Logic

By Greg Restall
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240 pages, 5.5 x 8.5 inches
Paperback : 9780773524231, February 2006
Ebook (PDF) : 9780773585928, February 2006
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Table of Contents

Table of Contents

Acknowledgements xiii
Introduction 1
For the student 1
For the instructor 3
PART 1
Propositional logic 7
1 Propositions and arguments 9
Propositions 10
Arguments 11
Argument forms 13
Summary 16
Further reading 16
Exercises 17
2 Connectives and argument forms 20
Conjunction and disjunction 20
Conditionals and Biconditionals 24
Negation 26
A language of forms 27
More argument forms 30
Summary 31
Exercises 32
3 Truth tables 36
Truth tables 36
Truth tables for arguments 43
Finding evaluations quickly 46
Summary 49
Exercises 50
4 Trees 55
The idea behind trees 57
Tree rules 61
Why the tree method works 68
Summary 74
Exercises 75
5 Vagueness and bivalence 77
The problem of vagueness 77
Alternatives 79
Other problems with bivalence 84
Further reading 85
Exercises 86
6 Conditionality 88
The paradoxes of material implication 88
Truth and assertibility 90
Possibilities 92
Relevance 98
Further reading 100
Exercises 100
7 Natural deduction 102
Conjunction, disjunction and negation 102
Negation 106
Further reading 108
Exercises 109
PART 2
Predicate logic 111
8 Predicates, names and quantifiers 113
Names and predicates 114
Quantifiers 116
Translation 121
Summary 123
Exercises 123
9 Models for predicate logic 128
Domains and extensions 128
Quantifiers 133
Constructing models 139
When finite domains suffice 144
Summary 145
Exercises 146
10 Trees for predicate logic 149
Tree rules for quantifiers 149
When trees don’t close 154
Why the tree method works 161
Exercises 164
11 Identity and functions 168
Identity 169
Translating some common quantifiers 173
Functions 175
Summary 179
Exercises 179
12 Definite descriptions 183
Russell’s solution 184
Nuances 189
Further reading 190
Exercises 190
13 Some things do not exist 192
Existential import and predicates 192
Existential import and names 194
Models 197
Tree rules 198
Nuances 200
Further reading 203
Exercises 203
14 What is a predicate? 205
An argument 205
Opaque contexts 207
Further reading 210
Exercises 211
15 What is logic? 212
Logic as invariance under permutation 213
Logic as necessary truth preservation 215
Further reading 217
Bibliography 218
Index 221

Greg Restall's Logic provides concise introductions to propositional and first-order predicate logic while showing how formal logic intersects with substantial philosophical issues such as vagueness, conditionals, relevance, propositional attitudes, and opaque contents. The author also examines the ideas behind modal logic, free logic, and other non-standard logics and discusses the nature of logic itself.
The book covers both natural deduction and tree methods for proving validity. Each chapter includes excellent suggestions for further reading and both elementary and more advanced exercises, with solutions provided on a website. It is flexibly designed to be useable for half or full-year courses, for courses focusing exclusively on formal logic, or for a variety of approaches that would integrate topics in philosophical logic.
Restall examines many of the interesting issues raised by basic logical techniques and will undoubtedly stimulate further study in the discipline. This is a logic book designed principally for philosophers but which will also be of interest to students of computer science, cognitive science, and linguistics.

"The text is wonderfully clear and avoids the tedium of many introductory logic texts. The examples, exercises, and suggestions for further reading are all good. This is the only introductory text I know of that introduces students to some of the philosophical problems logic pertains to and intersects with. It is the type of book I would like to use for an introductory course and recommend it enthusiastically." Michael Hallett, Philosophy Department, McGill University.