Introduction to Logic

Irving M. Copi was a philosopher and logician. He taught at the University of Illinois, the United States Air Force Academy, Princeton University, and the Georgetown University Logic Institute, before teaching logic at the University of Michigan, 1958-69, and at the University of Hawaii, 1969-90. His other works include Essentials of Logic, Informal Logic, and Symbolic Logic.   Carl Cohen is Professor of Philosophy at the Residential College of the University of Michigan. He has published many essays in moral and political philosophy in philosophical, medical, and legal journals. He has served as a member of the Medical School faculty of the University of Michigan, and as Chairman of the University of Michigan faculty, where he has been an active member of the philosophy faculty since 1955. His other works include The Animal Rights Debate (Rowman and Littlefield, 2001), with Prof. Tom Regan; he is also the author of Democracy (Macmillan, 1972); the author of Four Systems (Random House, 1982); the editor of Communism, Fascism, and Democracy (McGraw Hill, 1997); the co-author (with J. Sterba) of Affirmative Action and Racial Preference (Oxford, 2003)   Kenneth D. McMahon studied physics, philosophy, and English Literature as an undergraduate, then took graduate degrees in psychology and philosophy.  He has taught critical thinking, philosophy, statistics, and  psychology, and currently teaches logic for Hawaii Pacific University.  His professional interests include logic, epistemology, philosophy of science, and philosophy of mind, as well as cognitive science, psychometrics, computational theories of mind, and evolutionary psychology.

Foreward

Preface

Acknowledgments

 

PART I  LOGIC AND LAGUAGE

 

SECTION A  REASONING

 

Chapter 1     Basic Logical Concepts

1.1 What Logic Is

1.2 Propositions and Arguments

1.3 Recognizing Arguments

1.4 Arguments and Explanations

1.5 Deductive and Inductive Arguments

1.6 Validity and Truth

 

Chapter 2    Analyzing Arguments

2.1 Paraphrasing Arguments

2.2 Diagramming Arguments

2.3 Complex Argumentative Passages

2.4 Problems in Reasoning

 

SECTION B INFORMAL LOGIC

 

Chapter 3    Language and Definitions

3.1 Language Functions

3.2 Emotive Language, Neutral Language, and Disputes

3.3 Disputes and Ambiguity

3.4 Definitions and Their Uses

3.5 The Structure of Definitions: Extension and Intension

3.6 Definition by Genus and Difference

 

Chapter 4      Fallacies

4.1 What Is a Fallacy?

4.2 Classification of Fallacies

4.3 Fallacies of Relevance

4.4 Fallacies of Defective Induction

4.5 Fallacies of Presumption

4.6 Fallacies of Ambiguity

 

Part II  Deduction

 

Section A    Classical Logic

 

Chapter 5      Categorical Propositions

5.1 The Theory of Deduction

5.2 Classes and Categorical Propositions

5.3 The Four Kinds of Categorical Propositions

5.4 Quality, Quantity, and Distribution

5.5 The Traditional Square of Opposition

5.6 Further Immediate Inferences

5.7 Existential Import and the Interpretation of Categorical Propositions

5.8 Symbolism and Diagrams for Categorical Propositions

 

Chapter 6      Categorical Syllogisms

6.1 Standard-Form Categorical Syllogisms

6.2 The Formal Nature of Syllogistic Argument

6.3 Venn Diagram Technique for Testing Syllogisms

6.4 Syllogistic Rules and Syllogistic Fallacies

6.5 Exposition of the Fifteen Valid Forms of the Categorical Syllogism

Appendix: Deduction of the Fifteen Valid Forms of the Categorical Syllogism

 

Chapter 7      Syllogisms in Ordinary Language

7.1 Syllogistic Arguments

7.2 Reducing the Number of Terms to Three

7.3 Translating Categorical Propositions into Standard Form

7.4 Uniform Translation

7.5 Enthymemes

7.6 Sorites

7.7 Disjunctive and Hypothetical Syllogisms

7.8 The Dilemma

 

Section B    Modern Logic

 

Chapter 8      Symbolic Logic

8.1 Modern Logic and Its Symbolic Language

8.2 The Symbols for Conjunction, Negation, and Disjunction

8.3 Conditional Statements and Material Implication

8.4 Argument Forms and Refutation by Logical Analogy

8.5 The Precise Meaning of “Invalid” and “Valid”

8.6 Testing Argument Validity Using Truth Tables

8.7 Some Common Argument Forms

8. 8 Statement Forms and Material Equivalence

8.9 Logical Equivalence

8.10 The Three “Laws of Thought”

 

Chapter 9      Methods of Deduction

9.1  Formal Proof of Validity

9.2  The Elementary Valid Argument Forms

9.3  Formal Proofs of Validity Exhibited

9.4  Constructing Formal Proofs of Validity

9.5  Constructing More Extended Formal Proofs

9.6  Expanding the Rules of Inference: Replacement Rules

9.7  The System of Natural Deduction

9.8  Constructing Formal Proofs Using the Nineteen Rules of Inference

9.9  Proof of Invalidity

9.10 Inconsistency

9.11 Indirect Proof of Validity

9.12 Shorter Truth-Table Technique

 

Chapter 10     Quantification Theory

10.1 The Need for Quantification

10.2 Singular Propositions

10.3 Universal and Existential Quantifiers

10.4 Traditional Subject—Predicate Propositions

10.5 Proving Validity

10.6 Proving Invalidity

10.7 Asyllogistic Inference

 

Part III  Induction

 

Section A    Analogy and Causation

 

Chapter 11       Analogical Reasoning

11.1 Induction and Deduction Revisited

11.2 Argument by Analogy

11.3 Appraising Analogical Arguments

11.4 Refutation by Logical Analogy

 

Chapter 12     Causal Reasoning

12.1  Cause and Effect

12.2  Causal Laws and the Uniformity of Nature

12.3  Induction by Simple Enumeration

12.4  Methods of Causal Analysis

12.5  Limitations of Inductive Techniques

 

Section B    Science and Probability



 

Chapter 13       Science and Hypothesis

13.1 Scientific Explanation

13.2 Scientific Inquiry: Hypothesis and Confirmation

13.3 Evaluating Scientific Explanations

13.4 Classification as Hypothesis

 

Chapter 14     Probability

14.1     Alternative Conceptions of Probability

14.2     The Probability Calculus

14.3     Probability in Everyday Life

 

Appendix

 

Solutions to Selected Exercises

 

Glossary/Index