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Anonymous
Posted October 19, 2009
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Posted January 17, 2011
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More About This Textbook
Overview
Editorial Reviews
From the Publisher
"The book develops formal logic rigorously, but with an approach that students will find clear and accessible, especially with respect to the explanations of key concepts and the featured "walk-throughs" of proof techniques, etc."
"I would describe the book as a 'real logic book that is about as accessible as it gets."
Product Details
Related Subjects
Meet the Author
Alan Hausman received a Ph.D. in philosophy from Iowa State University and now teaches philosophy at Hunter College. He has published extensively on history of early modern philosophy, especially on the work of Hume, and on the work of Nelson Goodman.
Howard Kahane (deceased) is considered one of the founders of the critical-thinking movement, an approach to logic that makes it less abstract and more practical as a tool for analyzing political and social issues.
Paul Tidman received his Ph.D. in philosophy from the University of Notre Dame. He teaches philosophy at Mount Union College in Ohio.
Table of Contents
Preface to the Eleventh Edition ix
Preface to the Tenth Edition xi
Chapter 1 Introduction 1
1 The Elements of an Argument 1
2 Deduction and Induction 5
3 Deductive Argument Forms 7
4 Truth and Validity 8
5 Soundness 11
6 Consistency 12
7 Contexts of Discovery and Justification 14
8 The Plan of This Book 14
Key Terms 16
Part 1 Sentential Logic 17
Chapter 2 Symbolizing in Sentential Logic 19
1 Atomic and Compound Sentences 20
2 Truth-Functions 21
3 Conjunctions 21
4 Non-Truth-Functional Connectives 25
5 Variables and Constants 25
6 Negations 27
7 Parentheses and Brackets 28
8 Use and Mention 29
9 Disjunctions 30
10 "Not Both" and "Neither . . . Nor" 33
11 Material Conditionals 35
12 Material Biconditionals 38
13 "Only If" and "Unless" 40
14 Symbolizing Complex Sentences 41
15 Alternative Sentential Logic Symbols 48
Key Terms 50
Chapter 3 Truth Tables 53
1 Computing Truth-Values 53
2 Logical Form 58
3 Tautologies, Contradictions, and Contingent Sentences 63
4 Logical Equivalences 69
5 Truth Table Test of Validity 70
6 Truth Table Test of Consistency 73
7 Validity and Consistency 74
8 The Short Truth Table Test for Invalidity 76
9 The Short Truth Table Test for Consistency 80
10 A Method of Justification for the Truth Tables 81
Key Terms 85
Chapter 4 Proofs 86
1 Argument Forms 86
2 The Method of Proof: Modus Ponens and Modus Tollens 88
3 Disjunctive Syllogism and Hypothetical Syllogism 91
4 Simplification and Conjunction 93
5 Addition and Constructive Dilemma 94
6 Principles of Strategy 97
7 Double Negation and DeMorgan's Theorem 103
8 Commutation, Association, and Distribution 106
9Contraposition, Implication, and Exportation 107
10 Tautology and Equivalence 107
11 More Principles of Strategy 111
12 Common Errors in Problem Solving 115
Key Terms 122
Chapter 5 Conditional and Indirect Proofs 123
1 Conditional Proofs 123
2 Indirect Proofs 132
3 Strategy Hints for Using CP and IP 137
4 Zero-Premise Deductions 138
5 Proving Premises Inconsistent 139
6 Adding Valid Argument Forms 141
7 An Alternative to Conditional Proof? 142
8 The Completeness and Soundness of Sentential Logic 144
9 Introduction and Elimination Rules 146
Key Terms 149
Chapter 6 Sentential Logic Truth Trees 151
1 The Sentential Logic Truth Tree Method 151
2 The Truth Tree Rules 152
3 Details of Tree Construction 154
4 Normal Forms and Trees 160
5 Constructing Tree Rules for Any Function 161
Key Terms 163
Part 2 Predicate Logic 165
Chapter 7 Predicate Logic Symbolization 167
1 Individuals and Properties 167
2 Quantifiers and Free Variables 171
3 Universal Quantifiers 172
4 Existential Quantifiers 177
5 Basic Predicate Logic Symbolizations 178
6 The Square of Opposition 180
7 Common Pitfalls in Symbolizing with Quantifiers 180
8 Expansions 183
9 Symbolizing "Only," "None but," and "Unless" 186
Key Terms 190
Chapter 8 Predicate Logic Semantics 191
1 Interpretations in Predicate Logic 191
2 Proving Invalidity 193
3 Using Expansions to Prove Invalidity 196
4 Consistency in Predicate Logic 197
5 Validity and Inconsistency in Predicate Logic 198
Key Terms 199
Chapter 9 Predicate Logic Proofs 200
1 Proving Validity 200
2 The Four Quantifier Rules 202
3 The Five Main Restrictions 209
4 Precise Formulation of the Four Quantifier Rules 213
5 Mastering the Four Quantifier Rules 216
6 Quantifier Negation 220
Key Term 225
Chapter 10 Relational Predicate Logic 226
1 Relational Predicates 226
2 Symbolizations Containing Overlapping Quantifiers 229
3 Expansions and Overlapping Quantifiers 229
4 Places and Times 234
5 Symbolizing "Someone," "Somewhere," "Sometime," and So On 235
6 Invalidity and Consistency in Relational Predicate Logic 240
7 Relational Predicate Logic Proofs 241
8 Strategy for Relational Predicate Logic Proofs 248
9 Theorems and Inconsistency in Predicate Logic 250
10 Predicate Logic Metatheory 253
11 A Simpler Set of Quantifier Rules 254
Chapter 11 Rationale Behind the Precise Formulation of the Four Quantifier Rules 257
1 Cases Involving the Five Major Restrictions 257
2 One-to-One Correspondence Matters 260
3 Accidentally Bound Variables and Miscellaneous Cases 264
4 Predicate Logic Proofs with Flagged Constants 269
Chapter 12 Predicate Logic Truth Trees 272
1 Introductory Remarks 272
2 General Features of the Method 273
3 Specific Examples of the Method 273
4 Some Advantages of the Trees 278
5 Example of an Invalid Argument with at Least One Open Path 279
6 Metatheoretic Results 280
7 Strategy and Accounting 283
Key Terms 285
Chapter 13 Identity and Philosophical Problems of Symbolic Logic 286
1 Identity 286
2 Definite Descriptions 292
3 Properties of Relations 294
4 Higher-Order Logics 297
5 Limitations of Predicate Logic 299
6 Philosophical Problems 303
7 Logical Paradoxes 310
Key Terms 317
Chapter 14 Syllogistic Logic 319
1 Categorical Propositions 322
2 Existential Import 322
3 The Square of Opposition 323
4 Conversion, Obversion, Contraposition 326
5 Syllogistic Logic - Not Assuming Existential Import 329
6 Venn Diagrams 332
7 Syllogisms 334
8 Determining Syllogism Validity 336
9 Venn Diagram Proofs of Validity or Invalidity 337
10 Five Rules for Determining Validity or Invalidity 342
11 Syllogistics Extended 345
12 Enthymemes 348
13 Sorites 349
14 Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared 351
Key Terms 355
Answers to Even-Numbered Exercise Items 358
Bibliography 419
Special Symbols 421
Index 423