Logic Primer, third edition

by Colin Allen, Michael Hand

Overview

The new edition of a comprehensive and rigorous but concise introduction to symbolic logic.

Logic Primer offers a comprehensive and rigorous introduction to symbolic logic, providing concise definitions of key concepts, illustrative examples, and exercises. After presenting the definitions of validity and soundness, the book goes on to introduce a formal language, proof theory, and formal semantics for sentential logic (chapters 1–3) and for first-order predicate logic (chapters 4–6) with identity (chapter 7). For this third edition, the material has been reorganized from four chapters into seven, increasing the modularity of the text and enabling teachers to choose alternative paths through the book. New exercises have been added, and all exercises are now arranged to support students moving from easier to harder problems.

Its spare and elegant treatment makes Logic Primer unique among textbooks. It presents the material with minimal chattiness, allowing students to proceed more directly from topic to topic and leaving instructors free to cover the subject matter in the way that best suits their students. The book includes more than thirty exercise sets, with answers to many of them provided in an appendix. The book’s website allows students to enter and check proofs, truth tables, and other exercises interactively.

Product Details

ISBN-13:	9780262543644
Publisher:	MIT Press
Publication date:	02/15/2022
Pages:	174
Sales rank:	565,482
Product dimensions:	7.00(w) x 9.00(h) x 0.36(d)

About the Author

Colin Allen is Distinguished Professor in the Department of History and Philosophy of Science at the University of Pittsburgh. He is coauthor of Species of Mind and coeditor of Nature’s Purposes and The Cognitive Animal, all published by the MIT Press. Michael Hand is Professor of Philosophy at Texas A&M University.

Table of Contents

Preface ix

Acknowledgments xvii

1 Sentential Logic: Basic Concepts and a Formal Language 1

1.1 Basic Logical Notions 1

1.2 Elements of a Formal Language 3

1.3 Well-Formed Formulas 5

1.4 Translation of English to Sentential Wffs 10

2 Sentential Logic: Proofs 17

2.1 Primitive Rules of Proof 17

2.2 Sequents and Derived Rules 27

2.3 Theorems 33

Sentential Logic: Truth Tables 37

3.1 Truth Tables for Sentences 37

3.2 Truth Tables for Sequents 40

3.3 Tautologies 42

3-4 Indirect Truth Tables 44

3.5 English Counterexamples 47

4 Predicate Logic: Formal Language 51

4.1 A Formal Language for Predicate Logic 51

4.2 Translation of English to Quantified Wffs 58

5 Predicate Logic: Proofs 65

5.1 Primitive Rules of Proof 65

5.2 Theorems and Derived Rules of Proof 73

6 Predicate Logic: Models 77

6.1 Finite Interpretations and Expansions with One-Place Predicates 77

6.2 Finite Countermodels for Arguments with One-Place Predicates 81

6.3 Finite Countermodels for Arguments with Many-Place Predicates 84

6.4 Infinite Countermodels 88

7 Predicate Logic with Identity 91

7.1 Formal Language 91

7.2 Proofs 95

7.3 Countermodels 98

A Appendix: Answers to Selected Exercises 101

A.1 Chapter 1 Answers 101

A.2 Chapter 2 Answers 103

A.3 Chapter 3 Answers 127

A.4 Chapter 4 Answers 133

A.5 Chapter 5 Answers 139

A.6 Chapter 6 Answers 150

A.7 Chapter 7 Answers 154

What People are Saying About This

From the Publisher

“I have long been a huge fan of Logic Primer, so it’s very exciting to see it being released in a third edition. This edition retains the elegant and intuitive system developed by the authors in previous editions but introduces and presents the material in a more modularized structure, thereby making an already superb textbook more adaptable to different instructional preferences. I can’t wait to use this in my classes!”
—Amy Kind, Professor of Philosophy, Claremont McKenna
 
“I am very pleased to see that Logic Primer is coming out in a third edition. I have used the previous editions to great effect in turning my classes into learning communities of careful readers. My students and I have appreciated Logic Primer’s clear, direct, and intelligibly sequenced presentation of material.”
—William Robinson, Professor of Philosophy Emeritus, Iowa State University
 
“Superb. Logic Primer includes all and only the most essential material, presented with clarity and precision. The changes introduced in the third edition make an excellent book even better.”
—Torin Alter, Professor of Philosophy, University of Alabama