1st Edition

Critical Views of Logic

Edited By Mirja Hartimo, Frode Kjosavik, Øystein Linnebo Copyright 2024

    This book examines positions that challenge the Fregean logic-first view. It raises critical

    questions about logic by examining various ways in which logic may be entangled with mathematics and metaphysics.

    Is logic topic-neutral and general? Can we take the application of logic for granted? This book suggests that we should not be dogmatic about logic but ask similar critical questions about logic as those Kant raised about metaphysics and mathematics. It challenges the Fregean logic-first view according to which logic is fundamental and hence independent of any extra-logical considerations. Whereas Quine assimilated logic and mathematics to the theoretical parts of empirical science, the present volume explores views that stop short of his thoroughgoing holism but instead take logic to be answerable to or entangled with some particular disciplines. The contributions provide views that assign primacy to mathematical reasons, Kantian metaphysical grounds, Husserlian transcendental phenomenological reflection, or normative considerations about how terms ought to be defined in various fields of empirical science or mathematics. Space is thereby carved out between a Fregean position on the one hand and Quinean holism on the other.

    Critical Views of Logic will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science, as well as those engaged in various fields of empirical science. The chapters in this book, except for chapter 4, were originally published in the journal Inquiry.

    Introduction to “Critical Views of Logic”
    Mirja Hartimo, Frode Kjosavik and Øystein Linnebo

    1. Infinity and a Critical View of Logic
      Charles Parsons
    2. Dummett’s objection to the ontological route to intuitionistic logic: a rejoinder
      Mark van Atten
    3. The entanglement of logic and set theory, constructively,
      Laura Crosilla
    4. Critical Plural Logic
      Salvatore Florio and Øystein Linnebo
    5. Kant on the possibilities of mathematics and the scope and limits of logic
      Frode Kjosavik
    6. The infinite, the indefinite and the critical turn: Kant via Kripke models
      Carl Posy
    7. Husserl on Kant and the critical view of logic
      Mirja Hartimo
    8. Logical pluralism and normativity
      Teresa Kouri Kissel and Stewart Shapiro
    9. Disagreement about logic
      Ole Thomassen Hjortland


    Mirja Hartimo (University of Helsinki) works on phenomenological perspective to philosophy of mathematics and logic. Her recent publications include Husserl and Mathematics (2021).

    Frode Kjosavik (Norwegian University of Life Sciences) works on Kant, Husserl, metaphysics, philosophy of mathematics, and philosophy of science. He is the editor of Metametaphysics and the Sciences: Historical and Philosophical Perspectives (with Camilla Serck-Hanssen, 2020).

    Øystein Linnebo (University of Oslo) works on metaphysics and the philosophy of logic and mathematics. His recent publications include Thin Objects: An Abstractionist Account (2018) and The Many and the One: A Philosophical Study of Plural Logic (with Salvatore Florio, 2021).