1st Edition

A Philosophical Introduction to Higher-order Logics

By Andrew Bacon Copyright 2023
    482 Pages 57 B/W Illustrations
    by Routledge

    482 Pages 57 B/W Illustrations
    by Routledge

    This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages—their model theory and proof theory, the theory of λ-abstraction and its generalizations—and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. 

    A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study.

    Author Andrew Bacon organizes the book's 18 chapters around four main parts:
    I. Typed Language
    II. Higher-Order Languages
    III. General Higher-Order Languages
    IV. Higher-Order Model Theory 

    In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. 

    Key Features:

    • Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics
    • Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages
    • Offers an abundance of
      - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions
      - More difficult exercises designed to facilitate long-term learning
    • Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context


    Part I: Typed Languages

    1. Typed Languages
    2. An Informal Introduction to Abstraction
    3. λ-Languages

    Part II: Higher-Order Languages

    4 Higher-Order Languages
    5 Higher-Order Logics
    6 Application: Higher-Order Logic and Granularity
    7 Application: Modal Logicism
    8 Application: Consequences and Strengthenings of Classicism

    Part III: General Higher-Order Languages

    9 General λ-Languages
    10. Curry Typing
    11. Application: Structure I
    12. Application: Structure II
    13. Application: Structure III

    Part IV: Higher-Order Model Theory

    14. Applicative structures
    15. Models of Higher-Order Languages
    16. Logical Relations
    17. Modalized Sets, M-Sets and Cartesian Closed Categories
    18. The Model Theory of Classicism

    Part V: Appendices

    A The Curry-Howard Isomorphism
    B Definability semantics


    Andrew Bacon is Associate Professor at the University of Southern California. He is the author of Vagueness and Thought (Oxford UP, 2018) and has written numerous articles applying logical methods to topics in metaphysics, epistemology, and language.