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Full Description
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.
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
