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# Introduction to Logic / Edition 14

Introduction to Logic / Edition 14 available in Hardcover, Paperback, NOOK Book, Other Format

## Overview

The 14th Edition of *Introduction to Logic*, written by Copi, Cohen & McMahon, is dedicated to the many thousands of students and their teachers - *at hundreds of universities in the United States and around the world* - who have used its fundamental methods and techniques of correct reasoning in their everyday lives.

To those who have not previously used or reviewed *Introduction to Logic* we extend the very warmest welcome. Please join us and our international family of users! Let us help you teach students the methods and principles needed in order to distinguish correct from incorrect reasoning.

For, *Introduction to Logic* is a proven textbook that has been honed through the collaborative efforts of many scholars over the last five decades. Its scrupulous attention to detail and precision in exposition and explanation is matched by the greatest accuracy in all associated detail. In addition, it continues to capture student interest through its personalized human setting and current examples.

## Product Details

ISBN-13: | 9780205820375 |
---|---|

Publisher: | Taylor & Francis |

Publication date: | 11/25/2010 |

Series: | MyLogicLab Series |

Pages: | 654 |

Sales rank: | 149,884 |

Product dimensions: | 8.20(w) x 10.10(h) x 1.10(d) |

## Read an Excerpt

Preface

Many changes will be found in this new edition of *Introduction to Logic,* but instructors who have used previous editions may be assured that the integrity and spirit of this book have been retained. Much of the detail of previous editions and most of the exercises also have been retained. The changes introduced—of five different kinds—are designed to make this well-tested volume more accessible, and thus more effective as an instrument in the teaching of elementary logic. We recount these changes briefly here, addressing this report mainly to those acquainted with previous editions.

*A Revised Chapter 1.*

Structural changes have been made in the first part of the book. The expansion of the opening chapters in the preceding edition was found by many users to hinder student progress along what may be called "the main line" of instruction in logic. We have therefore compressed the material of what was Part One into a single opening chapter in which the same topics are addressed, but more crisply, and in ways likely to provide a better base for the more advanced material in the later chapters of the book. Chapter 1 has now become very hefty as a result—but it is also richer, more clearly formulated, and more fun to read.

*Exposition-Rules and Definitions.*

The most pervasive of the changes in this edition, and most important too, we think, are the very many adjustments in the ways in which theoretical matters are explained and expressed. We have long prided ourselves on the logical accuracy of *Introduction to Logic,* and of course we would do nothing to injure our hard-earned reputation forreliability. But our colleagues around the country have advised us, on many occasions, that our efforts to be exact, and to cut no corners, have in some parts of the book resulted in formulations rather difficult to digest—especially for beginning students.

This is not an easy matter to address. We have worked hard to ameliorate this problem—and if we have succeeded in this edition many of the resultant changes will be hardly noticeable. Explanations should be formulated in language that is transparent and thoroughly perspicuous, and (we hope) that will cause few brows to wrinkle.

Some illustrations of the kind of changes we have made are worth noting. Several of our colleagues observed that, where a set of rules or criteria have been put forward (as, for example, those to test the validity of categorical syllogisms, or to appraise the merit of analogical arguments), our exposition relied too heavily, in referring to a rule, upon the number assigned to it rather than to the substance of the rule itself. We have reformulated such exposition, consistently referring now to the rule itself.

Another example of reformulation will be noted in the chapter on definition. Previously, in explaining methods of defining, we caused needless confusion by using that much misunderstood word "connotation." The terms "connotation" and "denotation" were not employed erroneously, but to avoid confusion, we now rely fully upon the terms "intension" and "extension" in explaining techniques of definition.

Even format can serve to confuse, or to clarify. It was and remains our practice, in presenting deductive exercises in symbols, to mark the conclusion of an argument with the three triangular dots (.-.) that commonly represent "therefore." But in earlier editions we had sometimes placed this sign on the same line as the last premise of the argument, after a slash; and sometimes we had placed this sign on a separate line of its own. This proved to be a source of distraction if not confusion, so we now consistently place the three-dot "therefore" sign of conclusion on a separate line. This format enables students to see more sharply the claim that the argument is making, and what the target of a needed proof must be.

