Formal Logic
  • Publication Date: July 15, 2017
  • ISBN: 9781554812721 / 1554812720
  • 400 pages; 5" x 6"
Exam Copy

Availability: Worldwide

Formal Logic

  • Publication Date: July 15, 2017
  • ISBN: 9781554812721 / 1554812720
  • 400 pages; 5" x 6"

Formal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website (complimentary for anyone who buys the book) offers supplemental practice software and tutorial videos.


Formal Logic is clear, accessible, and intuitive, but it is also precise, explicit, and thorough. Complex and often confusing concepts are rolled out in a no-nonsense and direct manner with funny and demystifying terminology and helpful analogies. It's a pedagogical gem.” —Mary Kate McGowan, Wellesley College

“This is an excellent introductory text in symbolic logic. It is accessible, with clear and concise explanations of key concepts, along with many helpful examples and practice problems, but also rigorous enough to prepare students for a second course in logic; indeed, I do not know of any book that better combines these virtues. I am looking forward to using Formal Logic in my courses.” —Kevin Morris, Tulane University

I: Informal Notions
1: Informal Introduction

  • 1.1 What, Why, How?
    1.2 Arguments, Forms, and Truth Values
    1.3 Deductive Criteria
    1.4 Inductive Criteria
    1.5 Other Deductive Properties
    1.6 Chapter Glossary

II: Truth-Functional Logic
2: The Language S

  • 2.1 Introducing S
    2.2 Some Technical Bits
    2.3 The Syntax of S
    2.4 Symbolizations
    2.5 Chapter Glossary

3: Formal Semantics for S

  • 3.1 Truth Value Assignments and Truth Tables
    3.2 Semantic Properties of Individual Wffs
    3.3 Semantic Properties of Sets of Wffs
    3.4 Semantic Properties, Their Interrelations, and Simple Metalogic
    3.5 Truth Trees
    3.6 Chapter Glossary

4: SD: Natural Deduction in S

  • 4.1 The Basic Idea
    4.2 Derivations: Strategies and Notes
    4.3 Proof Theory in SD
    4.4 SDE, an Extension to SD
    4.5 Chapter Glossary

III: Quantificational Logic
5: The Language P

  • 5.1 Introducing P
    5.2 The Syntax of P
    5.3 Simple Symbolizations
    5.4 Complex Symbolizations
    5.5 Chapter Glossary

6: Formal Semantics for P

  • 6.1 Interpretations
    6.2 Semantic Properties of Individual Wffs
    6.3 Semantic Properties of Sets of Wffs
    6.4 Trees and Models
    6.5 Chapter Glossary

7: PD: Natural Deduction in P

  • 7.1 Derivation Rules for the Quantifiers
    7.2 Derivations: Strategies and Notes
    7.3 Proof Theory in PD
    7.4 Chapter Glossary

IV: Advanced Topics
8: Basic Set Theory, Paradox, and Infinity

  • 8.1 Intuitive Set Theory
    8.2 Russell’s Paradox
    8.3 The Axiom Schema of Separation
    8.4 Inclusion, Intersection, and Union
    8.5 Pairs, Ordered Pairs, Power Sets, Relations, and Functions
    8.6 Defining (Cardinal) Numbers
    8.7 Infinite Sets and Cantor’s Proof
    8.8 Chapter Glossary

9: Modal Logic

  • 9.1 Introducing Modalities
    9.2 Modal Logic
    9.3 Simple Semantics for M
    9.4 Kripke Semantics
    9.5 Modal Derivations
    9.6 Chapter Glossary

V: Appendices
A: Answers to Exercises
B: Glossary
C: Truth Tables, Tree Rules, and Derivation Rules

  • C.1 Characteristic Truth Tables
    C.2 Truth Tree Rules for S
    C.3 The Derivation System SD
    C.4 The Derivation System SDE
    C.5 The Derivation System PD

Paul A. Gregory is Head of the Department of Philosophy at Washington and Lee University.

Formal Logic includes access to companion websites for both students and instructors.

The student website hosts a logic proof checker and a series of video tutorials.

The instructor website hosts a test bank of questions.