Preface
Introduction
Part One: Language and Reasoning
Chapter 1: Classification
1.1 Concepts and Referents
1.2 Rules of Classification
1.2A Consistent Principle
1.2B Essential Attributes
1.3 Levels of Organization
Summary
Additional Exercises
Chapter 2: Definitions
2.1 The Functions of a Definition
2.2 Rules for Definitions
2.3 Constructing Definitions
Summary
Additional Exercises
Chapter 3: Propositions
3.1 Propositions and Word Meaning
3.1A Connotations
3.1B Metaphors
3.2 Propositions and Grammar
3.2A Propositions and Sentence Structure
3.2B Connectives
3.2C Restrictive and Nonrestrictive Clauses
3.2D Noun Clauses
Summary
Additional Exercises
Chapter 4: Argument Analysis
4.1 Elements of Reasoning
4.1A Premise, Conclusion, and Argument
4.1B Recognizing Arguments
4.2 Diagramming Arguments
4.3 Evaluating Arguments
4.4 Induction and Deduction
4.5 Implicit Premises
4.6 Distilling Arguments
Summary
Additional Exercises
Chapter 5: Fallacies
5.1 Subjectivist Fallacies
5.1A Subjectivism
5.1B Appeal to Majority
5.1C Appeal to Emotion
5.1D Appeal to Force (Argumentum ad Baculum)
5.2 Fallacies Involving Credibility
5.2A Appeal to Authority (Argumentum ad Verecundiam)
5.2B Ad Hominem
5.3 Fallacies of Context
5.3A False Alternative
5.3B Post Hoc
5.3C Hasty Generalization
5.3D Accident
5.3E Slippery Slope
5.3F Composition and Division
5.4 Fallacies of Logical Structure
5.4A Begging the Question (Circular Argument)
5.4B Equivocation
5.4C Appeal to Ignorance (Argumentum ad Ignorantiam)
5.4D Diversion
Summary
Additional Exercises
Part Two: Deductive Logic
Chapter 6: Categorical Propositions
6.1 Standard Form
6.1A Components of Categorical Propositions
6.1B Translating into Standard Form
6.2 The Square of Opposition
6.2A Contraries
6.2B Contradictories
6.2C Subalternates
6.2D Subcontraries
6.3 Existential Import
6.4 Venn Diagrams
6.5 Immediate Inference
6.5A Conversion
6.5B Obversion
6.5C Contraposition
Summary
Additional Exercises
Chapter 7: Categorical Syllogisms
7.1 The Structure of a Syllogism
7.2 Validity
7.3 Enthymemes
7.4 Rules of Validity
7.4A Distribution
7.4B The Rules
7.4C Enthymemes and Rules
7.5 Venn Diagrams
7.5A Diagramming Syllogisms
7.5B Enthymemes and Venn Diagrams
7.5C Venn Diagrams and Existential Import
Summary
Additional Exercises
Chapter 8: Reasoning with Syllogisms
8.1 Disjunctive Syllogisms
8.2 Hypothetical Syllogisms
8.2A Hypothetical Propositions
8.2B Forms of Hypothetical Syllogism
8.3 Distilling Deductive Arguments
8.3A Identifying the Form of a Syllogism
8.3B Nonstandard Quantifiers
8.4 Extended Arguments
8.4A Categorical Syllogisms in Extended Arguments
8.4B Hypothetical Syllogisms in Extended Arguments
8.4C Extended Arguments with Elements of Different Types
8.4D Compound Components
8.4E Distilling an Extended Argument
Summary
Additional Exercises
Chapter 9: Propositional Logic—Propositions
9.1 Connectives
9.1A Conjunction, Negation, and Disjunction
9.1B Conditional and Biconditional
9.1C Truth Functions
9.2 Statement Forms
9.3 Computing Truth Values
9.4 Formal Properties and Relationships
9.4A Tautologies, Self-Contradictions, and Contingencies
9.4B Equivalence, Contradiction, and Consistency
Summary
Additional Exercises
Chapter 10: Propositional Logic—Arguments
10.1 Truth Table Test of Validity
10.2 Truth Table Test: Short Form
10.3 Proof
10.3A Rules of Inference
10.3B Rules of Inference (Continued)
10.3C Constructing a Proof
10.4 Equivalence
10.4A Rules of Equivalence
10.4B Rules of Equivalence (Continued)
10.5 Conditional Proof and Reductio ad Absurdum
10.5A Conditional Proof
10.5B Reductio ad Absurdum
Summary
Additional Exercises
Chapter 11: Predicate Logic
11.1 Singular and Quantified Statements
11.1A Singular Statements
11.1B Quantified Statements
11.2 Categorical Statements
11.3 Quantifier Scope and Statement Forms
11.3A Compound Statements Within the Scope of a Quantifier
11.3B Combining Quantified Statements
11.4 Proof
11.4A Using Propositional Rules
11.4B Equivalence Rule: Quantifier Negation
11.4C Inference Rules
11.4D Strategies for Proof
11.4E Conditional Proof and Reductio ad Absurdum
11.5 Relations and Multiple Quantification
11.5A Relations
11.5B Overlapping Quantifiers
11.5C Proof with Relational Statements
Summary
Additional Exercises
Part Three: Inductive Logic
Chapter 12: Inductive Generalizations
12.1 Generalizing
12.1A Three Rules for Generalizing
12.2 Causality
12.3 Agreement and Difference
12.4 Concomitant Variations and Residues
Summary
Additional Exercises
Chapter 13: Argument by Analogy
13.1 Analogy and Similarity
13.2 Analysis and Evaluation
13.2A Finding the Connecting Term
13.2B Evaluation
Summary
Additional Exercises
Chapter 14: Statistical Reasoning
14.1 Logic and Statistics
14.2 Using Statistics in Argument
14.2A Totals and Ratios
14.2B Frequency and Distribution
14.2C Average and Median
14.3 Statistical Generalization
14.4 Statistical Evidence of Causality
14.4A Correlation and Causality
14.4B Evaluating Correlations
14.4C Experiments Versus Observational Studies
14.4D External Validity
Summary
Additional Exercises
Chapter 15: Explanation
15.1 Explanation and Argument
15.1A Diagramming Explanations
15.1B Evaluating Explanations
15.2 Adequacy of Hypotheses
15.2A Strength
15.2B Completeness
15.2C Informativeness
15.2D Combining the Standards
15.3 The Truth of Hypotheses
15.3A Testing Hypotheses
15.3B Plausibility
Summary
Additional Exercises
Chapter 16: Probability
16.1 Probability Measures
16.2 The Probability Calculus
16.2A Conjunction
16.2B Disjunction
16.2C Negation
16.2D Extending the Rules
Summary
Additional Exercises
Index