Logic: Inquiry, Argument, and Order

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An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures

Logic: Inquiry, Argument, and Order is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and its relevance to questions of meaning and value that arise in the world around us.

The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification.

Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux.

Logic: Inquiry, Argument, and Order is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic.

ACKNOWLEDGMENTS ix

CHAPTER ONE: THE SIGNIFICANCE OF LOGIC 1

1.1 The Problem of Abstraction 2

1.2 The Problem of Dualism 5

1.3 The Problem of Incommensurability 8

1.4 The Problem of Boundaries 11

1.5 Examples for Discussion 15

1.6 Premises and Conclusions 19

1.7 Exercises 23

CHAPTER TWO: WHAT IS LOGIC? 31

2.1 The Study of Logic 31

2.2 The Concepts of Truth and Inference 35

2.3 The Process of Inquiry 40

2.4 Exercises 48

2.5 Argument as Inquiry 52

2.6 Exercises 57

CHAPTER THREE: COMMUNICATIVE ACTION 61

3.1 Strategic and Communicative Action 61

3.2 Exercises 64

3.3 Lifeworlds 68

3.4 Exercises 71

3.5 Validity 72

3.6 Fallacies 75

3.7 Exercises 85

CHAPTER FOUR: THEORY OF THE SYLLOGISM 91

4.1 Nominalism, Realism, and Abduction 91

4.2 The Theory of the Syllogism 97

4.3 Standard Form Propositions 98

4.4 Exercises 105

4.5 Direct Inference 106

4.6 Exercises 111

4.7 The Validity of Syllogisms 112

4.8 Exercises 120

CHAPTER FIVE: INDUCTION AND THE LIMITS OF REASON 123

5.1 Limits of the Syllogism 123

5.2 The Principles of Induction 129

5.3 Analogical Arguments 139

5.4 Exercises 143

5.5 Causal Arguments 145

5.6 Exercises 148

5.7 Probability 151

5.8 Exercises 160

CHAPTER SIX: PRINCIPLES OF ORDER AND DEDUCTION 165

6.1 Introduction 165

6.2 Modes of Action 167

6.3 Principles of Order 171

6.4 Logic and the Act of Judgment 174

6.5 Deduction: The Logic of Assertions 178

6.6 Graphical Proofs of Validity 190

6.7 Exercises 194

CHAPTER SEVEN: AN OVERVIEW OF QUANTIFIED LOGIC 197

7.1 Introduction 197

7.2 Representing Relations 202

7.3 The Meaning of Quantifi ers 205

7.4 Exercises 207

7.5 Rules of Quantifi cational Logic 208

7.6 Exercises 210

7.7 The Validity of Syllogisms 211

7.8 Graphical Proofs of Validity 214

7.9 Exercises 217

7.10 Border Agents and the Problems of Logic 218

SOLUTIONS 223

BIBLIOGRAPHY 249

INDEX 255

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