Preface

Chapter 1 – The Basics of Logical Analysis

I. What is Logic?

II. Basic Notions: Propositions and Arguments

III. Recognizing and Explicating Arguments

Paraphrasing

Enthymemes: Tacit Propositions

Arguments vs. Explanations

IV. Deductive and Inductive Arguments

Deductive Arguments

Inductive Arguments

V. Diagramming Arguments

Independent Premises

Intermediate Premises

Joint Premises

Chapter 2 – Informal Logical Fallacies

I. Logical Fallacies: Formal and Informal 29

II. Fallacies of Distraction 31

Appeal to Emotion (Argumentum ad Populum) 31

Appeal to Force (Argumentum ad Baculum) 32

Straw Man 33

Red Herring 34

Argumentum ad Hominem 36

III. Fallacies of Weak Induction 30

Argument from Ignorance (Argumentum ad Ignorantiam) 40

Appeal to Inappropriate Authority 42

Post hoc ergo propter hoc 43

Slippery Slope 44

Hasty Generalization 45

IV. Fallacies of Illicit Presumption 46

Accident 46

Begging the Question (Petitio Principii) 48

Loaded Questions 49

False Choice 51

Composition 52

Division 53

V. Fallacies of Linguistic Emphasis 53

Accent 54

Quoting out of Context 55

Equivocation 57

Manipulative Framing 59

Chapter 3 – Deductive Logic I: Aristotelian Logic 68

I. Deductive Logics 68

II. Classes and Categorical Propositions 69

The Four Types of Categorical Proposition 71

Universal Affirmative (A) 71

Universal Negative (E) 74

Particular Affirmative (I) 74

Particular Negative (O) 76

A Note on Terminology 76

Standard Form for Sentences Expressing Categorical Propositions 77

III. The Square of Opposition 79

Contradictories 80

Contraries 81

Subcontraries 81

Subalterns 82

Inferences 83

IV. Operations on Categorical Sentences 84

Conversion 84

Obversion 86

Contraposition 87

Inferences 91

V. Problems with the Square of Opposition 96

Existential Import 97

Problems for the Square 97

Solution? 98

Boolean Solution 99

VI. Categorical Syllogisms 102

Logical Form 103

The Venn Diagram Test for Validity 104

Chapter 4 – Deductive Logic II: Propositional Logic 117

I. Why Another Method of Deductive Logic? 117

II. Syntax of PL 120

Conjunctions 121

Disjunctions 121

Negations 121

Conditionals 122

Biconditionals 122

Punctuation – Parentheses 123

II. Semantics of SL 126

Negations (TILDE) 127

Conjunctions (DOT) 128

Disjunctions (WEDGE) 128

Biconditionals (TRIPLE-BAR) 129

Conditionals (HORSESHOE) 130

III. Computing Truth-Values of Compound SL Sentences 133

IV. Translating from English into SL

Tilde, Dot, Wedge

Horseshoe and Triple-Bar

V. Testing for Validity in SL

Logical Argument Form in SL

The Truth Table Test for Validity

Chapter 5 – Deductive Logic III: Natural Proofs in Propositional Logic

I. Replacement and Rules of Inference

II. Rules of Inference

Modus Ponens (M.P.)

Modus Tollens (M.T.)

Hypothetical Syllogism (H.S.)

Disjunctive Syllogism (D.S.)

Constructive Dilemma (C.D.)

Simplification (Simp.)

Conjunction (Conj.)

Absorption (Abs.)

Addition (Add.)

Conclusion

III. Replacement Rules

Double Negation (D.N.)

Commutation (Com.)

Association (Assoc.)

Material Implication (Impl.)

De Morgan’s Theorems (De M.)

Distribution (Dist.)

Material Equivalence (Equiv.)

Exportation (Exp.)

Tautology (Taut.)

IV. Constructing Formal Proofs Using Rules of Inference and Replacement

V. Conditional Proofs

The Anatomy of a Conditional Proof

Using Multiple Conditional Proofs

Conditional Proofs for Tautologies

VI. Indirect Proofs

Proving Tautologies with Indirect Proofs

Chapter 6 – Deductive Logic IV: Quantification and Predicate Logic

I. Affirmative Singular Predicates

II. Existential and Universal Quantifiers

III. Subject-Predicate Propositions

IV. Instantiation, Generalization, and the Quantifier Negation Rule

V. Formal Proofs of Validity for Aristotelian Syllogisms

Universal Instantiation

Universal Generalization

Existential Generalization

Existential Instantiation

VI. Asyllogistic Inference

VII. Proving Validity and Invalidity with Predicate Logic