How to Think Logically

Gary Seay has taught logic at the City University of New York since 1979 and is currently Associate Professor of Philosophy at Medgar Evers College. He is the author of journal articles on moral philosophy and bioethics. With Susana Nuccetelli, he is the editor of Latin American Philosophy (Prentice Hall, 2004).   Susana Nuccetelli is Associate Professor of Philosophy at St. Cloud State University in Minnesota. She is editor of New Essays on Semantic Externalism and Self-Knowledge (MIT Press, 2003) and author of many journal articles on epistemology and philosophy of language. She has also written on Latin American philosophy.

 

Preface

Acknowledgments

About the Authors

 

 

PART I: THE BUILDING BLOCKS OF REASONING

  

CHAPTER ONE

What Is Logical Thinking? And Why Should We Care? 

 

1.1       The Study of Reasoning

                        Inference or Argument

1.2       Logic and Reasoning

                        Dimensions of the Subject

                        Formal Logic

                        Informal Logic

                        EXERCISES

1.3       Arguments and Non-Arguments

1.4         Argument Analysis

                        Reconstructing and Evaluating Arguments

                        Identifying Premises and Conclusion

                        Premise and Conclusion Indicators

                        Arguments with No Premise or Conclusion Indicator

                        EXERCISES

1.5       The Philosopher’s Corner

                        What is Philosophical About All This

                        EXERCISES

                        WRITING PROJECT

1.6       Chapter Summary

1.7       Key Words

 

CHAPTER TWO

Thinking Logically and Speaking One’s Mind 

2.1       Rational Acceptability

                        Logical Connectedness

                        Evidential Support

                        Truth and Evidence

2.2       Beyond Rational Acceptability

                        Linguistic Merit

                        Retorical Power

                        Rhetoric vs. Logical Thinking

                        EXERCISES

2.3       From Belief to Statement

                        Propositions

2.4       Uses of Language

                        Types of Sentence

                        Declarative Sentences

2.5       Indirect and Non-Literal Language

                        Indirect Language

                        Non-Literal Language

                        EXERCISES

2.6       The Philosopher’s Corner

                        The Study of Language and Its Dimensions

                        Type and Token

                        Use and Mention

                        EXERCISES

                        WRITING PROJECT

2.7       Chapter Summary

2.8       Key Words

 

CHAPTER THREE

The Virtues of Belief 

3.1       Belief, Disbelief, and Non-Belief

                        EXERCISES

3.2       Beliefs’ Virtues and Vices

3.3       Accuracy and Truth

                        Accuracy and Inaccuracy

                        Truth and Falsity

3.4       Reasonableness

                        Empirical and Conceptual Reasonableness

3.5       Consistency

                        Defining `Consistency’ and `Inconsistency’

                        Logically Possible Propositions

                        Logically Impossible Propositions

                        Consistency and Possible Worlds

                        Consistency in Logical Thinking

3.6       Conservatism and Revisability

                        Conservatism Without Dogmatism

                        Revisability Without Relativism

3.7       Rationality vs. Irrationality

                        EXERCISES

3.8       The Philosopher’s Corner

                        Evaluative Reasons

                        EXERCISES

                        WRITING PROJECT

3.9       Chapter Summary

3.10     Key Words

 

PART II: REASON AND ARGUMENT

 

CHAPTER FOUR

Tips for Argument Analysis

4.1       A Principled Way of Reconstructing Arguments

                        Faithfulness

                        Charity

                        When Faithfulness and Charity Conflict

4.2       Missing Premises

4.3       Extended Arguments

                        EXERCISES

4.4       Types of Reason and Types of Argument

                        Deductive vs. Inductive Arguments

4.5       Evaluative Arguments with Missing Premises

                        Evaluative Arguments

                        Moral Arguments and Moral Principles

                        Implicit Evaluative Premises

                        EXERCISES

4.6       The Philosopher’s Corner

                        Can `Ought’ Follow Deductively from `Is’? Hume’s Position

                        Searle’s Reply

                        EXERCISES

                        WRITING PROJECT

4.7       Chapter Summary

4.8       Key Words

 

CHAPTER FIVE

Evaluating Deductive Arguments 

5.1       Valid Arguments

                        `Validity’ as a Technical Term

                        EXERCISES

                        Some Valid Propositional Argument Forms

                        Some Valid Syllogistic Argument Forms

                        The Cash Value of Validity

                        EXERCISES

5.2       Sound vs. Unsound Arguments

                        The Cash Value of Soundness

5.3       Cogent vs. Non-Cogent Arguments

                        The Cash Value of Cogency

                        EXERCISES

5.4       The Philosopher’s Corner

                        Deductive Arguments and the A Priori/A Posteriori Distinction

                        EXERCISES

                        WRITING PROJECT

5.5       Chapter Summary

5.6       Key Words

  

CHAPTER SIX

Analyzing Inductive Arguments 

6.1       Reconstructing Inductive Arguments

                        What Is an Inductive Argument?

6.2       Some Types of Inductive Argument

                        Enumerative Induction

                        Statistical Syllogism
                        Causal Argument

                        Analogy

                        EXERCISES

6.3       Evaluating Inductive Arguments

                        Inductive Reliability

                        Inductive Strength

                        EXERCISES

6.4       The Philosopher’s Corner

                        Is Natural Science Inductive?

