Logic for Justice : An Introduction to Formal Logic with an Emphasis on Political Reform

An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. Furthermore, it motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features • Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be drawn to the subject. • Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. • Carefully explains the value of arguing well throughout oneâ€TMs life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. • Includes examples that run throughout the entire book, allowing students to see how the ideas presented in the book are related to each other. • Provides a large and diverse set of problems for each chapter. • Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works. Cover Half Title Title Page Copyright Page Dedication Contents Acknowledgements Preface (For Teachers) 1. Introduction PART I: Natural language arguments 2. Arguments in English 2.1. Arguments, Reasons, and Views 2.2. The Basics of Natural Language Arguments 2.3. Validity and Soundness 2.4. The Personal and Political Value of Arguments 2.5. Problems PART II: Propositional logic 3. The language of propositional logic 3.1. The Formal Language 3.1.1. Sentence Letters 3.1.2. Parentheses 3.1.3. Negation 3.1.4. Conjunction 3.1.5. Disjunction 3.1.6. Conditional 3.1.7. Biconditional 3.1.8. Summary 3.2. Translation Tips 3.3. Translating English Arguments 3.4. Sentences of P 3.5. Notation and Terminology 3.6. Applications to Justice 3.7. Problems 4. Truth and validity in P 4.1. Truth 4.2. Truth for Sentences of P: Detailed Examples 4.3. Validity 4.4. Justifying the Definition of Validity in P 4.5. Applications to Justice 4.6. Problems 5. The propositional approach to validity in English 5.1. Final Definitions 5.2. Applications to Justice 5.3. Problems 6. Extracting arguments 6.1. Extraction 6.2. Problems PART III: Shortcomings of propositional logic 7. From propositional logic to first-order logic 7.1. Shortcomings of Propositional Logic 7.2. Problems PART IV: First-order logic 8. The language of first-order logic 8.1. The Formal Language 8.1.1. Constants 8.1.2. Predicates 8.1.3. Parentheses and Logical Connectives 8.1.4. Variables 8.1.5. Quantifiers 8.1.6. Summary 8.2. Translating English Arguments 8.3. Sentences of F 8.4. Applications to Justice 8.5. Problems 9. Validity and truth in F 9.1. Proof Trees and Validity in F 9.1.1. Decomposing Conjunctions and Disjunctions 9.1.2. Decomposing Conditionals and Biconditionals 9.1.3. Validity 9.1.4. Decomposing Quantifiers 9.1.5. Decomposing Negations 9.1.6. Examples 9.2. Truth in F 9.3. Applications to Justice 9.4. Problems 10. The first-order approach to validity in English 10.1. Final Definitions 10.2. Applications to Justice 10.3. Comparing Two Accounts 10.4. Problems PART V: Review A. Summary B. Definitions Bibliography Index An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction.In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one's life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.