1st Edition

Logic for Justice An Introduction to Formal Logic with an Emphasis on Political Reform

By Isaac Wilhelm Copyright 2023
    258 Pages
    by Routledge

    258 Pages
    by Routledge

    An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction.

    In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues.

    Key Features

    • Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject.
    • Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations.
    • Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally.
    • Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other.
    • Provides a large and diverse set of problems for each chapter.
    • Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.

    1. Introduction

    Part I: Natural Language Arguments

    2. Arguments in English
        2.1 Arguments, Reasons, and Views
        2.2 The Basics of Natural Language Arguments
        2.3 Validity and Soundness
        2.4 The Personal and Political Value of Arguments
        2.5 Problems

    Part II: Propositional Logic

    3. The Language of Propositional Logic
        3.1 The Formal Language
        3.2 Translation Tips
        3.3 Translating English Arguments
        3.4 Sentences of P
        3.5 Notation and Terminology
        3.6 Applications to Justice
        3.7 Problems

    4. Truth and Validity in P
        4.1 Truth
        4.2 Truth for Sentences of P: Detailed Examples
        4.3 Validity
        4.4 Justifying the Definition of Validity in P
        4.5 Applications to Justice
        4.6 Problems

    5. The Propositional Approach to Validity in English
        5.1 Final Definitions
        5.2 Applications to Justice
        5.3 Problems

    6. Extracting Arguments
        6.1 Extraction
        6.2 Problems

    Part III: Shortcomings of Propositional Logic

    7. From Propositional Logic to First-Order Logic
        7.1 Shortcomings of Propositional Logic
        7.2 Problems

    Part IV: First-Order Logic

    8. The Language of First-Order Logic
        8.1 The Formal Language
        8.2 Translating English Arguments
        8.3 Sentences of F
        8.4 Applications to Justice
        8.5 Problems

    9. Validity and Truth in F
        9.1 Proof Trees and Validity in F
        9.2 Truth in F
        9.3 Applications to Justice
        9.4 Problems

    10. The First-Order Approach to Validity in English
        10.1 Final Definitions
        10.2 Applications to Justice
        10.3 Comparing Two Accounts
        10.4 Problems


    Isaac Wilhelm is Assistant Professor of Philosophy at the National University of Singapore who works on metaphysics, philosophy of science, and philosophy of physics.