# Logic: The Laws of Truth

ISBN-10: 0691151636

ISBN-13: 9780691151632

Pub. Date: 04/01/2012

Publisher: Princeton University Press

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques

## Overview

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents all the major forms of proof—trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website.

Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject.

• Provides an essential introduction to classical logic
• Emphasizes the how and why of logic
• Covers both formal and philosophical issues
• Presents all the major forms of proof—from trees to sequent calculus
• Features numerous exercises, with solutions available at http://www-personal.usyd.edu.au/~njjsmith/lawsoftruth
• The ideal textbook for undergraduates and graduate students

## Product Details

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

## 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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