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Introduction to logic and its philosophy Summary:Pages: 347 Date: 2006 Contents: 1 Introduction 1 1.1 What this book is about, and why . . . . . . . . . . . . . 1 1.2 What Makes Logic Difficult . . . . . . . . . . . . . . . . 3 Part One: The Classical Logic of Sentences 5 2 Introducing Sentence Logic 7 2.1 overview . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 A Formal Language . . . . . . . . . . . . . . . . . . . . 11 2.3 SL and Natural Language . . . . . . . . . . . . . . . . . 18 2.4 The Classical Perspective . . . . . . . . . . . . . . . . . 19 Essay or Discussion Questions and Topics . . . . . . . 20 3 Proof Theory of Sentence Logic 21 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Introducing the rules of CSL . . . . . . . . . . . . . . . . 22 3.3 Annotating Derivations . . . . . . . . . . . . . . . . . . 37 3.4 Some Formal Definitions . . . . . . . . . . . . . . . . . 38 3.5 Using the Rules . . . . . . . . . . . . . . . . . . . . . . 40 The Importance of Learning the Rules . . . . . . . . . 40 Winning Strategies . . . . . . . . . . . . . . . . . . . . 41 The Special Problems of Negation Elimination . 47 Common Mistakes, Pitfalls, and Other Problems . . . . 48 3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.7 Derivable Rules in CSL . . . . . . . . . . . . . . . . . . 58 Rules of Replacement . . . . . . . . . . . . . . 60 3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.9 Solutions to Selected Exercises . . . . . . . . . . . . . . 63 selected solutions to exercises 3.6 . . . . . . . . . . . . 63 Selected Solutions to Exercises 3.8 . . . . . . . . . . . 93 3.10 Rules of CSL Quick Reference . . . . . . . . . . . . . . 104 3.11 Definitions Quick Reference . . . . . . . . . . . . . . . 111 3.12 Derivable Rules Quick Reference . . . . . . . . . . . . 112 3.13 Replacement Rules Quick Reference . . . . . . . . . . 114 4 Semantics of Sentence Logic 115 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.2 The Connectives in Terms of Truth-Values . . . . . . . . 117 Conjunction . . . . . . . . . . . . . . . . . . . . . . . 117 Disjunction . . . . . . . . . . . . . . . . . . . . . . . . 119 Limits on Defining Connectives . . . . . . . . . . . . . 123 The Conditional . . . . . . . . . . . . . . . . . . . . . 124 Negation . . . . . . . . . . . . . . . . . . . . . . . . . 127 A New Connective . . . . . . . . . . . . . . . . . . . . 128 Biconditional . . . . . . . . . . . . . . . . . . . . . . . 129 4.3 The Key Logical Terms: CSL . . . . . . . . . . . . . . . 130 4.4 Truth-Value Calculations . . . . . . . . . . . . . . . . . 138 Common Mistakes and Pitfalls . . . . . . . . . . . . . 146 Remarks on truth-tables . . . . . . . . . . . . . . . . . 147 4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.6 Inferences in Natural Language . . . . . . . . . . . . . . 151 4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.8 Truth-tables Quick Reference . . . . . . . . . . . . . . . 160 4.9 Key Definitions Quick Reference . . . . . . . . . . . . . 161 5 Metalogic of Classical Sentence Logic 163 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.2 Notational Preliminaries . . . . . . . . . . . . . . . . . . 164 5.3 An Important Technique . . . . . . . . . . . . . . . . . . 165 5.4 Some Important Sets . . . . . . . . . . . . . . . . . . . 169 5.5 Specialized Kinds of Theory . . . . . . . . . . . . . . . 173 5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.7 Putting it Together Part 1 . . . . . . . . . . . . . . . . . 178 5.8 Putting it Together Part 2 . . . . . . . . . . . . . . . . . 180 5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 183 5.10 Overview of the Main Result of this Chapter . . . . . . 183 5.11 Essay and Discussion Topics and Questions . . . . . . . 186 5.12 Brief Historical Notes . . . . . . . . . . . . . . . . . . 