Many such adjustments appear in this edition, far too many to permit their identification in this Preface. In some cases the change is no more than the clarification of a transition, in others the tightening of a paragraph in which the prose was blurred. A textbook in logic ought to be concise, but it must also be precise; precision and clarity we have prized above all.

Along with such adjustments we have sought, where feasible, to strike a lighter and more friendly tone in this edition, to introduce illustrations or observations that may amuse as they instruct. The study of logic is sometimes laborious, but it need not be forbidding.

*Sidebars.*

Those who study logic with the help of this book differ very greatly in the range of their interests and in the degree of their preparation. We will not be satisfied if we fail to challenge those who are most well prepared and most acute; but those coming to systematic logic for the first time also deserve support and guidance appropriate for them. To this end, we have introduced a device that is wholly new to *Introduction to Logic:* We have sought to distinguish some portions in some chapters that may, for good reasons, be omitted in some learning contexts, or may be treated by instructors as tangential to "the main line." These portions can serve to challenge some students who feel ready for additional work.

Finding a way to do this without injury to the whole is problematic. We have adopted the simple device of a sidebar. These sidebars take two forms, "Advanced Material" and "For Enrichment." We emphasize that this contrivance is not meant to depreciate the passages so marked off, which are often especially interesting and demanding. But such sidebar material, we hope, will make it easier for instructors to guide their own students to a mastery of the elements of theory most critical for them—and perhaps to avoid some complexities not essential for their solid grasp of elementary logic. Many instructors will simply ignore these markings, and may do so without damage to the understanding of their students.

*Technical Changes.*

Some technical changes have been introduced into this edition of *Introduction to Logic*—changes that we think reduce ambiguity and thus support instruction.

For example, we have responded to the frequently expressed concern of colleagues by expanding the discussion of logical equivalence in Chapter 8, now more sharply emphasizing the differences between material equivalence as a truth-functional connective, and logical equivalence as a logical relation that justifies the rules of replacement. An entirely new section on this topic (section 8.6) has been inserted, and in this section we have introduced a new symbol for logical equivalence as well.

In earlier editions we allowed the equivalences expressed by the rules of replacement—the last 10 of the 19 Rules of Inference—to be symbolized by the same three-bar symbol with which material equivalence ("if and only if") is symbolized throughout. This practice had some justification, but it surely led to student confusion when, for example, rules of replacement were formulated in which the three-bar symbol appeared more than once, with more than one meaning. A distinct symbol was needed.

Selecting that symbol has been a matter of long-continuing deliberation. Many alternatives were considered and rejected for reasons pedagogical or theoretical or aesthetic. We have chosen to retain the three-bar symbol, *over* which a small T indicates that the equivalence confronted is a tautology. This achieves the teaching aim, we think, with a minimum of disruption. Students are rarely called upon to write the symbol for logical equivalence—but can (with this notation) recognize it unambiguously when it appears in the list of he rules of replacement that natural deduction employs.

Elsewhere in the treatment of deduction, we have changed the design of Venn diagrams in representing Categorical Syllogisms. Where previously we had used simple shading to mark off what the premises of the argument rule out, we have in this edition used slanted lines. This permits the impact of each of the two premises of a syllogism to be distinguished, and because their lines are slanted in opposite directions, a cross-hatching results when the logical impacts of the two premises overlap. Different colors we chose not to use, not wanting to convey the suggestion that students would need anything more than an ordinary pencil to employ Venn diagrams for themselves.

*Revised Exercises.*

Finally, exercise sets provided at the close of many sections have been enriched. Many exercises have been added, some removed. As in previous editions of *Introduction to Logic,* we have sought to provide a wide array of illustrative passages, where possible on controversial issues likely to be of genuine interest to college students. Some contrived exercises are still used, or course, but we take pride in the fact that the exercises are for the most part extracted from worthy books and periodicals of very great variety. We have not excluded the writing of classical, and even ancient philosophers—but we greatly favor arguments and illustrations produced in the push and pull of discourse in the twentieth and twenty-first centuries.

