The New Synthese Historical Library Ohad Nachtomy · Reed Winegar Editors Infi nity in Early Modern Philosophy The New Synthese Historical Library Texts and Studies in the History of Philosophy Volume 76 Managing Editor: Simo Knuuttila, University of Helsinki Associate Editors: Daniel Elliot Garber, Princeton University Richard Sorabji, University of London Miira Tuominen, University of Jyväskylä Editorial Consultants: Roger Ariew, University of South Florida E. Jennifer Ashworth, University of Waterloo Gail Fine, Cornell University R. J. