Front Cover
Valid Forms for Sentential Logic
Rules for Predicate Logic
Title Page
Copyright Page
Contents
Preface to the Thirteenth Edition
Preface to the Twelfth Edition
Chapter One: Introduction
1 The Elements of an Argument
2 Deduction and Induction
3 Deductive Argument Forms
4 Truth and Validity
5 Soundness
6 Consistency
7 Contexts of Discovery and Justification
8 The Plan of This Book
Part One: Sentential Logic
Chapter Two: Symbolizing in Sentential Logic
1 Atomic and Compound Sentences
2 Truth-Functions
3 Conjunctions
4 Non–Truth-Functional Connectives
5 Variables and Constants
6 Negations
7 Parentheses and Brackets
8 Use and Mention
9 Disjunctions
10 “Not Both” and “Neither . . . Nor”
11 Material Conditionals
12 Material Biconditionals
13 “Only If” and “Unless”
14 Symbolizing Complex Sentences
15 Alternative Sentential Logic Symbols
Chapter Three: Truth Tables
1 Computing Truth-Values
2 Logical Form
3 Tautologies, Contradictions, and Contingent Sentences
4 Logical Equivalences
5 Truth Table Test of Validity
6 Truth Table Test of Consistency
7 Validity and Consistency
8 The Short Truth Table Test for Invalidity
9 The Short Truth Table Test for Consistency
10 A Method of Justification for the Truth Tables
Chapter Four: Proofs
1 Argument Forms
2 The Method of Proof: Modus Ponens and Modus Tollens
3 Disjunctive Syllogism and Hypothetical Syllogism
4 Simplification and Conjunction
5 Addition and Constructive Dilemma
6 Principles of Strategy
7 Double Negation and DeMorgan’s Theorem
8 Commutation, Association, and Distribution
9 Contraposition, Implication, and Exportation
10 Tautology and Equivalence
11 More Principles of Strategy
12 Common Errors in Problem Solving
Chapter Five: Conditional and Indirect Proofs
1 Conditional Proofs
2 Indirect Proofs
3 Strategy Hints for Using CP and IP
4 Zero-Premise Deductions
5 Proving Premises Inconsistent
6 Adding Valid Argument Forms
7 The Completeness and Soundness of Sentential Logic
8 Introduction and Elimination Rules
Chapter Six: Sentential Logic Truth Trees
1 The Sentential Logic Truth Tree Method
2 The Truth Tree Rules
3 Details of Tree Construction
4 Normal Forms and Trees
5 Constructing Tree Rules for Any Function
Part Two: Predicate Logic
Chapter Seven: Predicate Logic Symbolization
1 Individuals and Properties
2 Quantifiers and Free Variables
3 Universal Quantifiers
4 Existential Quantifiers
5 Basic Predicate Logic Symbolizations
6 The Square of Opposition
7 Common Pitfalls in Symbolizing with Quantifiers
8 Expansions
9 Symbolizing “Only,” “None but,” and “Unless”
Chapter Eight: Predicate Logic Semantics
1 Interpretations in Predicate Logic
2 Proving Invalidity
3 Using Expansions to Prove Invalidity
4 Consistency in Predicate Logic
5 Validity and Inconsistency in Predicate Logic
Chapter Nine: Predicate Logic Proofs
1 Proving Validity
2 The Four Quantifier Rules
3 The Five Main Restrictions
4 Precise Formulation of the Four Quantifier Rules
5 Mastering the Four Quantifier Rules
6 Quantifier Negation
Chapter Ten: Relational Predicate Logic
1 Relational Predicates
2 Symbolizations Containing Overlapping Quantifiers
3 Expansions and Overlapping Quantifiers
4 Places and Times
5 Symbolizing “Someone,” “Somewhere,” “Sometime,” and So On
6 Invalidity and Consistency in Relational Predicate Logic
7 Relational Predicate Logic Proofs
8 Strategy for Relational Predicate Logic Proofs
9 Theorems and Inconsistency in Predicate Logic
10 Predicate Logic Metatheory
11 A Simpler Set of Quantifier Rules
Chapter Eleven: Rationale Behind the Precise Formulation of the Four Quantifier Rules
1 Cases Involving the Five Major Restrictions
2 One-to-One Correspondence Matters
3 Accidentally Bound Variables and Miscellaneous Cases
4 Predicate Logic Proofs with Flagged Constants
Chapter Twelve: Predicate Logic Truth Trees
1 Introductory Remarks
2 General Features of the Method
3 Specific Examples of the Method
4 Some Advantages of the Trees
5 Example of an Invalid Argument with at Least One Open Path
6 Metatheoretic Discussion
7 Strategy and Accounting
Chapter Thirteen: Identity, Higher-Order Logics, and Sets
1 Identity
2 Definite Descriptions
3 Properties of Relations
4 Higher-Order Logics
5 Sets and First-Order Predicate Logic
6 Set Theory and Second-Order Predicate Logic
7 Russell’s Paradox
8 Sets in Foundational Arithmetic
9 The Existence of Sets
Chapter Fourteen: Philosophical Problems of Symbolic Logic
1 Limitations of Predicate Logic
2 Philosophical Problems
3 Logical Paradoxes
Chapter Fifteen: Modal Logic
1 Modality and Modal Logics
2 Modal Symbols and Translations
3 Modal Logic Semantics
4 Accessibility
5 Modal Truth Trees
6 Quantified Modal Logic
7 Modal Realism, Modal Fictionalism, and Transworld Identity
8 Applications of Modal Logic
9 Objections to Modal Logic
Chapter Sixteen: Syllogistic Logic
1 Categorical Propositions
2 Existential Import
3 The Square of Opposition
4 Conversion, Obversion, Contraposition
5 Syllogistic Logic—Not Assuming Existential Import
6 Venn Diagrams
7 Syllogisms
8 Determining Syllogism Validity
9 Venn Diagram Proofs of Validity or Invalidity
10 Five Rules for Determining Validity or Invalidity
11 Syllogistics Extended
12 Enthymemes
13 Sorites
14 Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared
Appendix A An Alternative to Conditional Proof?
Appendix B Instantiations and Semantics
Appendix C A Final Note on Translations
Answers to Even-Numbered Exercise Items
Bibliography
Special Symbols
Index
Inside Back Cover
Back Cover