Leibniz: Writings on the Metaphysics of the Infinite

by Arthur, Richard T. W.; Ottaviani, Osvaldo

• ISBN13: 9780192865885
• ISBN10: 0192865889
• Format: Hardcover
• Copyright: 2025-12-30
• Publisher: Oxford University Press

Summary

Gottfried Wilhelm Leibniz (1646–1716) is famous in mathematics predominantly for his invention of the differential calculus, and in philosophy for his metaphysics of monads and system of pre-established harmony. But at the heart of his thinking in both fields lay his profound meditations on the infinite. In the 1690s Leibniz was engaged in promulgating his thought on the infinite in both its mathematical and its philosophical aspects. On the one hand, he had advertised his intention to write a treatise on the Science of the Infinite, De scientia infiniti, in which he would give an account of the foundations of mathematics. On the other, he was much occupied in the same years with promoting his own metaphysical system, both as the foundation for his new science of dynamics in his revised conception of substance, and as a superior alternative to the occasionalism of Malebranche and Sturm.

The selection of papers presented here should therefore be of great interest to scholars, since it contains material relevant to both projects, as well as throwing light on their interrelation. It consists of twelve texts written by Leibniz in the 1690s and early 1700s, none of which has appeared before in English translation. Ten of these are translations from new transcriptions made from original Latin manuscripts in the Leibniz Archives in Hanover (plus the texts given in Appendices 2 and 4); the remaining two are selections from Leibniz's correspondence with Johann Bernoulli, and excerpts from his written interchange with Gabriel Wagner, both translated from the Latin text of the Akademie edition. Each of the selected papers is accompanied by a detailed commentary explaining its significance for understanding Leibniz's thought, including substantial quotations from related sources and situating the text in relation to other writings in the Leibnizian corpus.

Author Biography

Richard T. W. Arthur, Emeritus Professor of Philosophy, McMaster University,Osvaldo Ottaviani, Postdoctoral researcher, Radboud University, Nijmegen

Richard T. W. Arthur is Professor Emeritus at McMaster University, living in Toronto. Specializing in early modern natural philosophy, mathematics, and the foundations of physics, he has taught at universities in Canada, Nigeria, the United States, Italy, and Britain. He has authored about 80 articles and eight books, including Monads, Composition, and Force (OUP, 2018), The Reality of Time Flow (2019), and Leibniz on Time, Space, and Relativity (OUP, 2021), and is currently finishing two other co-authored books, on Leibniz on the foundations of the calculus, and on Bertrand Russell's engagement with Leibniz's philosophy.

Osvaldo Ottaviani is currently a Postdoctoral Researcher (Radboud Excellence Initiative Fellowship) at the Radboud University of Nijmegen. His main interests are in the history of early modern philosophy and science. His PhD dissertation (2018) has been awarded with the VGL Dissertation Theses Award for Outstanding PhD Theses on Leibniz (Leibniz Gesellschaft, 2023). He had research positions at the University of Münster, Milano, and the Israel Institute of Technology. He published several papers on various aspects of Leibniz's philosophy, including the edition and translation of some of Leibniz's unpublished manuscripts. He is also working on a book on Leibniz's theory of existence and the development of his metaphysics of possible worlds.

Table of Contents

Introduction1. On the Infinite [1693?][De infinito]Commentary2. An Infinite Straight Line is not a Whole [after 1692][Linea recta infinita]Commentary3. Reflections on Froidmont's Labyrinthus [1693–5?][Excerpta et Notae -Fromondus, Labyrinthus]Appendix 1: Extracts from Froidmont's LabyrinthusCommentary4. Line and Time [1693–5?][Linea et Tempus]Commentary5. Is there a Midpoint in the Infinite? [1695?][Quaeritur an in infinito detur Medium]Commentary6. Every Thing Resists the Infinite [1695?][Omnis res infinito resistit]Commentary7. On the Incredible Subtlety of Things [1694–99][De incredibili rerum subtilitate]Commentary8. It is as if we are suspended between two infinities [1695–96?][Inter duo infinita velut suspensi sumus]Commentary9. Towards a Science of the Infinite [c. 1696?][Ad Scientiam Infiniti]CommentaryAppendix 2: Historical preface of De Scientia Infiniti...(?)10. From Leibniz's Exchange with Gabriel Wagner [December 1697–March 1698][Facing page dialogue]Commentary11. From Leibniz's Correspondence with Johann Bernoulli [1698–99][Consecutive letters]Commentary12. Place and Time, Matter and Change [1705?][Locus et tempus sunt continua...]Appendix 3: Excerpts from Leibniz's letters to De Volder and the Electress SophieCommentaryAppendix 4: Excerpt from "Even though nothing in nature happens by a leap..."