Logic: The Laws of Truth

Logic: The Laws of Truth

by Nicholas J.J. Smith
     
 

"Smith's book combines accessibility with comprehensiveness in a way that I have not found in other texts. It is very readable and well paced, but does not sacrifice precision. Difficult issues aren't glossed over or skipped, but are introduced at a gentle pace for novice logicians. As a teacher of logic, I see real benefits in Smith's approach."—Jennifer

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Overview

"Smith's book combines accessibility with comprehensiveness in a way that I have not found in other texts. It is very readable and well paced, but does not sacrifice precision. Difficult issues aren't glossed over or skipped, but are introduced at a gentle pace for novice logicians. As a teacher of logic, I see real benefits in Smith's approach."—Jennifer Duke-Yonge, Macquarie University, Australia

"Lots of books aim to provide a first introduction to symbolic logic. I predict that this one will be widely adopted throughout the English-speaking world. One of its unique strengths is that it broaches important philosophical issues that naturally arise in connection with symbolic logic. The book thus serves both as an introduction to logic itself and to the philosophy of logic."—Stewart Shapiro, editor of The Oxford Handbook of Philosophy of Mathematics and Logic

Product Details

ISBN-13:
9780691151632
Publisher:
Princeton University Press
Publication date:
04/01/2012
Edition description:
New Edition
Pages:
576
Sales rank:
1,148,253
Product dimensions:
6.40(w) x 9.30(h) x 1.60(d)

Related Subjects

Table of Contents

Preface xi

Acknowledgments xv

Part I Propositional Logic 1

Chapter 1: Propositions and Arguments 3

1.1 What Is Logic? 3

1.2 Propositions 5

1.3 Arguments 11

1.4 Logical Consequence 14

1.5 Soundness 21

1.6 Connectives 23

Chapter 2: The Language of Propositional Logic 32

2.1 Motivation 32

2.2 Basic Propositions of PL 32

2.3 Connectives of PL 36

2.4 Wff Variables 39

2.5 Syntax of PL 40

Chapter 3: Semantics of Propositional Logic 49

3.1 Truth Tables for the Connectives 49

3.2 Truth Values of Complex Propositions 51

3.3 Truth Tables for Complex Propositions 54

3.4 Truth Tables for Multiple Propositions 58

3.5 Connectives and Truth Functions 59

Chapter 4: Uses of Truth Tables 63

4.1 Arguments 63

4.2 Single Propositions 67

4.3 Two Propositions 69

4.4 Sets of Propositions 74

4.5 More on Validity 75

Chapter 5: Logical Form 79

5.1 Abstracting from Content: From Propositions to Forms 81

5.2 Instances: From Forms to Propositions 82

5.3 Argument Forms 84

5.4 Validity and Form 87

5.5 Invalidity and Form 91

5.6 Notable Argument Forms 94

5.7 Other Logical Properties 95

Chapter 6: Connectives: Translation and Adequacy 97

6.1 Assertibility and Implicature 97

6.2 Conjunction 103

6.3 Conditional and Biconditional 110

6.4 Disjunction 117

6.5 Negation 122

6.6 Functional Completeness 124

7 Trees for Propositional Logic 134

7.1 Tree Rules 136

7.2 Applying the Rules 140

7.3 Uses of Trees 146

7.4 Abbreviations 156

Part II Predicate Logic 161

Chapter 8: The Language of Monadic Predicate Logic 163

8.1 The Limitations of Propositional Logic 164

8.2 MPL, Part I: Names and Predicates 167

8.3 MPL, Part II: Variables and Quantifiers 172

8.4 Syntax of MPL 182

Chapter 9: Semantics of Monadic Predicate Logic 189

9.1 Models; Truth and Falsity of Uncomplicated Propositions 191

9.2 Connectives 196

9.3 Quantified Propositions: The General Case 197

9.4 Semantics of MPL: Summary 204

9.5 Analyses and Methods 206

Chapter 10: Trees for Monadic Predicate Logic 211

10.1 Tree Rules 212

10.2 Using Trees 223

10.3 Infinite Trees 228

Chapter 11: Models, Propositions, and Ways the World Could Be 242

11.1 Translation 243

11.2 Valuation 247

11.3 Axiomatization 251

11.4 Propositions 253

11.5 Logical Consequence and NTP 257

11.6 Postulates 261

Chapter 12: General Predicate Logic 264

12.1 The Language of General Predicate Logic 264

12.2 Semantics of GPL 276

12.3 Trees for General Predicate Logic 282

12.4 Postulates 286

12.5 Moving Quantifiers 293

Chapter 13: Identity 298

13.1 The Identity Relation 299

13.2 The Identity Predicate 303

13.3 Semantics of Identity 306

13.4 Trees for General Predicate Logic with Identity 311

13.5 Numerical Quantifiers 321

13.6 Definite Descriptions 326

13.7 Function Symbols 343

Part III Foundations and Variations 355

14 Metatheory 357

14.1 Soundness and Completeness 358

14.2 Decidability and Undecidability 368

14.3 Other Logical Properties 374

14.4 Expressive Power 382

15 Other Methods of Proof 385

15.1 Axiomatic Systems 386

15.2 Natural Deduction 407

15.3 Sequent Calculus 421

16 Set Theory 438

16.1 Sets 438

16.2 Ordered Pairs and Ordered n-tuples 449

16.3 Relations 453

16.4 Functions 454

16.5 Sequences 458

16.6 Multisets 460

16.7 Syntax 462

Notes 467

References 509

Index 515

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