As in the past, we have scrupulously avoided partisanship in selecting these materials. When some passage provides a telling example of some mistake in reasoning, or a fine illustration of some argumentative technique, we have included it whatever our judgment of its conclusion might be. What we wrote in the Preface to the preceding edition we again affirm: The argumentative chips must be allowed to fall where they may.

Finally, we draw attention to the substantial influence of criticisms and suggestions received from colleagues, senior and junior—whose names and institutions are noted elsewhere in these pages. We strive to make *Introduction to Logic* a teaching instrument ever more finely tuned, and the responses of readers around the world have given us splendid help in spotting errors and identifying deficiencies. We earnestly welcome this thoughtful engagement-and for this continuing and widespread support we express here, not for the first or the last time, our heartfelt appreciation.

## First Chapter

Preface

Many changes will be found in this new edition of *Introduction to Logic,* but instructors who have used previous editions may be assured that the integrity and spirit of this book have been retained. Much of the detail of previous editions and most of the exercises also have been retained. The changes introduced—of five different kinds—are designed to make this well-tested volume more accessible, and thus more effective as an instrument in the teaching of elementary logic. We recount these changes briefly here, addressing this report mainly to those acquainted with previous editions.

*A Revised Chapter 1.*

Structural changes have been made in the first part of the book. The expansion of the opening chapters in the preceding edition was found by many users to hinder student progress along what may be called "the main line" of instruction in logic. We have therefore compressed the material of what was Part One into a single opening chapter in which the same topics are addressed, but more crisply, and in ways likely to provide a better base for the more advanced material in the later chapters of the book. Chapter 1 has now become very hefty as a result—but it is also richer, more clearly formulated, and more fun to read.

*Exposition-Rules and Definitions.*

The most pervasive of the changes in this edition, and most important too, we think, are the very many adjustments in the ways in which theoretical matters are explained and expressed. We have long prided ourselves on the logical accuracy of *Introduction to Logic,* and of course we would do nothing to injure our hard-earned reputation forreliability. But our colleagues around the country have advised us, on many occasions, that our efforts to be exact, and to cut no corners, have in some parts of the book resulted in formulations rather difficult to digest—especially for beginning students.

This is not an easy matter to address. We have worked hard to ameliorate this problem—and if we have succeeded in this edition many of the resultant changes will be hardly noticeable. Explanations should be formulated in language that is transparent and thoroughly perspicuous, and (we hope) that will cause few brows to wrinkle.

Some illustrations of the kind of changes we have made are worth noting. Several of our colleagues observed that, where a set of rules or criteria have been put forward (as, for example, those to test the validity of categorical syllogisms, or to appraise the merit of analogical arguments), our exposition relied too heavily, in referring to a rule, upon the number assigned to it rather than to the substance of the rule itself. We have reformulated such exposition, consistently referring now to the rule itself.

Another example of reformulation will be noted in the chapter on definition. Previously, in explaining methods of defining, we caused needless confusion by using that much misunderstood word "connotation." The terms "connotation" and "denotation" were not employed erroneously, but to avoid confusion, we now rely fully upon the terms "intension" and "extension" in explaining techniques of definition.

Even format can serve to confuse, or to clarify. It was and remains our practice, in presenting deductive exercises in symbols, to mark the conclusion of an argument with the three triangular dots (.-.) that commonly represent "therefore." But in earlier editions we had sometimes placed this sign on the same line as the last premise of the argument, after a slash; and sometimes we had placed this sign on a separate line of its own. This proved to be a source of distraction if not confusion, so we now consistently place the three-dot "therefore" sign of conclusion on a separate line. This format enables students to see more sharply the claim that the argument is making, and what the target of a needed proof must be.

Many such adjustments appear in this edition, far too many to permit their identification in this Preface. In some cases the change is no more than the clarification of a transition, in others the tightening of a paragraph in which the prose was blurred. A textbook in logic ought to be concise, but it must also be precise; precision and clarity we have prized above all.

