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Introduction to Formal Logic with Philosophical Applications

Russell Marcus

Publication Date - December 2017

ISBN: 9780199386482

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

In Stock

Retail Price to Students: $99.95

The most intuitive, engaging, yet still rigorous, introduction to formal logic--with philosophical applications


Rigorous yet engaging and accessible, Introduction to Formal Logic with Philosophical Applications is composed of two parts. The first part (Chapters 1-5) provides a focused, "nuts-and-bolts" introduction to formal deductive logic that covers syntax, semantics, translation, and natural deduction for propositional and predicate logics. The second part (Chapters 6-7) presents stand-alone, student-friendly essays on logic and its application in philosophy and beyond, with writing prompts and suggestions for further readings.

For instructors who prefer an exceptionally clear introduction to formal logic without the extra philosophical applications, Introduction to Formal Logic, an abbreviated, alternate version of Introduction to Formal Logic with Philosophical Applications, is also available.


  • 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/index
  • Emphasizes the connection between philosophy and logic with two chapters (6 and 7) that offer stand-alone, accessible essays on logic and its application in philosophy and beyond
  • "Tell Me More" boxes at the ends of sections in Chapters 1-5 help instructors and their students to use the essays in Chapters 6 and 7 to deepen their understanding of logic
  • 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 with Philosophical Applications 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

"Hurley has the advantage of breadth, but lacks the depth, whereas Hausman has depth, but lacks the clarity of Marcus. Chapter 7 is my favorite chapter, as Marcus addresses philosophical issues of logic. What I like is that this chapter can be used throughout the semester. And I loved the paper topics suggested throughout the book."--Reginald Raymer, University of North Carolina, Charlotte

"Introduction to Formal Logic with Philosophical Applications is better than what I now use. It's an excellent introductory text--precise, detailed, and clear, with lots of exercises and a wealth of interesting supplementary material."--Jeff Buechner, Rutgers University, Newark

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
    Chapter 6. Beyond Basic Logic
    6.1: Notes on Translation with PL
    6.2: Conditionals
    6.3: Three-Valued Logics
    6.4: Metalogic
    6.5: Modal Logics
    6.6: Notes on Translation with M
    Key Terms
    Chapter 7. Logic and Philosophy
    7.1: Deduction and Induction
    7.2: Fallacies and Argumentation
    7.3: Logic and Philosophy of Mind: Syntax, Semantics, and the Chinese Room
    7.4: Logic and the Philosophy of Religion
    7.5: Truth and Liars
    7.6: Names, Definite Descriptions, and Logical Form
    7.7: Logicism
    Appendix on the Logical Equivalence of the Rules of Equivalence
    Solutions to Selected Exercises

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