Deleuze, Mathematics, Metaphysics: Difference and Necessity

by Michael J. Ardoline

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.

Product Details

ISBN-13:	9781399536332
Publisher:	Edinburgh University Press
Publication date:	09/30/2024
Series:	Intersections in Continental and Analytic Philosophy
Pages:	240
Product dimensions:	6.14(w) x 9.21(h) x 0.00(d)

About the Author

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.

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

Editorial 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