Preface p. xi Introduction p. 1 The Elements of an Argument p. 1 Deduction and Induction p. 5 Deductive Argument Forms p. 7 Truth and Validity p. 8 Soundness p. 11 Consistency p. 12 Consistency and Validity Compared p. 13 Contexts of Discovery and Justification p. 15 The Plan of This Book p. 15 Key Terms p. 16 Sentential Logic p. 19 Symbolizing in Sentential Logic p. 21 Atomic and Compound Sentences p. 22 Truth-Functions p. 23 Conjunctions p. 23 Non-Truth-Functional Connectives p. 27 Variables and Constants p. 27 Negations p. 29 Parentheses and Brackets p. 30 Use and Mention p. 31 Disjunctions p. 32 "Not Both" and "Neither... Nor" p. 35 Material Conditionals p. 37 Material Biconditionals p. 40 "Only If" and "Unless" p. 42 Symbolizing Complex Sentences p. 43 Alternative Sentential Logic Symbols p. 50 Key Terms p. 52 Truth Tables p. 55 Computing Truth-Values p. 55 Logical Form p. 60 Tautologies, Contradictions, and Contingent Sentences p. 65 Logical Equivalences p. 71 Truth Table Test of Validity p. 72 Truth Table Test of Consistency p. 75 Validity and Consistency p. 76 The Short Truth Table Test for Invalidity p. 78 The Short Truth Table Test for Consistency p. 82 A Method of Justification for the Truth Tables p. 83
Key Terms p. 87 Proofs p. 88 Argument Forms p. 88 The Method of Proof: Modus Ponens and Modus Tollens p. 90 Disjunctive Syllogism and Hypothetical Syllogism p. 93 Simplification and Conjunction p. 95 Addition and Constructive Dilemma p. 96 Principles of Strategy p. 99 Double Negation and DeMorgan's Theorem p. 105 Commutation, Association, and Distribution p. 108 Contraposition, Implication, and Exportation p. 109 Tautology and Equivalence p. 109 More Principles of Strategy p. 113 Common Errors in Problem Solving p. 117 Key Terms p. 124 Conditional and Indirect Proofs p. 125 Conditional Proofs p. 125 Indirect Proofs p. 134 Strategy Hints for Using CP and IP p. 139 Zero-Premise Deductions p. 140 Proving Premises Inconsistent p. 141 Adding Valid Argument Forms p. 143 The Completeness and Soundness of Sentential Logic p. 144 Introduction and Elimination Rules p. 145 Key Terms p. 149 Sentential Logic Truth Trees p. 150 The Sentential Logic Truth Tree Method p. 150 The Truth Tree Rules p. 151 Details of Tree Construction p. 153 Normal Forms and Trees p. 159 Constructing Tree Rules for Any Function p. 160 Key Terms p. 162 Predicate Logic p. 163 Predicate Logic Symbolization p. 165 Individuals and Properties p. 165 Quantifiers and Free Variables p. 169 Universal Quantifiers p. 170 Existential Quantifiers p. 175 Basic Predicate Logic Symbolizations p. 176 The Square of Opposition p. 178 Common Pitfalls in Symbolizing with Quantifiers p. 178
Expansions p. 181 Symbolizing "Only," "None but," and "Unless" p. 184 Key Terms p. 187 Predicate Logic Semantics p. 189 Interpretations in Predicate Logic p. 189 Proving Invalidity p. 191 Using Expansions to Prove Invalidity p. 194 Consistency in Predicate Logic p. 195 Validity and Inconsistency in Predicate Logic p. 196 Key Terms p. 197 Predicate Logic Proofs p. 198 Proving Validity p. 198 The Four Quantifier Rules p. 199 The Five Main Restrictions p. 205 Precise Formulation of the Four Quantifier Rules p. 210 Mastering the Four Quantifier Rules p. 212 Quantifier Negation (QN) p. 216 Key Term p. 221 Relational Predicate Logic p. 222 Relational Predicates p. 222 Symbolizations Containing Overlapping Quantifiers p. 225 Expansions and Overlapping Quantifiers p. 225 Places and Times p. 230 Symbolizing "Someone," "Somewhere," "Sometime," and So On p. 231 Invalidity and Consistency in Relational Predicate Logic p. 236 Relational Predicate Logic Proofs p. 237 Strategy for Relational Predicate Logic Proofs p. 244 Theorems and Inconsistency in Predicate Logic p. 247 Predicate Logic Metatheory p. 250 A Simpler Set of Quantifier Rules p. 250 Rationale Behind the Precise Formulation of the Four Quantifier Rules p. 254 Cases Involving the Five Major Restrictions p. 254 One-to-One Correspondence Matters p. 257 Accidentially Bound Variables and Miscellaneous Cases p. 261 Predicate Logic Proofs with Flagged Constants p. 265 Predicate Logic Truth Trees p. 269 Introductory Remarks p. 269 General Features of the Method p. 270 Specific Examples of the Method p. 270 Some Advantages of the Trees p. 275 Example of an Invalid Argument with at Least One Open Path p. 275
Metatheoretic Results p. 276 Strategy and Accounting p. 280 Key Terms p. 282 Identity and Philosophical Problems of Symbolic Logic p. 283 Identity p. 283 Definite Descriptions p. 289 Properties of Relations p. 291 Higher-Order Logics p. 294 Limitations of Predicate Logic p. 296 Philosophical Problems p. 300 Logical Paradoxes p. 307 Key Terms p. 314 Syllogistic Logic p. 316 Categorical Propositions p. 316 Existential Import p. 319 The Square of Opposition p. 320 Conversion, Obsersion, Contraposition p. 323 Syllogistic Logic-Not Assuming Existential Import p. 326 Venn Diagrams p. 329 Syllogisms p. 331 Determining Syllogism Validity p. 333 Venn Diagram Proofs of Validity or Invalidity p. 334 Five Rules for Determining Validity or Invalidity p. 339 Syllogistics Extended p. 342 Enthymemes p. 345 Sorites p. 346 Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared p. 348 Key Terms p. 352 Other Systems of Logic p. 355 Informal Fallacies p. 357 The Nature of Fallacy p. 357 Fallacy Classification p. 359 Key Terms p. 375 Inductive Logic p. 376 A Mistaken View of Induction and Deduction p. 376 Kinds of Inductive Arguments p. 378 Cause and Effect p. 388 Mill's Methods p. 391 Inductive Probability p. 398 The Probability Calculus p. 399 Bayes' Theorem p. 401
Induction Is Unjustified-The Old Riddle of Induction p. 403 Not All Instances of Theories Confirm Them-The New Riddle of Induction p. 406 Key Terms p. 409 Axiom Systems p. 411 The Nature of an Axiom System p. 411 Interpreted and Uninterpreted Systems p. 412 Properties of Axiom Systems p. 413 Outline of an Axiom System for Sentential Logic p. 416 Axiom Systems for Predicate Logic p. 421 Other Kinds of Axiom Systems p. 422 Objections to Axiom Systems p. 423 Key Terms p. 423 Alternative Logics p. 425 Modal Logic p. 425 Strict Implication p. 426 Modal Axioms p. 428 Modal Theorems p. 429 Modal Paradoxes p. 430 A Philosophical Problem p. 430 Modal Predicate Logic p. 431 Epistemic Logic: The Logic of Knowledge and Belief p. 433 Epistemic Theorems p. 435 Deontic Logic p. 437 Problems with Deontic Systems p. 438 Key Terms p. 440 Answers to Even-Numbered Exercise Items p. 441 Bibliography p. 505 Special Symbols p. 509 Index p. 511 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.