Along with such adjustments we have sought, where feasible, to strike a lighter and more friendly tone in this edition, to introduce illustrations or observations that may amuse as they instruct. The study of logic is sometimes laborious, but it need not be forbidding.

*Sidebars.*

Those who study logic with the help of this book differ very greatly in the range of their interests and in the degree of their preparation. We will not be satisfied if we fail to challenge those who are most well prepared and most acute; but those coming to systematic logic for the first time also deserve support and guidance appropriate for them. To this end, we have introduced a device that is wholly new to *Introduction to Logic:* We have sought to distinguish some portions in some chapters that may, for good reasons, be omitted in some learning contexts, or may be treated by instructors as tangential to "the main line." These portions can serve to challenge some students who feel ready for additional work.

Finding a way to do this without injury to the whole is problematic. We have adopted the simple device of a sidebar. These sidebars take two forms, "Advanced Material" and "For Enrichment." We emphasize that this contrivance is not meant to depreciate the passages so marked off, which are often especially interesting and demanding. But such sidebar material, we hope, will make it easier for instructors to guide their own students to a mastery of the elements of theory most critical for them—and perhaps to avoid some complexities not essential for their solid grasp of elementary logic. Many instructors will simply ignore these markings, and may do so without damage to the understanding of their students.

*Technical Changes.*

Some technical changes have been introduced into this edition of *Introduction to Logic*—changes that we think reduce ambiguity and thus support instruction.

For example, we have responded to the frequently expressed concern of colleagues by expanding the discussion of logical equivalence in Chapter 8, now more sharply emphasizing the differences between material equivalence as a truth-functional connective, and logical equivalence as a logical relation that justifies the rules of replacement. An entirely new section on this topic (section 8.6) has been inserted, and in this section we have introduced a new symbol for logical equivalence as well.

In earlier editions we allowed the equivalences expressed by the rules of replacement—the last 10 of the 19 Rules of Inference—to be symbolized by the same three-bar symbol with which material equivalence ("if and only if") is symbolized throughout. This practice had some justification, but it surely led to student confusion when, for example, rules of replacement were formulated in which the three-bar symbol appeared more than once, with more than one meaning. A distinct symbol was needed.

Selecting that symbol has been a matter of long-continuing deliberation. Many alternatives were considered and rejected for reasons pedagogical or theoretical or aesthetic. We have chosen to retain the three-bar symbol, *over* which a small T indicates that the equivalence confronted is a tautology. This achieves the teaching aim, we think, with a minimum of disruption. Students are rarely called upon to write the symbol for logical equivalence—but can (with this notation) recognize it unambiguously when it appears in the list of he rules of replacement that natural deduction employs.

Elsewhere in the treatment of deduction, we have changed the design of Venn diagrams in representing Categorical Syllogisms. Where previously we had used simple shading to mark off what the premises of the argument rule out, we have in this edition used slanted lines. This permits the impact of each of the two premises of a syllogism to be distinguished, and because their lines are slanted in opposite directions, a cross-hatching results when the logical impacts of the two premises overlap. Different colors we chose not to use, not wanting to convey the suggestion that students would need anything more than an ordinary pencil to employ Venn diagrams for themselves.

*Revised Exercises.*

Finally, exercise sets provided at the close of many sections have been enriched. Many exercises have been added, some removed. As in previous editions of *Introduction to Logic,* we have sought to provide a wide array of illustrative passages, where possible on controversial issues likely to be of genuine interest to college students. Some contrived exercises are still used, or course, but we take pride in the fact that the exercises are for the most part extracted from worthy books and periodicals of very great variety. We have not excluded the writing of classical, and even ancient philosophers—but we greatly favor arguments and illustrations produced in the push and pull of discourse in the twentieth and twenty-first centuries.

As in the past, we have scrupulously avoided partisanship in selecting these materials. When some passage provides a telling example of some mistake in reasoning, or a fine illustration of some argumentative technique, we have included it whatever our judgment of its conclusion might be. What we wrote in the Preface to the preceding edition we again affirm: The argumentative chips must be allowed to fall where they may.

