Critical Views of Logic

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Mirja Hartimo (University of Helsinki, Finland) Frode Kjosavik (Norwegian University of Life Sciences, Norway)

Critical Views of Logic

Mirja Hartimo (University of Helsinki, Finland), Frode Kjosavik (Norwegian University of Life Sciences, Norway), Øystein Linnebo (University of Oslo, Norway)

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English

Routledge
31 October 2023

Philosophy: epistemology & theory of knowledge; Philosophy: logic; Philosophy of mathematics; Computing: general; Computer science

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.

Edited by: Mirja Hartimo (University of Helsinki Finland), Frode Kjosavik (Norwegian University of Life Sciences, Norway), Øystein Linnebo (University of Oslo, Norway)
Imprint: Routledge
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 590g
ISBN: 9781032573519
ISBN 10: 1032573511
Pages: 220
Publication Date: 31 October 2023
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Introduction to “Critical Views of Logic” 1. Infinity and a Critical View of Logic 2. Dummett’s objection to the ontological route to intuitionistic logic: a rejoinder 3. The entanglement of logic and set theory, constructively 4. Critical Plural Logic 5. Kant on the possibilities of mathematics and the scope and limits of logic 6. The infinite, the indefinite and the critical turn: Kant via Kripke models 7. Husserl on Kant and the critical view of logic 8. Logical pluralism and normativity 9. Disagreement about logic

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).