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 developed 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. Cover Half Title Endorsements Title Page Copyright Page Dedication Contents Abbreviations and Conventions General Introduction PART I: The Ubiquity of Each Thing Introduction 1. The Rejection of Restrictive Essence: Spinoza and Leibniz 1.1. The Traditional Notion of Restrictive Essence 1.2. Absolute Rationalism 1.3. The Rejection of General Knowledge 2. Defined by Everything: Spinoza’s Reconception of Essence 2.1. The Perspectival Difference Between Essence and Existence 2.2. Modes as In Alio 2.3. Individual Form as Affective Capacity 3. A Mirror of the Universe: Leibniz’s Infinite Individuals 3.1. Superessentialism 3.2. Infinite Individuals 4. A Concrescence of the Universe: Whitehead’s Actual Occasions 4.1. The Reformation of Monadology: From Monads to Actual Occasions 4.2. A New Spinozism: Actual Occasions as Modes of Creativity 4.3. The Critique of Simple Location Conclusion PART II: The Immanence of Space Introduction 5. Leibniz’s Space of Individual Relations 5.1. The Individuality of Actual Relations 5.2. Ideal Space 5.3. Actual Space 6. Whitehead and the Immanence of Extension 6.1. The Doctrine of Internal Relations 6.2. The Development of Structure from the Uniform Scheme of Relationality 6.3. The Actualisation of the Extensive Continuum Conclusion PART III: A New Quantification of Nature Introduction 7. Spinoza’s Concept of Quantity: Unique, Indivisible, and Infinite 7.1. Unique 7.2. Indivisible 7.3. Infinite 8. Leibniz’s New Quantification of Nature 8.1. The Lack of Unity, Activity, and Difference in Cartesian Matter 8.2. Monads Providing Unity, Activity, and Difference 8.3. Nothing but Simple Substances 8.4. The New Quantification of Nature: Monads as Degrees 9. Bergson’s Philosophy of Degrees 9.1. The Rejection of Intensive Magnitude 9.2. Adopting Intensive Magnitude: Beyond the Quantity-Quality Dichotomy 10. Deleuze’s Theory of Intensive Magnitude 10.1. Intensive Magnitude as the Nature of Difference 10.2. The Genesis of Quantity and Quality from Intensive Magnitude Conclusion General Conclusion: A Geometry of Sufficient Reason Glossary of Technical Terms References Index