Logic Philosophy A Modern Introduction 13th Edition by Howard Kahane,Alan Hausman,Frank Boardman 9781624669354 1624669352

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