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Logic and Philosophy

by: Tidman, Paul; Kahane, Howard

Logic and Philosophy

by: Tidman, Paul; Kahane, Howard

ISBN 13:
9780534526146
ISBN 10:
0534526144
Edition: CD
Format: Hardcover
Copyright: 09/01/1998
Publisher: Wadsworth Pub Co
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Summary

This text is designed for those who desire a complete set of rules for first order predicate logic with identity; the text includes a solid range of additional material. Through all editions, the goal has been to make symbolic logic understandable for the typical student. Careful explanation and pedagogy make this the easiest text from which to learn symbolic logic.

Preface

xiii

Part One: Sentential Logic

(130)

Chapter One: Introduction

(15)

1. The Elements of an Argument

(3)

2. Deduction and Induction

(2)

3. Argument Forms

(2)

4. Truth and Validity

(3)

5. Soundness

(1)

6. Consistency

(1)

7. Consistency and Validity Compared

(2)

8. Contexts of Discovery and Justification

(1)

Key terms

(1)

Chapter Two: Truth-Functions

(27)

1. Atomic and Compound Sentences

(1)

2. Truth-Functions

(1)

3. Conjunctions

(2)

4. Variables and Constants

(1)

5. Negations

(2)

6. Parentheses and Brackets

(1)

7. Disjunctions

(3)

8. "Not Both" and "Neither...Nor"

(2)

9. Material Conditionals

(2)

10. Material Biconditionals

(2)

11. "Only If" and "Unless"

(2)

12. Symbolizing Complex Sentences

(6)

Key terms

(2)

Chapter Three: Truth Tables

(30)

1. Computing Truth-Values

(5)

2. Tautologies, Contradictions, and Contingent Sentences

(5)

3. Logical Equivalences and Conditionals

(3)

4. Truth Table Test of Validity

(2)

5. Truth Table Test of Consistency

(1)

6. Validity and Consistency

(1)

7. The Short Truth Table Test for Invalidity

(4)

8. The Short Truth Table Test for Consistency

(1)

9. Sentence Forms and Substitution Instances

(5)

10. Truth Tables and Forms

(2)

Key terms

(1)

Chapter Four: Proofs

(35)

1. Argument Forms

(2)

2. Modus Ponens and Modus Tollens

(2)

3. Disjunctive Syllogism and Hypothetical Syllogism

(3)

4. Simplification and Conjunction

(1)

5. Addition and Constructive Dilemma

(2)

6. Principles of Strategy

(7)

7. Double Negation and DeMorgan's Theorem

(2)

8. Commutation, Association, and Distribution

(1)

9. Contraposition, Implication, and Exportation

(1)

10. Tautology and Equivalence

(3)

11. More Principles of Strategy

(4)

12. Common Errors in Problem Solving

101

(6)

Key terms

107

(1)

Chapter Five: Conditional and Indirect Proofs

108

(23)

1. Conditional Proofs

108

(8)

2. Indirect Proofs

116

(5)

3. Strategy Hints for Using Conditional Proof and Indirect Proof

121

(1)

4. Theorems

122

(1)

5. Proving Premises Inconsistent

123

(1)

6. Adding Valid Argument Forms

124

(1)

7. The Completeness of Sentential Logic

125

(2)

8. Material Implication and Valid Argument Forms

127

(3)

Key terms

130

(1)

Part Two: Predicate Logic

131

(152)

Chapter Six: Predicate Logic Symbolizations

131

(22)

1. Individuals and Properties

131

(4)

2. Quantifiers and Free Variables

135

(1)

3. Universal Quantifiers

136

(4)

4. Existential Quantifiers

140

(1)

5. Basic Predicate Logic Symbolizations

141

(2)

6. The Square of Opposition

143

(1)

7. Common Pitfalls in Symbolizing with Quantifiers

144

(3)

8. Expansions

147

(2)

9. Symbolizing "Only," "None But," and "Unless"

149

(2)

Key terms

151

(2)

Chapter Seven: Predicate Logic Invalidity

153

(8)

1. Interpretations in Predicate Logic

153

(1)

2. Proving Invalidity

154

(3)

3. Using Expansions to Prove Invalidity

157

(2)

4. Consistency in Predicate Logic

159

(1)

5. Validity and Inconsistency in Predicate Logic

160

(1)

Key terms

160

(1)

Chapter Eight: Predicate Logic Proofs

161

(24)

1. Proving Validity

161

(1)

2. The Four Quantifier Rules

162

(6)

3. The Five Main Restrictions

168

(4)

4. Precise Formulation of the Four Quantifier Rules

172

(2)

5. Mastering the Four Quantifier Rules

174

(5)

6. Quantifier Negation (QN)

179

(5)

Key terms

184

(1)

