Logic : An Introduction

The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing and linguistics. Greg Restall's Logic is a comprehensive introduction to the major concepts and techniques involved in the study of logic, including propositions and arguments, truth tables, tree methods, conditionality and natural deduction. Restall explores both formal and philosophical logic and examines the ways in which we can achieve good reasoning. “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.”--Publisher's description

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.

During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,,an, find the largest natural number (called the Frobenius number and denoted by g(a1,,an) that is not representable as a nonnegative integer combination of a1,,an.
At first glance FB may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience. During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an,. At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience. Book Cover 1 Half-Title 2 Series 3 Title 5 Copyright 6 Dedication 7 Contents 8 Acknowledgements 10 Introduction 11 PART 1 Prepositional logic 15 Chapter 1 Propositions and arguments 16 Chapter 2 Connectives and argument forms 24 Chapter 3 Truth tables 36 Chapter 4 Trees 50 Chapter 5 Vagueness and bivalence 67 Chapter 6 Conditionality 75 Chapter 7 Natural deduction 85 PART 2 Predicate logic 92 Chapter 8 Predicates, names and quantifiers 93 Chapter 9 Models for predicate logic 104 Chapter 10 Trees for predicate logic 120 Chapter 11 Identity and functions 135 Chapter 12 Definite descriptions 147 Chapter 13 Some things do not exist 154 Chapter 14 What is a predicate? 165 Chapter 15 What is logic? 170 Bibliography 174 Index 177 The methods of logic are essential to an understanding of philosophy and are crucial in the study of mathematics, computing, linguistics and many other subjects. Introducing the major concepts and techniques involved in the study of logic, this authoritative book explores both formal and philosophical logic, and the ways in which we can achieve good reasoning. Individual chapters include:• Propositions and Arguments• Truth Tables• Trees• Conditionality• Natural Deduction• Predicates, Names and Quantifiers• Definite Descriptions.This exceptionally clear introduction to the subject is ideally suited to students taking introductory courses in logic. A number of methods, from several areas of mathematics have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight these viewpoints, ideas and applications to a broader audience