Logic An Emphasis on Formal Logic

Featuring an exceptionally clear writing style and a wealth of real-world examples and exercises, Logic: An Emphasis on Formal Logic, Fifth Edition (Chapters 1, 4-9) shows how logic relates to everyday life, demonstrating its applications in such areas as the workplace, media and entertainment, politics, science and technology, student life, and elsewhere. The examples and exercises were chosen to be interesting, thought-provoking, and relevant to students.

Stan Baronett is a master teacher and the author of several books, including Why Did the Logician Cross the Road?: Finding Humor in Logical Reasoning (2021) and Journey Into Philosophy: An Introduction with Classic and Contemporary Readings (2016).

Preface

Part I: Setting the Stage

Chapter 1: What Logic Studies
A. Statements and Arguments
B. Recognizing Arguments
Exercises 1B
C. Arguments and Explanations
Exercises 1C
D. Truth and Logic
E. Deductive and Inductive Arguments
Exercises 1E
F. Deductive Arguments: Validity and Soundness
Argument Form
Counterexamples
Summary of Deductive Arguments
Exercises 1F
G. Inductive Arguments: Strength and Cogency
Techniques of Analysis
The Role of New Information
Summary of Inductive Arguments
Exercises 1G
H. Reconstructing Arguments
Exercises 1H
Summary
Key Terms
Logic Challenge: The Problem of the Hats

Part II: Informal Logic

Chapter 4: Informal Fallacies
A. Why Study Fallacies?
B. Fallacies Based on Personal Attacks or Emotional Appeals
Fallacies Based on Personal Attacks
1. Ad Hominem Abusive
2. Ad Hominem Circumstantial
3. Poisoning the Well
4. Tu Quoque
Fallacies Based on Emotional Appeals
5. Appeal to the People
6. Appeal to Pity
7. Appeal to Fear or Force
Summary of Fallacies Based on Personal Attacks
Summary of Fallacies Based on Emotional Appeals
Exercises 4B
C. Weak Inductive Argument Fallacies
Generalization Fallacies
8. Rigid Application of a Generalization
9. Hasty Generalization
10. Composition
11. Division
12. Biased Sample
False Cause Fallacies
13. Post Hoc
14. Slippery Slope
Summary of Weak Inductive Argument Fallacies
Exercises 4C
D. Fallacies of Unwarranted Assumption or Diversion
Unwarranted Assumption
15. Begging the Question
16. Complex Question
17. Appeal to Ignorance
18. Appeal to an Unqualified Authority
19. False Dichotomy
Fallacies of Diversion
20. Equivocation
21. Straw Man
22. Red Herring
23. Misleading Precision
24. Missing the Point
Summary of Fallacies of Unwarranted Assumption and Diversion
Exercises 4D
E. Recognizing Fallacies in Ordinary Language
Exercises 4E
Summary
Key Terms
Logic Challenge: A Clever Problem

Part III: Formal Logic

Chapter 5: Categorical Propositions
A. Categorical Propositions
Exercises 5A
B. Quantity, Quality, and Distribution
Exercises 5B
C. Existential Import
D. The Modern Square of Opposition and Venn Diagrams
Venn Diagrams
Exercises 5D
E. Conversion, Obversion, and Contraposition in the Modern Square
Conversion
Obversion
Contraposition
Diagrams
Summary of Conversion, Obversion, and Contraposition
Exercises 5E
F. The Traditional Square of Opposition and Venn Diagrams
Exercises 5F.1
Venn Diagrams and the Traditional Square
Exercises 5F.2
G. Conversion, Obversion, and Contraposition in the Traditional Square
Summary of Conversion, Obversion, and Contraposition
Conversion
Obversion
Contraposition
Exercises 5G
H. 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
Exercises 5H
Summary
Key Terms
Logic Challenge: Group Relationship

Chapter 6: Categorical Syllogisms
A. Standard-Form Categorical Syllogisms
B. Mood and Figure
Exercises 6B
C. 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?
Exercises 6C
D. Rules and Fallacies Under the Modern Interpretation
Rule 1: The middle term must be distributed in at least one premise.
Associated Fallacy: Undistributed Middle
Rule 2: If a term is distributed in the conclusion, then it must be distributed in a premise.
Associated Fallacies: Illicit Major/Illicit Minor
Rule 3: A categorical syllogism cannot have two negative premises.
Associated Fallacy: Exclusive Premises
Rule 4: A negative premise must have a negative conclusion.
Associated Fallacy: Affirmative Conclusion/Negative Premise
Rule 5: A negative conclusion must have a negative premise.
Associated Fallacy: Negative Conclusion/Affirmative Premises
Rule 6: Two universal premises cannot have a particular conclusion.
Associated Fallacy: Existential Fallacy
Summary of Rules
Exercises 6D
E. Diagramming in the Traditional Interpretation
A-Propositions
E-Propositions
Exercises 6E
F. Rules and Fallacies Under the Traditional Interpretation
Exercises 6F
G. Ordinary Language Arguments
Reducing the Number of Terms in an Argument
Exercises 6G.1
Paraphrasing Ordinary Language Arguments
Categorical Propositions and Multiple Arguments
Exercises 6G.2
H. Enthymemes
Exercises 6H
I. Sorites
Exercises 6I
Summary
Key Terms
Logic Challenge: Relationships Revisited

