Logic is the science of determining whether an argument is good or bad. Achieving this goal requires a great many things. First, it requires specifying what an argument is and what we mean when we say an argument is "good" or "bad". Second, we not only want to know what it means for an argument to be "good", but also how to identify good and bad arguments. Third, we want to know how to construct good arguments.

This is a first course in symbolic (formal) logic. The course is divided into three parts.

In addition to learning about logic, students will also be exposed to the multitude of ways that logic applies and intersects with other subject matters and daily life. The course includes countless extra-credit opportunities involving the use of spreadsheets, cryptography, logic puzzles, search engines, typesetting mathematics, and human cognition.



S5: PL - Propositional Logic Proofs
S9: RL - Variable Assignments (Slides)

Other Handouts

  • H3: Conditionals and the LSAT
  • H4s: Six Tips For Truth Trees
  • H4e: Four Theories of Truth
  • H8s: Further Explanation on the use of Existential Elimination (EE)
  • H9: RL: Variable Assignments, Identity, Functions, Definite Descriptions
  • LX: LaTeX Commands for Logic
  • LSAT: Logic Games
  • Quantificational Ambiguities
  • Practice Exams

    Starred exams are the practice examples we will use to review during the review sessions.


    PL - Symbols, Syntax, Semantics, Translation

    For a comprehensive video, see An Introduction to Symbolic Logic - 2022.

    PL - Truth Tables

    PL: Truth Tables: Introduction
    PL: Truth Tables: Practice, Part 1
    PL: Truth Tables: Relations between Semantic Properties

    PL - Truth Trees

    PL: Truth Trees, Part 1 (Introduction and Setup)
    PL: Truth Trees, Part 2 (Decomposition Rules)
    PL: Truth Trees, Part 3 (Tree Terminology)
    PL: Truth Trees, Part 4 (Recovering an Interpretation)
    PL: Truth Trees, Part 6 (Contradiction, Tautology, Contingency)
    PL: Truth Trees, Part 7 (Equivalence)
    PL: Truth Trees, Part 8 (Validity)
    PL: Tips for Trees

    PL - Derivations / Proofs

    Predicate Logic (RL) - Symbols, Syntax, Semantics, Translation

    RL - Truth Trees

    RL - Proofs


    In the Spring of 2009, I began writing Symbolic Logic: Syntax, Semantics, and Proof. The first edition took the form of lecture notes and handouts that I distributed in the summer of 2009, a course packet in the fall of 2009, and finally I used it as a textbook in the Summer 2010, Fall 2010, and Spring 2011 semesters.

    The development of the textbook benefited greatly from the feedback I received from instructors and students at Penn State: Deniz Durmus (Spring 2011); Mark Fisher (Spring 2011); Cameron O'Mara (Summer 2011); Ryan Pollock (Fall 2011), Christopher Allaman, Ashley Brooks, Aurora Cooper, Maureen Dunn, Elliannies Duran, Ariel Endresen, Nayib Felix, Joy Garcia, Alex Kirk, Edward Lackner, Brooke Santkiewicz, Ariel Valdez, Isaac Bishop, Kristin Nuss, Karintha Parker, Sarah Mack, Amanda Wise, Meghan Barnett, Alexander McCormack, and Kevin Bogle.

    The textbook is in its 2nd printing. The erratum (list of corrections from the first printing) can be found here: Errata for Symbolic Logic: Syntax, Semantics, and Proof. I am currently working on a second edition!

    Image of Textbook