Overview

Deleuze, Mathematics, Metaphysics provides new solutions to the central problems of the philosophy of mathematics by reconstructing Deleuze's metaphysics. It does so through direct engagement with analytic and continental philosophy, along with the formal and natural sciences. These new Deleuzian solutions reject equally other-worldly accounts of mathematics, such as Platonism, and accounts which treat mathematics as a useful fiction or an empty formalist game. Instead, Deleuze, Mathematics, Metaphysics argues that mathematical truth is grounded in the necessity of difference itself. Since difference is entirely this-worldly, the truth of mathematics does not require us to posit the reality of transcendent entities or possible worlds. Doing so not only provides a new metaphysics of mathematics; it also explains the usefulness of mathematics for science and why mathematical truth appear to have such otherworldly properties in the first place.

Full Product Details

Author:   Michael J. Ardoline (Post-Doctoral Researcher, Louisiana State University.)
Publisher:   Edinburgh University Press
Imprint:   Edinburgh University Press
ISBN:  

9781399536332

ISBN 10:   1399536338
Pages:   240
Publication Date:   30 September 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Acknowledgements Introduction: Necessity, Eternity, and Infinity in a Dying Cosmos Mathematical Addendum: Griss’s Negationless Mathematics Chapter 1 Nothing is Possible: Truthmakers, Difference, and Dispositionalist Grounds for Necessity Logical Addendum: Schrödinger Logics Chapter 2 Modalities of Difference: Deleuze’s Ontology of the Actual, Intensive, and Virtual Chapter 3 Individuation and Becoming-Continuous: The Production of the New Against Quine and Marcus Chapter 4 Inscription and Eternity: Aion, Chronos, and the Asymmetry Between Temporality and Modality Chapter 5 Essence and Excess: The Production of Multiplicities and Symmetry through Powers, History and Repetition Chapter 6 Transfinite Truths Without the Infinite: Cantor’s Theorem, Skolem’s Paradox, and the Objective Grounds of Set Theory Conclusion: Expression and Formalization: The Production of Mathematical Objects within Formalisms References

Reviews

By proposing a creative, clever, and novel reconstruction of Deleuze's modal metaphysics of difference, Michael J. Ardoline's Deleuze, Mathematics, Metaphysics: Difference and Necessity invents a compelling new foundation for grounding mathematics in the finite, temporary, changing, and chaotic world portrayed in contemporary sciences. Groundbreaking, original, and cutting-edge, Ardoline's book serves as the perfect model for a new generation interested in conducting a fruitful and unbiased analytic/continental hybrid mode of thinking.--Corry Shores, Middle East Technical University, Turkey

Author Information

Michael J. Ardoline is Assistant Professor of Philosophy at Louisiana State University. He completed his PhD at the University of Memphis in 2021. He has published articles in journals such as Deleuze and Guattari Studies, Philosophies, and Open Philosophy.

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