Michael J. Ardoline, Deleuze, Mathematics, Metaphysics: Difference and Necessity – Edinburgh University Press, September 2024, paperback March 2026

Provides new solutions to the central problems of the philosophy of mathematics by reconstructing Deleuze’s metaphysics

• Defends a new position in the metaphysics of mathematics
• Provides a systematic reconstruction of major portions of Deleuze’s metaphysics on his own terms rather than in terms of his more well-known predecessors such as Bergson, Nietzsche, or Spinoza
• Connects historical debates and clarifies positions from analytic and continental philosophy to be accessible to readers from both traditions
• Relevant to scholars working in major areas of contemporary analytic philosophy (modality, grounding, and metaphysics of mathematics) and continental philosophy (Deleuze, poststructuralism generally, and Speculative Realism)

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.