Logical Options: An Introduction to Classical and Alternative Logics by John L. Bell (PDF)

Description

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.

User’s Reviews

Editorial Reviews: Review “I love this book; I would have written it if I’d known how!” ― Richard Jeffrey, Princeton University “Logic teachers will love this book. Trees are probably the most accessible way to present logical systems to students and Bell, DeVidi and Solomon give tree formulations of a wide range of central logical systems―including truth-functional and quantificational logic, modal logic, provability logic, intuitionistic logic, three-valued logic, and free logic.… An excellent job.” ― B. Jack Copeland, University of Canterbury From the Back Cover Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work. About the Author John L. Bell and David DeVidi are members of the Departments of Philosophy at the University of Western Ontario and the University of Waterloo, respectively. The late Graham Solomon was a member of the Department of Philosophy at Wilfrid Laurier University. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have not read this book yet, but I got the table of contents from the book’s Website. This will be helpful to anyone deciding whether to buy this book.Table of Contents:Preface1. Classical Propositional Logic1.1. Introductory Remarks1.1.1. Some Basic Concepts1.1.2. Formal Logics1.2. Propositional Logic1.2.1. Preliminaries1.2.2. Truth Values, Valuations, and validity1.2.3. Implication, Tautology, and Other Important Concepts1.2.4. Equivalence and Expressive Completeness1.2.5. Arithmetical Representation of Statements and Logical Operations1.3. Trees for Classical Propositional Logic1.3.1. Tree Rules for Classical Propositional Logic1.3.2. Trees as a Test for Validity1.3.3. Further Applications of the Tree Method1.4. Metatheorems1.5. Other Proof Methods1.5.1. Classical Propositional Calculus1.5.2. Natural Deduction1.5.3. Sequent Calculus2. Classical Predicate Logic2.1. Introductory Remarks2.2. Tree Rules for Classical Predicate Logic2.2.1. Rules for Quantifiers2.2.2. Identity2.2.3. Functions2.3. Predicate Languages and Their Interpretations2.3.1. The Languages2.3.2. Interpretations: Preliminary Remarks2.4. Set Theory2.4.1. Sets2.4.2. Relations2.4.3. Equivalence Relations2.4.4. Orderings2.4.5. Functions2.5. Interpretations of Languages for Predicate Logic2.6. Validity, Satisfiability, and Models2.7. Correctness and Adequacy2.7.1. Some Difficulties2.7.2. Dealing with Difficulties2.7.3. The Proofs3. Using and Extending Predicate Logic3.1. Postulate Systems3.1.1. Postulate Systems for Arithmetic3.1.2. Noncategoricity of First-Order Peano Arithmetic3.2. Many Sorted Logic3.2.1. Introductory Remarks3.2.2. Many Sorted Languages and Interpretations3.2.3. Reducing Many Sorted to Unsorted Logic3.3. Second-Order Logic3.3.1. Languages and Interpretations3.3.2. Second-Order Trees3.3.3. The Strength of Second-Order Logic3.3.4. Metatheory of Second-Order Logic4. Introducing Contextual Operators: Modal Logics4.1. The Propositional Modal Language and Models4.1.1. The Language4.1.2. Interpretations4.1.3. Classes of Frames and Different Logics4.2. Trees for Contextual Logics4.2.1. Proving Correctness for 4.2.2. Counterexamples4.2.3. Proving Adequacy for 4.3. Other Systems of Contextual (Modal) Logic4.3.1. Correctness and Adequacy for Trees4.4. Provability Logic4.4.1. Arithmetic Provability and Contextual Logic4.4.2. Frames and Provability Logic4.4.3. Trees for Provability Logic4.5. Multi-Modal Logic4.6. Quantificational Contextual Logic4.6.1. The Languages4.6.2. Introduction4.6.3. Semantics for Contextual Predicate Logic4.6.4. Concluding Remarks5. Getting Away From Bivalence: Three-Valued and Intuitionistic Logic5.1. Three-Valued Logics5.1.1. Trees for Three-Valued Logic5.2. Intuitionistic Logic5.2.1. Introduction – Constructivism5.2.2. A More General Account5.2.3. Semantics and Countermodels5.2.4. Metatheorems for Intuitionistic Propositional Logic5.2.5. Comparing Intutionistic Logic to Other Logics5.3. Intuitionistic Predicate Logic5.3.1. Interpretations5.3.2. Trees for Intuitionistic Predicate Logic5.3.3. Intuitionistic Identity6. A Sampling of Other Logics6.1. Fuzzy Logic6.2. Algebraic Logic6.3. Term Forming Operators and Free Logics6.3.1. Term Forming Operators6.3.2. Free Logics7. Solutions to *-ed Exercises7.1. Solutions for Chapter 17.2. Solutions for Chapter 27.3. Solutions for Chapter 37.4. Solutions for Chapter 47.5. Solutions for Chapter 57.6. Solutions for Chapter 6

⭐This book is great for beginners. I learned how to perform deduction for second-order logic based on the tableau method, from this book.There is a wealth of other topics too, as you can see from the table of contents.

⭐This book is unique in that it covers a great many alternative logics, a lot of which I did not know existed prior to reading this book. It manages this in 200-300 pages, by only only covering the required information and proofs without going into too much depth. A quick way to bring you up in the whats what of the logic field. I however found the author’s attempt to explain some of the more difficult concepts to be hard to understand, an example are the proofs given in section 3.1.2, which leaves me scratching my head still. This is not an isolated case, as I found other proofs here and there to be hard to digest. Yet skipping the odd proof won’t really affect the flow of the book as it is the stated theorems which are the most important.The suggested proof method using trees is a nice method for doing logic proofs, because of its systematic nature requiring less imagination than natural deduction proofs. this makes it good for beginners since you are more likely to complete the proofs if you apply all the taught steps.

⭐Good value for money.

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