Chapter 7: Propositional Logic
A. Logical Operators and Translations
Simple and Compound Statements
Negation
Conjunction
Disjunction
Conditional
Distinguishing "If" from "Only If"
Sufficient and Necessary Conditions
Biconditional
Summary of Operators and Ordinary Language
Exercises 7A
B. Compound Statements
Well-Formed Formulas
Exercises 7B.1
Main Operator
Exercises 7B.2
Translations and the Main Operator
Exercises 7B.3
C. Truth Functions
Defining the Five Logical Operators
Negation
Conjunction
Disjunction
Conditional
Biconditional
Exercises 7C.1
Operator Truth Tables and Ordinary Language
Propositions with Assigned Truth Values
Exercises 7C.2
D. Truth Tables for Propositions
Arranging the Truth Values
The Order of Operations
Exercises 7D
E. Contingent and Noncontingent Statements
Tautology
Self-Contradiction
Exercises 7E
F. Logical Equivalence and Contradictory, Consistent, and Inconsistent Statements
Logical Equivalence
Exercises 7F.1
Contradictory, Consistent, and Inconsistent Statements
Exercises 7F.2
G. Truth Tables for Arguments
Validity
Analyzing Sufficient and Necessary Conditions in Arguments
Technical Validity
Exercises 7G.1
Argument Forms
Exercises 7G.2
H. Indirect Truth Tables
Thinking Through an Argument
A Shorter Truth Table
Exercises 7H.1
Using Indirect Truth Tables to Examine Statements for Consistency
Exercises 7H.2
Summary
Key Terms
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
Exercises 8B
C. Tactics and Strategy
Applying the First Four Implication Rules
Exercises 8C
D. Implication Rules II
Simplification (Simp)
Conjunction (Conj)
Addition (Add)
Constructive Dilemma (CD)
Applying the Second Four Implication Rules
Exercises 8D
E. Replacement Rules I
De Morgan (DM)
Double Negation (DN)
Commutation (Com)
Association (Assoc)
Distribution (Dist)
Applying the First Five Replacement Rules
Exercises 8E
F. Replacement Rules II
Transposition (Trans)
Material Implication (Impl)
Material Equivalence (Equiv)
Exportation (Exp)
Tautology (Taut)
Applying the Second Five Replacement Rules
Exercises 8F
G. Conditional Proof
Exercises 8G
H. Indirect Proof
Exercises 8H
I. Proving Logical Truths
Exercises 8I
Summary
Key Terms
Logic Challenge: The Truth

Chapter 9: Predicate Logic
A. Translating Ordinary Language
Singular Statements
Universal Statements
Particular Statements
Summary of Predicate Logic Symbols
Paying Attention to Meaning
Exercises 9A
B. Four New Rules of Inference
Universal Instantiation (UI)
Universal Generalization (UG)
Existential Generalization (EG)
Existential Instantiation (EI)
Summary of the Four Rules
Tactics and Strategy
Exercises 9B
C. Change of Quantifier (CQ)
Exercises 9C
D. Conditional and Indirect Proof
Conditional Proof (CP)
Indirect Proof (IP)
Exercises 9D
E. Demonstrating Invalidity
Counterexample Method
Finite Universe Method
Indirect Truth Tables
Exercises 9E
F. Relational Predicates
Translations
Exercises 9F.1
Proofs
A New Restriction
Change of Quantifier
Conditional Proof and Indirect Proof
Exercises 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
Exercises 9G.1
Proofs
Exercises 9G.2
Summary
Key Terms
Logic Challenge: Your Name and Age, Please

Chapter 15, located on the companion website.
Online Chapter 15: Analyzing a Long Essay
A. Childbed Fever
B. Vienna
Exercises 15B
C. Miasm and Contagion
Exercises 15C
D. Semmelweis's Account of the Discovery
Exercises 15D
E. Initial Questions
Exercises 15E
F. A New Interpretation
Exercises 15F
Summary
Bibliography

Appendix A: Cognitive Bias
A. Introduction
B. Heuristics
C. Heuristics and Algorithms
D. The Link Between Heuristics and Cognitive Biases
E. Theories of Judgment
F. Cognitive Biases
1. Belief bias
2. Confirmation bias
3. Status quo bias
4. Availability bias
5. Halo bias
6. Functional fixedness bias
7. Anchoring bias
8. Gambling biases
9. Frequency bias
10. Ingroup bias
11. Fundamental attribution bias
G. Can We Overcome Cognitive Biases?

Appendix B: The LSAT and Logical Reasoning
Introduction
1. Logical Reasoning
2. Deductive and Inductive Arguments
3. Identifying Conclusions and Premises
A. Identifying the Conclusion
B. Choosing the Best Missing Conclusion
C. Assumptions: Choosing the Best Missing Premise
4. Additional Information That Strengthens or Weakens an Argument
5. Arguments That Use Either Analogical, Statistical, or Causal Reasoning
A. Analogical Reasoning
B. Statistical Reasoning
C. Causal Reasoning
6. Explaining or Resolving Given Information
7. Argument Flaws
A. Fallacies Based on Personal Attacks or Emotional Appeals
B. Weak Inductive Argument Fallacies
C. Fallacies of Unwarranted Assumption or Diversion
8. Recognizing Reasoning Patterns
A. Class Terms
B. Conditional Statements
C. Translating Conditional Statements
D. Distinguishing "If" from "Only If"
E. Conditionals and Arguments
F. Sufficient and Necessary Conditions
9. Continuing the Process

Glossary
Answers to Selected Exercises
Index