Classical Logic and Its Rabbit-Holes

A First Course

Nelson P. Lande

• Publisher: Hackett Publishing Company, Inc.
• Year: 2013
• eBook ISBN: 9781624660443
• Edition: 0
• Topic: Philosophy
• Subtopic: Logic in Philosophy

Many students ask, 'What is the point of learning formal logic?' This book gives them the answer. Using the methods of deductive logic, Nelson Lande introduces each new element in exquisite detail, as he takes students through example after example, proof after proof, explaining the thinking behind each concept. Shaded areas and appendices throughout the book provide explanations and justifications that go beyond the main text, challenging those students who wish to delve deeper, and giving instructors the option of confining their course to the basics, or expanding it, when they wish, to more rigorous levels. Lande encourages students to think for themselves, while at the same time providing them with the level of explanation they need to succeed. It is a rigorous approach presented in a style that is informal, engaging, and accessible. Students will come away with a solid understanding of formal logic and why it is not only important, but also interesting and sometimes even fun. It is a text that brings the human element back into the teaching of logic. --Hans Halvorson, Princeton University

Table of contents

• Title Page
• Copyright Page
• Contents
• Acknowledgments
• Note to the Reader
• CHAPTER ONE Propositional Logic: A Formal Language, Part One
• 1. Introduction: What Logic Is
• 2. Arguments: Valid and Invalid; Sound and Unsound
• 3. Sentences/Statements/Propositions: Bearers of Truth-Value
• 4. The Artificial Language L1: Propositional Symbols and Connectives
• 5. More on the Wedge
• 6. Truth-Tables: Definitions
• 7. Translating ‘But’
• 8. Parentheses and Interpretations
• 9. Logically Equivalent Propositions
• 10. Translations
• CHAPTER TWO Propositional Logic: A Formal Language, Part Two
• 1. Connectives: Truth-Functionaland Non-Truth-Functional
• 2. Translating ‘Only If’
• 3. Translating ‘Unless’
• 4. Truth-Tables: Valid and Invalid Arguments
• 5. Tautologies, Contradictions, and Contingent Sentences
• 6. A Formal System
• 7. Appendix I: Expressive Completeness: Too Few Connectives?
• 8. Appendix II: Sheffer’s Razor: Too Many Connectives?
• 9. Appendix III: Truth-Functional Connectives Reconsidered
• CHAPTER THREE Propositional Logic: A Deductive Apparatus, Part One
• 1. Introduction
• 2. Derivation Rules: The First Seven
• 3. From Arguments to Sequents
• 4. Constructing Derivations: The Mechanics and the Strategies
• 5. A Recapitulation of the First Seven Derivation Rules
• 6. Constructing Derivations Using Only the First Seven Derivation Rules
• 7. A Schematic Recapitulation of the First Seven Derivation Rules
• 8. Derivation Rules: The Last Four
• 9. A Recapitulation of the Last Four Derivation Rules
• CHAPTER FOUR Propositional Logic: A Deductive Apparatus, Part Two
• 1. Theorems
• 2. Derived Derivation Rules: The First Two
• 3. Interlude: Substitution-Instances
• 4. Derived Derivation Rules: The Last Two
• 5. A Tricky Sequent—and the Reductio Assumption Revisited
• 6. A Schematic Recapitulation of the Last Four Derivation Rules
• 7. The Cheat Sheet
• 8. Appendix I: Deductive Completeness: A Next Logic Course
• 9. Appendix II: →I and ─I Revisited
• CHAPTER FIVE Predicate Logic: A Formal Language, Part One
• 1. Introduction
• 2. Things and Properties: Proper Names and Predicates
• 3. The Universal Quantifier
• 4. The Existential Quantifier
• 5. The Square of Opposition
• 6. Free and Bound Variables, Open and Closed Wffs, and Quantifier Scope
• 7. Translations
• CHAPTER SIX Predicate Logic: A Formal Language, Part Two
• 1. Multiple Quantifiers and Polyadic/Multiplace Predicates
• 2. The Formal Language L2
• 3. Identity
• 4. The Square of Opposition Revisited
• 5. Restricted Domains and the (In)dispensability of Quantifiers
• 6. Quantifier Negation (QN)
• 7. Invalid Arguments
• 8. Appendix I: Logically Valid Wffs/Logical Truths
• 9. Appendix II: Quantifier Shift (QS)
• CHAPTER SEVEN Predicate Logic: A Deductive Apparatus, Part One
• 1. Introduction
• 2. ∀E: An Introduction to Universal Quantifier Elimination
• 3. ∃I: An Introduction to Existential Quantifier Introduction
• 4. ∀I: An Introduction to Universal Quantifier Introduction
• 5. ∃E: An Introduction to Existential Quantifier Elimination
• 6. Derivations
• 7. The Refined Version of the Quantifier Rules: Preliminary Matters
• 8. ∀E: The Refined Version
• 9. ∃I: The Refined Version
• 10. ∀I: The Refined Version
• 11. ∃E: The Refined Version
• CHAPTER EIGHT Predicate Logic: A Deductive Apparatus, Part Two
• 1. Derivations Involving Multiplace Predicates
• 2. Identity Elimination (=E)
• 3. Identity Introduction (=I)
• 4. Odds and Ends
• 5. Appendix I: Undecidability
• 6. Appendix II: ∀I vs. ∃I: Restriction vs. No Restriction
• LIST OF DEFINITIONS
• INDEX