Essentials of Logic

Table of Contents

Table of Contents

Preface

 

Acknowledgments

 

CHAPTER 1 Basic Logical Concepts

1.1 What Logic Is

1.2 Propositions and Sentences

1.3 Arguments, Premises, and Conclusions

1.4 Arguments and Explanations

1.5 Recognizing Arguments

    A. Premise- and Conclusion-Indicators

    B. Arguments in Context

    C. Premises Not in Declarative Form

    D. Unstated Propositions

1.6 Deduction and Validity

1.7 Validity and Truth

1.8 Induction and Probability

1.9 Analyzing Arguments

    A. Paraphrasing

    B. Diagramming Arguments

    C. Interwoven Arguments

1.10 Complex Argumentative Passages

Essentials of Chapter 1

 

CHAPTER 2 Informal Fallacies

2.1 What Is a Fallacy?

2.2 Fallacies of Relevance

    R1. Argument from Ignorance (argumentum ad ignoratiam)

    R2. Appeal to Illegitimate Authority (argumentum ad verecundiam)

    R3. Argument Against the Person (Personal Attack, argumentum ad hominem)

    R4. Appeal to Emotion (Mob Appeal, argumentum ad populum)

    R5. Appeal to Pity (argumentum ad misericordiam)

    R6. Appeal to Force (argumentum ad baculum)

    R7. Irrelevant Conclusion (ignoratio elenchi; non sequitur)

2.3 Fallacies of Presumption

    P1. Complex Question

    P2. False Cause (post hoc, ergo propter hoc; non causa pro causa)

    P3. Begging the Question (petitio principii)

    P4. Accident

    P5. Converse Accident (Hasty Generalization)

    P6. Suppressed Evidence

    P7. False Dichotomy

2.4 Fallacies of Ambiguity

    A1. Equivocation

    A2.Amphiboly

    A3. Accent

    A4. Composition

    A5. Division

Essentials of Chapter 2

 

CHAPTER 3 Categorical Propositions

3.1 Categorical Logic

3.2 Categorical Propositions and Classes

3.3 Symbolism and Venn Diagrams for Categorical Propositions

3.4 Distribution

3.5 Existential Import

3.6 The Aristotelian Square of Opposition and Immediate Inferences

    A. Contradictories

    B. Contraries

    C. Subcontraries

    D. Subalternation

3.7 The Boolean Square of Opposition

3.8 Logical Equivalence and Immediate Inferences

    A. Conversion

    B. Obversion

    C. Contraposition

Essentials of Chapter 3

 

CHAPTER 4 Categorical Syllogisms

4.1 Standard Form Categorical Syllogisms

    A. Major, Minor, and Middle Terms

    B. Mood

    C. Figure

4.2 The Nature of Syllogistic Arguments

4.3 Venn Diagram Technique for Testing Syllogisms

4.4 Syllogistic Rules and Syllogistic Fallacies

Essentials of Chapter 4

 

CHAPTER 5 Arguments in Ordinary Language

5.1 Syllogistic Arguments in Ordinary Language

5.2 Reducing the Number of Terms in a Syllogistic Argument

5.3 Translating Categorical Propositions into Standard Form

    A. Singular Propositions

    B. Categorical Propositions with Adjectives or Adjectival Phrases as Predicates

    C. Categorical Propositions with Verbs Other Than the Standard Form Copula To Be

    D. Categorical Propositions in Nonstandard Order

    E. Categorical Propositions with Nonstandard Quantifiers

    F. Exclusive Propositions

    G. Propositions Without Quantifiers

    H.Propositions Not in Standard Form that Have Logically Equivalent Standard Form Alternatives

    I. Exceptive Propositions

    J. More Complex Quantifiers

5.4 Uniform Translation

5.5 Enthymemes

Essentials of Chapter 5

 

CHAPTER 6 Symbolic Logic

6.1 The Symbolic Language of Modern Logic

6.2 Symbolese 101: The Language of Propositional Logic

    A. Negation

    B. Conjunction

    C. Disjunction

    D. Material Implication (Material Conditionality)

    E. Biconditionals (Material Equivalence)

    F. Grouping Indicators

6.3 Truth Tables as Tools for Analyzing Compound Propositions

6.4 Tautologous, Contradictory, and Contingent Statement Forms

6.5 Truth Tables as a Test for the Validity of Arguments

    A.Some Common Valid Argument Forms

    B. Some Common Invalid Argument Forms

    C. More Complex Arguments

6.6 Incomplete and Reverse Truth Tables

    A. Incomplete Truth Tables

    B. Reverse Truth Tables

6.7 Arguments, Conditionals, and Tautologies

Essentials of Chapter 6

 

CHAPTER 7 The Method of Deduction

7.1 Natural Deduction Versus Truth Tables

7.2 Formal Proofs of Validity

7.3 The Rule of Replacement (1)

7.4 The Rule of Replacement (2)

7.5 Conditional Proof

7.6 Indirect Proof

Essentials of Chapter 7

 

CHAPTER 8 Quantification Theory

8.1 When Propositional Logic Is Not Enough

8.2 Symbolese 102: The Language of Quantificational Logic

    A. Singular Propositions, Subjects, and Predicates

    B. Universal and Particular Propositions

    C. And Sometimes the Statements Are More Complex

8.3 Proving Validity

8.4 Conditional and Indirect Proof

8.5 Proving Invalidity

Essentials of Chapter 8

 

CHAPTER 9 Induction

9.1 Introduction to Induction

9.2 Arguments by Analogy

9.3 Appraising Arguments by Analogy

9.4 Explanations and Hypotheses

9.5 Arguments to the Best Explanation

Essentials of Chapter 9

 

Appendix: Truth Trees

A.1 Propositional Logic

A.2 Quantificational Logic

Essentials of the Appendix

 

Solutions to the Odd-Numbered Problems

 

Glossary/Index