Chapter Nine: Relational Predicate Logic

185

(28)

1. Relational Predicates

185

(2)

2. Symbolizations Containing Overlapping Quantifiers

187

(1)

3. Expansions and Overlapping Quantifiers

188

(2)

4. Places and Times

190

(2)

5. Symbolizing "Someone," "Somewhere," "Sometime," and So On

192

(5)

6. Invalidity and Consistency in Relational Predicate Logic

197

(1)

7. Relational Predicate Logic Proofs

198

(7)

8. Strategy for Relational Predicate Logic Proofs

205

(2)

9. Theorems and Inconsistency in Predicate Logic

207

(3)

10. A Simpler Set of Quantifier Rules

210

(3)

Chapter Ten: Rationale Behind the Precise Formulation of the Four Quantifier Rules

213

(12)

1. Cases Involving the Five Major Restrictions

213

(3)

2. One-to-One Correspondence Matters

216

(4)

3. Accidentally Bound Variables

220

(5)

Chapter Eleven: Identity and Philosophical Problems of Symbolic Logic

225

(33)

1. Identity

225

(6)

2. Definite Descriptions

231

(2)

3. Properties of Relations

233

(3)

4. Higher-Order Logics

236

(2)

5. Limitations of Predicate Logic

238

(3)

6. Philosophical Problems

241

(8)

7. Logical Paradoxes

249

(6)

Key terms

255

(3)

Chapter Twelve: Truth Trees

258

(25)

1. The Sentential Logic Truth Tree Method

258

(1)

2. The Truth Tree Rules

259

(7)

3. Details of Tree Construction

266

(6)

4. Rationale Behind the Tree Method

272

(2)

5. Putting Truth Trees to Work

274

(1)

6. The Predicate Logic Truth Tree Method

275

(5)

7. Infinite Trees

280

(2)

Key terms

282

(1)

Part Three: Other Systems of Logic

283

(104)

Chapter Thirteen: Syllogistic Logic

283

(38)

1. Categorical Propositions

283

(3)

2. Existential Import

286

(1)

3. The Square of Opposition

286

(4)

4. Conversion, Obversion, Contraposition

290

(3)

5. Syllogistic Logic-Not Assuming Existential Import

293

(2)

6. Venn Diagrams

295

(3)

7. Syllogisms

298

(2)

8. Determining Syllogism Validity

300

(1)

9. Venn Diagram Proofs of Validity or Invalidity

301

(5)

10. Five Rules for Determining Validity or Invalidity

306

(3)

11. Syllogistics Extended

309

(3)

12. Enthymemes

312

(1)

13. Sorites

313

(2)

14. Technical Restrictions and Limitations

315

(3)

Key terms

318

(3)

Chapter Fourteen: Inductive Logic

321

(35)

1. A Mistaken View of Induction and Deduction

321

(2)

2. Kinds of Inductive Arguments

323

(10)

3. Cause and Effect

333

(3)

4. Mill's Methods

336

(7)

5. Inductive Probability

343

(1)

6. The Probability Calculus

344

(2)

7. Bayes' Theorem

346

(2)

8. Induction Is Unjustified-The Old Riddle of Induction

348

(3)

9. Not All Instances of Theories Confirm Them-The New Riddle of Induction

351

(3)

Key terms

354

(2)

Chapter Fifteen: Axiom Systems

356

(14)

1. The Nature of an Axiom System

356

(1)

2. Interpreted and Uninterpreted Systems

357

(1)

3. Properties of Axiom Systems

358

(3)

4. Outline of an Axiom System for Sentential Logic

361

(5)

5. Axiom Systems for Predicate Logic

366

(1)

6. Other Kinds of Axiom Systems

367

(1)

7. Objections to Axiom Systems

368

(1)

Key terms

368

(2)

Chapter Sixteen: Alternative Logics

370

(17)

1. Modal Logic

370

(1)

2. Strict Implication

371

(2)

3. Modal Axioms

373

(1)

4. Modal Theorems

374

(1)

5. Modal Paradoxes

375

(1)

6. A Philosophical Problem

375

(1)

7. Modal Predicate Logic

376

(2)

8. Epistemic Logic: The Logic of Knowledge and Belief

378

(3)

9. Epistemic Theorems

381

(1)

10. Deontic Logic

382

(1)

11. Problems with Deontic Systems

383

(2)

Key terms

385

(2)

Answers to Even-Numbered Exercise Items

387

(62)

Bibliography

449

(4)

Special Symbols

453

(2)

Index

455

Amazon no longer offers textbook rentals. We do!

Logic and Philosophy

Logic and Philosophy

9780534526146

0534526144

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Logic and Philosophy

Logic and Philosophy

9780534526146

0534526144

Summary

Table of Contents

Supplemental Materials

Write a Review

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