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Table of Contents

Each chapter ends with a Summary, Key Terms, and a Logic Challenge.

PART I. SETTING THE STAGE

CHAPTER 1. WHAT LOGIC STUDIES
A. Statements and Arguments
B. Recognizing Arguments
Check Your Understanding 1B
C. Arguments and Explanations
Check Your Understanding 1C
D. Truth and Logic
E. Deductive and Inductive Arguments
Check Your Understanding 1E
F. Deductive Arguments: Validity and Truth
Logical Form
Counterexamples
Check Your Understanding 1F
G. Inductive Arguments: Strength and Truth
Techniques of Analysis
Check Your Understanding 1G
LOGIC CHALLENGE: The Problem of the Hats

PART II. INFORMAL LOGIC

CHAPTER 2. LANGUAGE MATTERS
A. Intension and Extension
Terms, Use, and Mention
Two Kinds of Meaning
Proper Names
Check Your Understanding 2A
B. Using Intensional Definitions
Synonymous Definitions
Word Origin Definitions
Operational Definitions
Definition by Genus and Difference
C. Using Extensional Definitions
Ostensive Definitions
Enumerative Definitions
Definition by Subclass
Check Your Understanding 2C
D. Applying Definitions
Stipulative Definitions
Lexical Definitions
Functional Definitions
Precising Definitions
Theoretical Definitions
Persuasive Definitions
Check Your Understanding 2D
E. Guidelines for Informative Definitions
Check Your Understanding 2E
F. Cognitive and Emotive Meaning
Check Your Understanding 2F
G. Factual and Verbal Disputes
Check Your Understanding 2G
LOGIC CHALLENGE: The Path

CHAPTER 3. DIAGRAMS AND ANALYSIS
A. The Basics of Diagramming Arguments
Check Your Understanding 3A
B. Incomplete Arguments
Check Your Understanding 3B
C. Rhetorical Language
Rhetorical Questions
Rhetorical Conditionals
Rhetorical Disjunctions
Check Your Understanding 3C
D. Necessary and Sufficient Conditions
Check Your Understanding 3D
LOGIC CHALLENGE: The Train to Vegas

CHAPTER 4. INFORMAL FALLACIES
A. Fallacies of Relevance
1. Argument Against the Person
2. Tu Quoque
3. Appeal to the People
4. Appeal to Pity
5. Appeal to Force
6. Appeal to Ignorance
7. Missing the Point
8. Appeal to an Unqualified Authority
Summary of Fallacies of Relevance
Check Your Understanding 4A
B. Fallacies of Unwarranted Assumption
9. Begging the Question
10. Complex Question
11. Biased Sample
12. Accident
13. Hasty Generalization
14. Misleading Precision
15. False Dichotomy
16. False Dilemma
17. Coincidence
18. Post Hoc Fallacy
19. Common Cause Fallacy
20. Slippery Slope
Summary of Fallacies of Unwarranted Assumption
Check Your Understanding 4B
C. Fallacies of Ambiguity or Diversion
21. Equivocation
22. Amphiboly
23. Composition
24. Division
25. Emphasis
26. Straw Man Fallacy
27. Red Herring Fallacy
Check Your Understanding 4C
Summary of Fallacies of Ambiguity or Diversion
D. Recognizing Fallacies in Ordinary Language
Check Your Understanding 4D
LOGIC CHALLENGE: A Clever Problem

PART III. FORMAL LOGIC

CHAPTER 5. CATEGORICAL PROPOSITIONS
A. Categorical Propositions
Check Your Understanding 5A
B. Quantity, Quality, and Distribution
Check Your Understanding 5B
C. The Square of Opposition
Check Your Understanding 5C
D. Conversion, Obversion, and Contraposition
Conversion
Obversion
Contraposition
Check Your Understanding 5D
E. Existential Import
F. The Modern Square of Opposition
G. Conversion, Obversion, and Contraposition Revisited
Check Your Understanding 5G
H. Venn Diagrams and the Traditional Square
Check Your Understanding 5H
I. Translating Ordinary Language into Categorical Propositions
Missing Plural Nouns
Nonstandard Verbs
Singular Propositions
Adverbs and Pronouns
“It Is False That . . .”
Implied Quantifiers
Nonstandard Quantifiers
Conditional Statements
Exclusive Propositions
“The Only”
Propositions Requiring Two Translations
Check Your Understanding 5I
LOGIC CHALLENGE: Group Relationship

