Provides new solutions to the central problems of the philosophy of mathematics by reconstructing Deleuze’s metaphysics
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.
Arvustused
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
Acknowledgements
Introduction: Necessity, Eternity, and Infinity in a Dying Cosmos
Mathematical Addendum: Grisss Negationless Mathematics
Chapter 1 Nothing is Possible: Truthmakers, Difference, and Dispositionalist
Grounds for Necessity
Logical Addendum: Schrödinger Logics
Chapter 2 Modalities of Difference: Deleuzes 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: Cantors Theorem, Skolems
Paradox, and the Objective Grounds of Set Theory
Conclusion: Expression and Formalization: The Production of Mathematical
Objects within Formalisms
References
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.