Finally, we draw attention to the substantial influence of criticisms and suggestions received from colleagues, senior and junior—whose names and institutions are noted elsewhere in these pages. We strive to make *Introduction to Logic* a teaching instrument ever more finely tuned, and the responses of readers around the world have given us splendid help in spotting errors and identifying deficiencies. We earnestly welcome this thoughtful engagement-and for this continuing and widespread support we express here, not for the first or the last time, our heartfelt appreciation.

## Table of Contents

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

## Reading Group Guide

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

## Interviews

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

## Preface

*Introduction to Logic,*but instructors who have used previous editions may be assured that the integrity and spirit of this book have been retained. Much of the detail of previous editions and most of the exercises also have been retained. The changes introduced—of five different kinds—are designed to make this well-tested volume more accessible, and thus more effective as an instrument in the teaching of elementary logic. We recount these changes briefly here, addressing this report mainly to those acquainted with previous editions.

*A Revised Chapter 1.*

Structural changes have been made in the first part of the book. The expansion of the opening chapters in the preceding edition was found by many users to hinder student progress along what may be called "the main line" of instruction in logic. We have therefore compressed the material of what was Part One into a single opening chapter in which the same topics are addressed, but more crisply, and in ways likely to provide a better base for the more advanced material in the later chapters of the book. Chapter 1 has now become very hefty as a result—but it is also richer, more clearly formulated, and more fun to read.

*Exposition-Rules and Definitions.*

The most pervasive of the changes in this edition, and most important too, we think, are the very many adjustments in the ways in which theoretical matters are explained and expressed. We have long prided ourselves on the logical accuracy of *Introduction to Logic,* and of course we would do nothing to injure our hard-earned reputation for reliability. But ourcolleagues around the country have advised us, on many occasions, that our efforts to be exact, and to cut no corners, have in some parts of the book resulted in formulations rather difficult to digest—especially for beginning students.

This is not an easy matter to address. We have worked hard to ameliorate this problem—and if we have succeeded in this edition many of the resultant changes will be hardly noticeable. Explanations should be formulated in language that is transparent and thoroughly perspicuous, and (we hope) that will cause few brows to wrinkle.

Some illustrations of the kind of changes we have made are worth noting. Several of our colleagues observed that, where a set of rules or criteria have been put forward (as, for example, those to test the validity of categorical syllogisms, or to appraise the merit of analogical arguments), our exposition relied too heavily, in referring to a rule, upon the number assigned to it rather than to the substance of the rule itself. We have reformulated such exposition, consistently referring now to the rule itself.

Another example of reformulation will be noted in the chapter on definition. Previously, in explaining methods of defining, we caused needless confusion by using that much misunderstood word "connotation." The terms "connotation" and "denotation" were not employed erroneously, but to avoid confusion, we now rely fully upon the terms "intension" and "extension" in explaining techniques of definition.

Even format can serve to confuse, or to clarify. It was and remains our practice, in presenting deductive exercises in symbols, to mark the conclusion of an argument with the three triangular dots (.-.) that commonly represent "therefore." But in earlier editions we had sometimes placed this sign on the same line as the last premise of the argument, after a slash; and sometimes we had placed this sign on a separate line of its own. This proved to be a source of distraction if not confusion, so we now consistently place the three-dot "therefore" sign of conclusion on a separate line. This format enables students to see more sharply the claim that the argument is making, and what the target of a needed proof must be.

Many such adjustments appear in this edition, far too many to permit their identification in this Preface. In some cases the change is no more than the clarification of a transition, in others the tightening of a paragraph in which the prose was blurred. A textbook in logic ought to be concise, but it must also be precise; precision and clarity we have prized above all.

Along with such adjustments we have sought, where feasible, to strike a lighter and more friendly tone in this edition, to introduce illustrations or observations that may amuse as they instruct. The study of logic is sometimes laborious, but it need not be forbidding.