                        EXERCISES

                        WRITING PROJECT

6.5       Chapter Summary

6.6       Key Words

 

PART III: INFORMAL FALLACIES

 

CHAPTER SEVEN

Some Ways an Argument Can Fail 

7.1       What Is a Fallacy?

7.2       Classification of Informal Fallacies

7.3       When Inductive Arguments Go Wrong

                        Hasty Generalization

                        Weak Analogy

                        False Cause

                        Appeal to Ignorance

                        Appeal to Unqualified Authority

                        EXERCISES

7.4       The Philosopher’s Corner

                        Appeal to Ignorance in Philosophical Arguments

                        EXERCISES

                        WRITING PROJECT

7.5       Chapter Summary

7.6       Key Words

 

CHAPTER EIGHT

Avoiding Ungrounded Assumptions

 8.1       Fallacies of Presumption

8.2       Begging the Question

                        Circular Reasoning

                        The Burden of Proof

8.3       Begging-the-Question-Against

                        EXERCISES

8.4       Complex Question

8.5       False Alternatives

8.6       Accident

                        EXERCISES

8.7       The Philosopher’s Corner

                        Is the Open Question Argument Viciously Circular?

                        EXERCISES

                        WRITING PROJECT

8.8       Chapter Summary

8.9       Key Words

 

CHAPTER NINE

From Unclear Language to Unclear Reasoning

9.1       Unclear Language and Argument Failure

9.2       Semantic Unclarity

9.3       Vagueness

                        The Sorites Paradox

                        The Slippery Slope Fallacy

9.4       Ambiguity

                        Equivocation

                        Amphiboly

9.5       Confused Predication

                        Composition

                        Division

9.6       Antidote to Unclear Language: Semantic Definitions

                        Reportive Definitions

                        The Method of Counterexample

                        Ostensive and Contextual Definitions

9.7       The Philosopher’s Corner

                        Real Definitions

                        Philosophical Analysis

                        EXERCISES

                        WRITING PROJECT

9.8       Chapter Summary

9.9       Key Words

 

CHAPTER TEN

Avoiding Irrelevant Premises  

10.1     Fallacies of Relevance

10.2     Appeal to Pity

10.3     Appeal to Force

10.4     Appeal to Emotion

                        The Bandwagon Appeal

                        Appeal to Vanity

10.5     Ad Hominem

                        The Abusive Ad Hominem

                        Tu Quoque

                        Non-Fallacious Ad Hominem

10.6     Beside the Point

10.7     Straw Man

                        EXERCISES

10.8     The Philosopher’s Corner

                        Is the Appeal to Emotion Always Fallacious?

                        EXERCISES

                        WRITING PROJECT

10.9     Chapter Summary

10.10   Key Words

 

PART IV: MORE ON DEDUCTIVE REASONING

 

CHAPTER ELEVEN

Compound Propositions 

 

11.1     Argument as a Relation Between Propositions

11.2     Simple and Compound Propositions

                        Negation

                        Conjunction

                        Disjunction

                        Material Conditional

                        Material Biconditional

11.3     A Closer Look at Compound Propositions

                        Punctuation Symbols

                        Well-Formed Formulas

                        EXERCISES

11.4     Defining Connectives with Truth Tables

11.5     Truth Tables for Compound Propositions

11.6     Logically Necessary and Logically Contingent Propositions

                        Tautologies

                        Contradictions

                        Contingencies

                        EXERCISES

11.7     The Philosopher’s Corner

                        Tautologies and Other Necessary Propositions

                        EXERCISES

                        WRITING PROJECT

11.8     Chapter Summary

11.9     Key Words

 

CHAPTER TWELVE

Checking the Validity of Propositional Arguments 

12.1     Checking Validity with Truth Tables

                        EXERCISES

12.2     Reviewing Some Standard Argument Forms

                        Modus Ponens

                        Modus Tollens

                        Contraposition

                        Hypothetical Syllogism

                        Disjunctive Syllogism

                        EXERCISES

12.3     Formal Fallacies

                        Affirming the Consequent

                        Denying the Antecedent

                        Affirming a Disjunct

                        EXERCISES

12.4     An Informal Approach to Proofs of Validity

                        The Basic Rules

                        What Is a Proof of Validity

                        How to Construct a Proof of Validity

                        Proofs vs. Truth Tables

                        EXERCISES

12.5     The Philosopher’s Corner

                        Reductio ad Absurdum Arguments

                        Reductio in Philosophy

                        EXERCISES

                        WRITING PROJECT

12.6     Chapter Summary

12.7     Key Words

 

CHAPTER THIRTEEN

Categorical Propositions 

 

13.1     What Is a Categorical Proposition?

                        Categorical Propositions

                        Standard Form Categorical Propositions

                        Non-Standard Categorical Propositions

                        EXERCISES

13.2     Venn Diagrams for Categorical Propositions

                        EXERCISES

13.3     The Square of Opposition

                        The Traditional Square of Opposition

                        Existential Import

                        The Modern Square of Opposition

                        EXERCISES

13.4     Other Immediate Inferences

                        Conversion

                        Obversion

                        Contraposition

                        EXERCISES

13.5     The Philosopher’s Corner

                        Generalization and the Appeal to Counterexample

                        EXERCISES

                        WRITING PROJECT

13.6     Chapter Summary

13.7     Key Words

 

CHAPTER FOURTEEN

Categorical Syllogisms 

14.1     What Is a Categorical Syllogism

                        Recognizing Categorical Syllogisms

14.2     Mood and Figure

                        EXERCISES

14.3     Testing for Valid ity with Venn Diagrams

                        EXERCISES

14.4     Distribution of Terms

14.5     Rules of Validity and Fallacies

                        EXERCISES

14.6     The Philosopher’s Corner

                        Standard Syllogisms and Singular Propositions

                        EXERCISES

                        WRITING PROJECT

14.7     Chapter Summary

14.8     Key Words

 

Appendix: Summary of Informal Fallacies

Answers to Selected Exercises

Glossary/Index