CHAPTER 6. CATEGORICAL SYLLOGISMS
A. Standard-Form Categorical Syllogisms
B. Diagramming in the Modern Interpretation
Diagramming A-propositions
Diagramming E-propositions
Diagramming I-propositions
Diagramming O-propositions
Wrapping Up the X
Is the Syllogism Valid?
Check Your Understanding 6B
C. Diagramming in the Traditional Interpretation
A-propositions
E-propositions
When Both Interpretations Give the Same Results
Check Your Understanding 6C
D. Mood and Figure
Check Your Understanding 6D
E. Rules and Fallacies
Check Your Understanding 6E
F. Ordinary Language Arguments
Reducing the Number of Terms in an Argument
Check Your Understanding 6F.1
Paraphrasing Ordinary Language Arguments
Categorical Propositions and Multiple Arguments
Check Your Understanding 6F.2
G. Enthymemes
Check Your Understanding 6G
H. Sorites
Check Your Understanding 6H
LOGIC CHALLENGE: The Four Circles

CHAPTER 7. PROPOSITIONAL LOGIC
A. Logical Operators and Translations
Simple and Compound Statements
Negation
Conjunction
Disjunction
Conditional Statements
Distinguishing "If" from "Only if"
Biconditional

Check Your Understanding 7A
B. Complex Statements
Well-Formed Formulas
Check Your Understanding 7B.1
Main Operator
Check Your Understanding 7B.2
Translations and the Main Operator
Check Your Understanding 7B.3
C. Truth Functions
Defining the Five Logical Operators
Negation
Conjunction
Disjunction
Conditional
Biconditional
Check Your Understanding 7C
Operator Truth Tables and Ordinary Language
D. Truth Tables for Propositions
Arranging the Truth Values
The Order of Operations
Check Your Understanding 7D.1
Propositions with Assigned Truth Values
Check Your Understanding 7D.2
E. Contingent and Noncontingent Statements
Tautology
Self-Contradiction
Check Your Understanding 7E
F. Logical Equivalence
Check Your Understanding 7F
G. Contradictory, Consistent, and Inconsistent Statements
Check Your Understanding 7G
H. Truth Tables for Arguments
Validity
Technical Validity
Check Your Understanding 7H
I. Indirect Truth Tables
Thinking Through An Argument
A Shorter Truth Table
Check Your Understanding 7I.1
Necessary and Sufficient Conditions
Argument Form
Check Your Understanding 7I.2
Examining Statements for Consistency
Check Your Understanding 7I.3
LOGIC CHALLENGE: A Card Problem

CHAPTER 8. NATURAL DEDUCTION
A. Natural Deduction
B. Implication Rules I
Modus Ponens (MP)
Modus Tollens (MT)
Hypothetical Syllogism (HS)
Disjunctive Syllogism (DS)
Justification—Applying the Rules of Inference
Check Your Understanding 8B
C. Tactics and Strategy
Working Through a Proof
Check Your Understanding 8C
D. Implication Rules II
Constructive Dilemma (CD)
Simplification (Simp)
Conjunction (Conj)
Addition (Add)
Check Your Understanding 8D
E. Replacement Rules I
De Morgan (DM)
Commutation (Com)
Association (Assoc)
Distribution (Dist)
Double Negation (DN)
Check Your Understanding 8E
F. Replacement Rules II
Transposition (Trans)
Material Implication (Impl)
Material Equivalence (Equiv)
Exportation (Exp)
Tautology (Taut)
Check Your Understanding 8F
G. Conditional Proof
Check Your Understanding 8G
H. Indirect Proof
Check Your Understanding 8H
LOGIC CHALLENGE: The Truth

