Infinity in Early Modern Philosophy

Abstract

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity (before early modern thought) up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic. Intro; Acknowledgments; Contents; Contributors; Chapter 1: Introduction: Infinity in Early Modern Philosophy; References; Chapter 2: Descartes's ens summe perfectum et infinitum and its Scholastic Background; 2.1 Introduction; 2.2 The Scholastic Debate on the Ratio Formalis of God's Infinity; 2.3 Descartes's Ens Summe Perfectum et Infinitum; 2.4 Is There a Historical Relationship Between Descartes and the Debate on the Ratio Formalis of God's Infinity?; References; Chapter 3: The Ontic and the Iterative: Descartes on the Infinite and the Indefinite; 3.1 Introduction; 3.2 Three Distinctions 3.3 The Epistemological Distinction: Ignorance3.4 The Metaphysical Distinction: Respects; 3.5 The Metaphysical Distinction: Cardinality; 3.6 The Ontic Reading; References; Chapter 4: Descartes on the Infinity of Space vs. Time; 4.1 Introduction; 4.2 Letter to Chanut I: Space; 4.3 Digression: Imaginary Space; 4.4 Letter to Chanut II: Time; 4.5 Cartesian Duration and Time; 4.6 Creation from Eternity; 4.7 The Mereological Independence Doctrine; 4.8 Temporal Infinitists; 4.9 Descartes and Early Spinoza; 4.10 Conclusion; References Chapter 5: "A Substance Consisting of an Infinity of Attributes": Spinoza on the Infinity of Attributes5.1 Introduction; 5.2 Bennett on the Infinity of the Attributes; 5.3 The Textual Evidence; 5.4 Responses to Bennett's Arguments; 5.5 Conclusion; References; Chapter 6: Infinity in Spinoza's Therapy of the Passions; 6.1 Introduction; 6.2 The Role of Necessity in Therapy; 6.3 The Role of Infinity in Necessity; 6.4 Perspectives on Infinity. The Twofold Distinction; 6.5 Species of Infinity. The Threefold Distinction; 6.6 Concluding Remarks; References Chapter 7: The Road to Finite Modes in Spinoza's Ethics7.1 Introduction; 7.2 The Correspondence with Tschirnhaus; 7.3 Descartes, Extension and the Impossibility of Particular Bodies; 7.4 Back to Spinoza; 7.5 Two Possible Objections; 7.6 Conclusion; References; Chapter 8: All the Forms of Matter: Leibniz, Regis and the World's Infinity; 8.1 Introduction; 8.2 First Pass: Leibniz's Critique of Descartes; 8.3 Second Pass: Regis's Two Replies; 8.4 Third Pass: Leibniz's Two-Part Rejoinder; 8.5 Fourth Pass: Regis on the Indeterminacy of the World 8.6 Fifth Pass (Conjectural): Leibniz on the Infinity of the World8.7 Conclusion: Why Did Leibniz Not Reply?; References; Chapter 9: Leibniz's Early Encounters with Descartes, Galileo, and Spinoza on Infinity; 9.1 Introduction: Leibniz and the Significance of His Encounters; 9.2 Leibniz's Encounter with Descartes; 9.3 Leibniz's Encounter with Galileo; 9.4 Leibniz's Encounter with Spinoza; 9.5 Leibniz Reads Spinoza's Letter on the Infinite; 9.6 Conclusion; References; Chapter 10: Leibniz's Syncategorematic Actual Infinite; 10.1 Introduction; 10.2 The Infinite and Infinitely Small as Fictions