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Introduction to Formal Logic

Russell Marcus

Publication Date - February 2018

ISBN: 9780190861780

504 pages
7-1/2 x 9-1/4 inches

In Stock

The most intuitive, engaging, yet still rigorous, introduction to formal logic


Rigorous yet intuitive and accessible, Introduction to Formal Logic provides a focused, "nuts-and-bolts" introduction to formal deductive logic that covers syntax, semantics, translation, and natural deduction for propositional and predicate logics.

For instructors who want to go beyond a basic introduction to explore the connection between formal logic techniques and philosophy, Oxford also publishes Introduction to Formal Logic with Philosophical Applications, an extended version of this text that incorporates two chapters of stand-alone essays on logic and its application in philosophy and beyond.


  • Offers exceptional clarity and accessibility, explaining key concepts using a conversational tone and examples that speak to students without oversimplifying the topics
  • More than 2,000 in-text exercises--presented progressively, from easier to more challenging-- provide plenty of opportunity for students to apply and practice what they learn. Solutions to approximately 20% of the in-text exercises are included at the back of the book.
  • Incorporates several formal topics and exercise types that are usually omitted from standard logic texts, including seven rules for biconditionals, parallel to the standard rules for conditionals; exercises on interpreting and modeling short theories; two sections on functions at the end of Chapter 5; and exercises on determining whether an argument is valid or invalid, or whether a proposition is a logical truth or not, and then constructing either a derivation or a counterexample
  • Integrates numerous student-friendly learning aids including section summaries, lists of important points to keep in mind, bolded key terms with marginal definitions, and a glossary
  • Dashboard for Introduction to Formal Logic with Philosophical Applications delivers an interactive eBook, auto-graded exercises, a symbolic proof checking tool, additional study resources, and a gradebook in a simple, informative, and mobile-friendly form

About the Author(s)

Russell Marcus is Associate Professor of Philosophy at Hamilton College.


"Introduction to Formal Logic is a superb treatment of the subject. It is unusually lucid, meeting students where they are and guiding them in a step-by-step manner through the rigors of symbolic logic. All of this without sacrificing the kind of detail and precision that is a sine qua non for textbooks of this kind."--Michael Futch, University of Tulsa

"This is a superb treatment of formal logic. In my opinion, it's not too difficult and not too easy."--Leemon McHenry, California State University, Northridge

"This is a book that enables students to become comfortable with the basics of logic while also allowing them to understand why they are doing logic."--Andrew Winters, Slippery Rock University of Pennsylvania

Table of Contents

    Chapter 1. Introducing Logic
    1.1: Defining "Logic"
    1.2: Logic and Languages
    1.3: A Short History of Logic
    1.4: Separating Premises from Conclusions
    1.5: Validity and Soundness
    Key Terms
    Chapter 2. Propositional Logic: Syntax and Semantic
    2.1: Logical Operators and Translation
    2.2: Syntax of PL: Wffs and Main Operators
    2.3: Semantics of PL: Truth Functions
    2.4: Truth Tables
    2.5: Classifying Propositions
    2.6: Valid and Invalid Arguments
    2.7: Indirect Truth Tables
    Key Terms
    Chapter 3. Inference in Propositional Logic
    3.1: Rules of Inference 1
    3.2: Rules of Inference 2
    3.3: Rules of Equivalence 1
    3.4: Rules of Equivalence 2
    3.5: Practice with Derivations
    3.6: The Biconditional
    3.7: Conditional Proof
    3.8: Logical Truths
    3.9: Indirect Proof
    3.10: Chapter Review
    Key Terms
    Chapter 4. Monadic Predicate Logic
    4.1: Introducing Predicate Logic
    4.2: Translation Using M
    4.3: Syntax for M
    4.4: Derivations in M
    4.5: Quantifier Exchange
    4.6: Conditional and Indirect Proof in M
    4.7: Semantics for M
    4.8: Invalidity in M
    Key Terms
    Chapter 5. Full First-Order Logic
    5.1: Translation Using Relational Predicates
    5.2: Syntax, Semantics, and Invalidity in F
    5.3: Derivations in F
    5.4: The Identity Predicate: Translation
    5.5: The Identity Predicate: Derivations
    5.6: Translation with Functions
    5.7: Derivations with Functions
    Key Terms
    Appendix on Fallacies and Argumentation
    Appendix on the Logical Equivalence of the Rules of Equivalence