CHAPTER 9. PREDICATE LOGIC
A. Translating Ordinary Language
Singular Statements
Universal Statements
Particular Statements
Paying Attention to Meaning
Check Your Understanding 9A
B. Four New Rules of Inference
Universal Instantiation
Universal Generalization
Existential Generalization
Existential Instantiation
Summary of the Four Rules
Tactics and Strategy
Check Your Understanding 9B
C. Change of Quantifier
Check Your Understanding 9C
D. Conditional and Indirect Proof
Conditional Proof
Indirect Proof
Check Your Understanding 9D
E. Proving Invalidity
Counterexample Method
Finite Universe Method
Indirect Truth Tables
Check Your Understanding 9E
F. Relational Predicates
Translations
Check Your Understanding 9F.1
Proofs
A New Restriction
Change of Quantifier
Conditional Proof and Indirect Proof
Check Your Understanding 9F.2
G. Identity
Simple Identity Statements
“Only”
“The Only”
“No . . . Except”
“All Except”
Superlatives
“At Most”
“At Least”
“Exactly”
Definite Descriptions
Summary of Identity Translations
Check Your Understanding 9G.1
Proofs
Check Your Understanding 9G.2
LOGIC CHALLENGE: Your Name and Age, Please
PART IV. INDUCTIVE LOGIC

CHAPTER 10. ANALOGICAL ARGUMENTS
A. The Framework of Analogical Arguments
Check Your Understanding 10A
B. Analyzing Analogical Arguments
Criteria for Analyzing Analogical Arguments
Check Your Understanding 10B
C. Strategies of Evaluation v Disanalogies
Counteranalogy
Unintended Consequences
Combining Strategies
Check Your Understanding 10C
LOGIC CHALLENGE: Beat the Cheat

CHAPTER 11. LEGAL ARGUMENTS
A. Deductive and Inductive Reasoning
B. Conditional Statements
C. Necessary and Sufficient Conditions
D. Disjunction and Conjunction
E. Analyzing a Complex Rule
Check Your Understanding 11E
F. Analogies
G. The Role of Precedent
Check Your Understanding 11G
LOGIC CHALLENGE: A Guilty Problem

CHAPTER 12. MORAL ARGUMENTS
A. Value Judgments
Justifying “Should”
Types of Value Judgments
Taste and Value
Check Your Understanding 12A
B. Moral Theories
Emotivism
Consequentialism
Egoism
Utilitarianism
Deontology
Situation Ethics
Relativism
Contrasting Moral Theories
Check Your Understanding 12B
C. The Naturalistic Fallacy
D. The Structure of Moral Arguments
E. Analogies and Moral Arguments
Check Your Understanding 12E
F. Justifying Moral Premises
Check Your Understanding 12F
LOGIC CHALLENGE: Dangerous Cargo

CHAPTER 13. STATISTICAL ARGUMENTS AND PROBABILITY
A. Samples and Populations
Check Your Understanding 13A
B. Statistical Averages
Check Your Understanding 13B
C. Standard Deviation
Dividing the Curve
The Size of the Standard Deviation
How to Calculate Standard Deviation
Check Your Understanding 13C
D. What If the Results Are Skewed?
E. The Misuse of Statistics
Check Your Understanding 13E
F. Probability Theories
A Priori Theory
Relative Frequency Theory
Subjectivist Theory
G. Probability Calculus
Conjunction Methods
Disjunction Methods
Negation Method
Check Your Understanding 13G
H. True Odds in Games of Chance
I. Bayesian Theory
Check Your Understanding 13I
LOGIC CHALLENGE: The Second Child

CHAPTER 14. CAUSALITY AND SCIENTIFIC ARGUMENTS
A. Causality
B. Mill’s Methods
Method of Agreement
Method of Difference
Joint Method of Agreement and Difference
Method of Residues
Method of Concomitant Variations
Check Your Understanding 14B
C. Limitations of Mill’s Methods
D. Theoretical and Experimental Science
E. Inference to the Best Explanation
F. Hypothesis Testing, Experiments, and Predictions
Controlled Experiments
Determining Causality
G. Science and Superstition
The Need for a Fair Test
Verifiable Predictions
Nontrivial Predictions
Connecting the Hypothesis and Prediction
Science and Superstition
The Allure of Superstition
Check Your Understanding 14G
LOGIC CHALLENGE: The Scale and the Coins

CHAPTER 15. ANALYZING A LONG ESSAY
A. Childbed Fever
B. Vienna
Check Your Understanding 15B
C. Miasm and Contagion
Check Your Understanding 15C
D. Semmelweis’ Account of the Discovery
Check Your Understanding 15D
Summary of Semmelweis’ Account
E. Initial Questions
Check Your Understanding 15E
F. A New Interpretation
Check Your Understanding 15F
LOGIC CHALLENGE: A Relative Problem

Bibliography
Glossary
Answers to Selected Exercises
Index

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