A Geometry of Sufficient Reason Space and Quantity in the Works of Spinoza, Leibniz, Bergson, Whitehead, and Deleuze

This book explores and compares the reflections on space and quantity found in the works of five philosophers: Spinoza, Leibniz, Bergson, Whitehead, and Deleuze. What unites these philosophers is a series of metaphysical concerns rooted in 17th-century rationalism and embraced in 20th-century philosophies of process and difference.

At the heart of these concerns is the need for a comprehensive metaphysical account of the diversity and individuality of things. This demand leads to a shared critique of Cartesian and Newtonian conceptions of space. The most problematic aspect of those notions of space is homogeneity. In essence, uniform space fails to explain the differences between locations, thus violating the principle of sufficient reason. Cartesian and Newtonian theories of space thereby fail to meet the metaphysical requirement for explaining diversity and individuality. The traditional concept of quantity faces similar issues. Motivated by these problems, these five philosophers develop an alternative conception of space and quantity. By examining these theories, the book sheds new light on an unexplored relation between rationalism and 20th-century Continental philosophy.

A Geometry of Sufficient Reason will appeal to scholars and graduate students working in Continental philosophy, history of philosophy, metaphysics, and the history and philosophy of science.

General Introduction Part 1: The Ubiquity of Each Thing Introduction 1. The Rejection of Restrictive Essence: Spinoza and Leibniz 2. Defined by Everything: Spinoza’s Reconception of Essence 3. A Mirror of the Universe: Leibniz’s Infinite Individuals 4. A Concrescence of the Universe: Whitehead’s Actual Occasions Conclusion Part 2: The Immanence of Space Introduction 5. Leibniz’s Space of Individual Relations 6. Whitehead and the Immanence of Extension Conclusion Part 3: A New Quantification of Nature Introduction 7. Spinoza’s Concept of Quantity: Unique, Indivisible, and Infinite 8. Leibniz’s New Quantification of Nature 9. Bergson’s Philosophy of Degrees 10. Deleuze’s Theory of Intensive Magnitude Conclusion General Conclusion: A Geometry of Sufficient Reason

Florian Vermeiren is a postdoctoral researcher at the Husserl-Archives: Centre for Phenomenology and Continental Philosophy, Institute of Philosophy, KU Leuven, Belgium. He is the author of a dozen journal articles on Spinoza, Leibniz, Bergson, Whitehead, and Deleuze.