.2.6 Satisfying the criteria of adequacy 138
5.2.7 Logical constants 139
5.3 Interpretational and representational semantics 140
6 Logical Consequence via Proofs 145
6.1 Introduction rules as self-justifying 145
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
6.2 Prawitz's proof-theoretic account of consequence 151
6.2.1 Arguments 152
6.2.2 Validity 152
6.2.3 ∧ Intro and Elim 153
6.2.4 ∨ 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 Changing the subject? 163
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 169
7.1 Motivations for relevance logic 170
7.2 The Lewis Argument 171
7.2.1 Rejecting Disjunctive Weakening 172
7.2.2 Rejecting transitivity 173
7.2.3 Rejecting Disjunctive Syllogism 175
7.3 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 Dialetheism 186
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 Semantics for connectives 194
8.2.2 Defining validity in multivalued logics 196
8.2.3 Application to the sorites 196
8.3 Fuzzy logics 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
8.4 Supervaluations 203
8.4.1 Application to sorites 206
8.4.2 Higher-order vagueness 207
8.4.3 The logic of definiteness 208
8.5 Vagueness in the world? 209
8.5.1 Evans on vague identity 210
8.5.2 Evans and quine 212
Appendix A Greek Letters 215
Appendix B Set-Theoretic Notation 217
Appendix C Proving Unrepresentable 219
References 223
Index 231