187 5.13 Yes, but what does it all mean? . . . . . . . . . . . . . 188 5.14 Essay and Discussion Topics and Questions . . . . . . . 189 5.15 Rules Quick Reference . . . . . . . . . . . . . . . . . . 190 6 Philosophy of Logic 191 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 191 6.2 The Nature of the Beast . . . . . . . . . . . . . . . . . . 191 Essay or Discussion Questions and Topics . . . . . . . 198 6.3 Which Comes First: Syntax or Semantics? . . . . . . . . 198 Essay or Discussion Questions and Topics . . . . . . . 201 6.4 Which Comes First: Inference or Logical Truth? . . . . . 201 Essay or Discussion Questions and Topics . . . . . . . 203 6.5 Where Does Logic Fit in Philosophy? . . . . . . . . . . 204 Essay or Discussion Questions and Topics . . . . . . . 207 6.6 Is Classical Logic Two-Valued? . . . . . . . . . . . . . . 208 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 212 Part Two: The Classical Logic of Elements 213 7 Introducing The Logic of Elements 215 7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.2 Expanding our Formal Language . . . . . . . . . . . . . 217 7.3 Essay or Discussion Questions and Topics . . . . . . . . 226 7.4 Translation Issues . . . . . . . . . . . . . . . . . . . . . 227 7.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 235 7.6 Properties of Relations . . . . . . . . . . . . . . . . . . 237 7.7 Definitions and Rules of Thumb Quick Reference . . . . 243 8 Proof Theory of Elementary Logic 245 8.1 Introduction to the New Rules . . . . . . . . . . . . . . . 245 8.2 How to use the new rules . . . . . . . . . . . . . . . . . 250 8.3 Common Errors . . . . . . . . . . . . . . . . . . . . . . 250 8.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Selected Solutions for Exercises 8.4 . . . . . . . . . . . 252 8.5 Key Definitions . . . . . . . . . . . . . . . . . . . . . . 259 8.6 Derivable Rules in CEL . . . . . . . . . . . . . . . . . . 260 8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 260 8.8 Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 8.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . 264 8.10 Some Puzzles . . . . . . . . . . . . . . . . . . . . . . . 265 8.11 Relational Properties Revisited . . . . . . . . . . . . . 266 8.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 267 8.13 Numerical Quantification . . . . . . . . . . . . . . . . 268 8.14 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 270 8.15 Identity and Singular Terms . . . . . . . . . . . . . . . 270 Singular Terms and Definite Descriptions . . . . . . . . 273 Essay or Discussion Questions and Topics . . . . . . . 279 Rules for Free Descriptions . . . . . . . . . . . . . . . 280 8.16 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 281 8.17 Rules Quick Reference . . . . . . . . . . . . . . . . . . 283 8.18 Solutions to Selected Exercises . . . . . . . . . . . . . 287 Exercise 8.4 . . . . . . . . . . . . . . . . . . . . . . . 287 Exercise 8.7 . . . . . . . . . . . . . . . . . . . . . . . 292 Exercise 8.9 . . . . . . . . . . . . . . . . . . . . . . . 297 9 Model Theory: Semantics of Elementary Logic 299 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 299 9.2 A Partial Truth Definition and Satisfaction . . . . . . . . 304 9.3 The Key Definitions . . . . . . . . . . . . . . . . . . . . 308 10 Metalogic of Elementary Logic 309 10.1 Special Sets . . . . . . . . . . . . . . . . . . . . . . . . 309 10.2 Overview of Metalogical Results . . . . . . . . . . . . 312 10.3 Dealing with Identity . . . . . . . . . . . . . . . . . . . 322 Extensionalizing Omega Sets . . . . . . . . . . . . . . 323 An Alternative Method for Dealing with Identity . . . . 324 10.4 Model Theory for Free Logic . . . . . . . . . . . . . . 326 References 331 Index 333 Index of Symbols 341 password:kodiak Please select one mirror to download
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