*Sidebars.*

Those who study logic with the help of this book differ very greatly in the range of their interests and in the degree of their preparation. We will not be satisfied if we fail to challenge those who are most well prepared and most acute; but those coming to systematic logic for the first time also deserve support and guidance appropriate for them. To this end, we have introduced a device that is wholly new to *Introduction to Logic:* We have sought to distinguish some portions in some chapters that may, for good reasons, be omitted in some learning contexts, or may be treated by instructors as tangential to "the main line." These portions can serve to challenge some students who feel ready for additional work.

Finding a way to do this without injury to the whole is problematic. We have adopted the simple device of a sidebar. These sidebars take two forms, "Advanced Material" and "For Enrichment." We emphasize that this contrivance is not meant to depreciate the passages so marked off, which are often especially interesting and demanding. But such sidebar material, we hope, will make it easier for instructors to guide their own students to a mastery of the elements of theory most critical for them—and perhaps to avoid some complexities not essential for their solid grasp of elementary logic. Many instructors will simply ignore these markings, and may do so without damage to the understanding of their students.

*Technical Changes.*

Some technical changes have been introduced into this edition of *Introduction to Logic*—changes that we think reduce ambiguity and thus support instruction.

For example, we have responded to the frequently expressed concern of colleagues by expanding the discussion of logical equivalence in Chapter 8, now more sharply emphasizing the differences between material equivalence as a truth-functional connective, and logical equivalence as a logical relation that justifies the rules of replacement. An entirely new section on this topic (section 8.6) has been inserted, and in this section we have introduced a new symbol for logical equivalence as well.

In earlier editions we allowed the equivalences expressed by the rules of replacement—the last 10 of the 19 Rules of Inference—to be symbolized by the same three-bar symbol with which material equivalence ("if and only if") is symbolized throughout. This practice had some justification, but it surely led to student confusion when, for example, rules of replacement were formulated in which the three-bar symbol appeared more than once, with more than one meaning. A distinct symbol was needed.

Selecting that symbol has been a matter of long-continuing deliberation. Many alternatives were considered and rejected for reasons pedagogical or theoretical or aesthetic. We have chosen to retain the three-bar symbol, *over* which a small T indicates that the equivalence confronted is a tautology. This achieves the teaching aim, we think, with a minimum of disruption. Students are rarely called upon to write the symbol for logical equivalence—but can (with this notation) recognize it unambiguously when it appears in the list of he rules of replacement that natural deduction employs.

Elsewhere in the treatment of deduction, we have changed the design of Venn diagrams in representing Categorical Syllogisms. Where previously we had used simple shading to mark off what the premises of the argument rule out, we have in this edition used slanted lines. This permits the impact of each of the two premises of a syllogism to be distinguished, and because their lines are slanted in opposite directions, a cross-hatching results when the logical impacts of the two premises overlap. Different colors we chose not to use, not wanting to convey the suggestion that students would need anything more than an ordinary pencil to employ Venn diagrams for themselves.

*Revised Exercises.*

Finally, exercise sets provided at the close of many sections have been enriched. Many exercises have been added, some removed. As in previous editions of *Introduction to Logic,* we have sought to provide a wide array of illustrative passages, where possible on controversial issues likely to be of genuine interest to college students. Some contrived exercises are still used, or course, but we take pride in the fact that the exercises are for the most part extracted from worthy books and periodicals of very great variety. We have not excluded the writing of classical, and even ancient philosophers—but we greatly favor arguments and illustrations produced in the push and pull of discourse in the twentieth and twenty-first centuries.

As in the past, we have scrupulously avoided partisanship in selecting these materials. When some passage provides a telling example of some mistake in reasoning, or a fine illustration of some argumentative technique, we have included it whatever our judgment of its conclusion might be. What we wrote in the Preface to the preceding edition we again affirm: The argumentative chips must be allowed to fall where they may.

Finally, we draw attention to the substantial influence of criticisms and suggestions received from colleagues, senior and junior—whose names and institutions are noted elsewhere in these pages. We strive to make *Introduction to Logic* a teaching instrument ever more finely tuned, and the responses of readers around the world have given us splendid help in spotting errors and identifying deficiencies. We earnestly welcome this thoughtful engagement-and for this continuing and widespread support we express here, not for the first or the last time, our heartfelt appreciation.

## Recipe

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