Logical Methods
by Restall, Standefer
ISBN: 9780262372695 | Copyright 2022
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An accessible introduction to philosophical logic, suitable for undergraduate courses and above.
Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed.
Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic's development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy.
This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs.
Features:
• An accessible introduction to proof theory for readers with no background in logic
• Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics
• Provides tools and techniques of particular interest to philosophers and philosophical logicians
• Features short summaries of key concepts and skills at the end of each chapter
• Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students' understanding and developing skills in new directions
| Expand/Collapse All | |
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| Contents (pg. vii) | |
| How to Read This Book (pg. xi) | |
| I. Propositional Logic (pg. 1) | |
| 1. Introduction (pg. 3) | |
| 1.1 Arguments and Trees (pg. 4) | |
| 1.2 Sentences and Formulas (pg. 8) | |
| 1.3 Appendix: Some Useful Background (pg. 13) | |
| 1.4 Key Concepts and Skills (pg. 16) | |
| 1.5 Questions for You (pg. 17) | |
| 2. Connectives: and & if (pg. 19) | |
| 2.1 Conjunction (pg. 19) | |
| 2.2 Conditional (pg. 23) | |
| 2.3 Biconditional (pg. 29) | |
| 2.4 Derived Rules (pg. 29) | |
| 2.5 Key Concepts and Skills (pg. 31) | |
| 2.6 Questions for You (pg. 31) | |
| 3. More Connectives: not & or (pg. 35) | |
| 3.1 Negation and Falsum (pg. 35) | |
| 3.2 Disjunction (pg. 38) | |
| 3.3 Our System of Proofs (pg. 41) | |
| 3.4 Comments on Negation and Falsum (pg. 43) | |
| 3.5 Key Concepts and Skills (pg. 45) | |
| 3.6 Questions for You (pg. 45) | |
| 4. Facts about Proofs & Provability (pg. 49) | |
| 4.1 Facts about Provability (pg. 49) | |
| 4.2 Normalization (pg. 53) | |
| 4.3 The Subformula Property (pg. 62) | |
| 4.4 Consequences of Normalization (pg. 68) | |
| 4.5 Key Concepts and Skills (pg. 70) | |
| 4.6 Questions for You (pg. 72) | |
| 5. Models & Counterexamples (pg. 75) | |
| 5.1 Models and Truth Tables (pg. 76) | |
| 5.2 Counterexamples and Validity (pg. 79) | |
| 5.3 Model-Theoretic Validity (pg. 83) | |
| 5.4 Key Concepts and Skills (pg. 85) | |
| 5.5 Questions for You (pg. 86) | |
| 6. Soundness & Completeness (pg. 91) | |
| 6.1 Soundness (pg. 92) | |
| 6.2 Completeness (pg. 94) | |
| 6.3 Proofs First or Models First? (pg. 101) | |
| 6.4 Appendix: Heyting Algebras (pg. 103) | |
| 6.5 Appendix: Some Three-Valued Logics (pg. 108) | |
| 6.6 Key Concepts and Skills (pg. 110) | |
| 6.7 Questions for You (pg. 111) | |
| II. Modal Logic (pg. 115) | |
| 7. Necessity & Possibility (pg. 117) | |
| 7.1 Possible Worlds Models (pg. 117) | |
| 7.2 Counterexamples and Validity (pg. 122) | |
| 7.3 Two Applications (pg. 129) | |
| 7.4 More Modal Models (pg. 133) | |
| 7.5 Appendix: Intuitionistic Kripke Models (pg. 141) | |
| 7.6 Key Concepts and Skills (pg. 148) | |
| 7.7 Questions for You (pg. 149) | |
| 8. Actuality & 2D Logic (pg. 153) | |
| 8.1 Actuality Models (pg. 154) | |
| 8.2 Validity (pg. 155) | |
| 8.3 Double Indexing (pg. 156) | |
| 8.4 Real-World Validity (pg. 160) | |
| 8.5 Key Concepts and Skills (pg. 163) | |
| 8.6 Questions for You (pg. 163) | |
| 9. Modal Natural Deduction (pg. 167) | |
| 9.1 Natural Deduction for S4 (pg. 167) | |
| 9.2 Natural Deduction for S5 (pg. 173) | |
| 9.3 Features of S5 (pg. 174) | |
| 9.4 Soundness and Completeness (pg. 179) | |
| 9.5 Key Concepts and Skills (pg. 183) | |
| 9.6 Questions for You (pg. 184) | |
| III. Predicate Logic (pg. 187) | |
| 10. Proofs for Predicate Logic (pg. 189) | |
| 10.1 Syntax (pg. 189) | |
| 10.2 Natural Deduction for CQ (pg. 199) | |
| 10.3 Features of Proofs with Quantifiers (pg. 205) | |
| 10.4 Discussion (pg. 211) | |
| 10.5 Key Concepts and Skills (pg. 213) | |
| 10.6 Questions for You (pg. 213) | |
| 11. Models for Predicate Logic (pg. 217) | |
| 11.1 Defining Models (pg. 217) | |
| 11.2 Features of Models (pg. 224) | |
| 11.3 Counterexamples and Validity (pg. 226) | |
| 11.4 The Power and Limits of Predicate Logic (pg. 234) | |
| 11.5 Key Concepts and Skills (pg. 239) | |
| 11.6 Questions for You (pg. 240) | |
| 12. Coda (pg. 245) | |
| 12.1 Quantified Modal Logic (pg. 245) | |
| 12.2 Suggestions for Further Reading (pg. 248) | |
| 12.3 Key Concepts and Skills (pg. 252) | |
| 12.4 Questions for You (pg. 252) | |
| Glossary (pg. 255) | |
| References (pg. 261) | |
| Symbol Index (pg. 267) | |
| Subject Index (pg. 269) | |
Greg Restall
Greg Restall is Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. He is the author of Logic: An Introduction and coauthor of Logical Pluralism.Shawn Standefer
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