Logic: An Introduction

by Greg Restall

Overview

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.

Product Details

ISBN-13:	9780773524231
Publisher:	McGill-Queens University Press
Publication date:	02/02/2006
Series:	Fundamentals of Philosophy , #8
Edition description:	New Edition
Pages:	240
Product dimensions:	5.40(w) x 8.40(h) x 0.60(d)

About the Author

Greg Restall is professor of philosophy, Macquarie University, Australia.

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

Editorial Reviews

"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.

From the Publisher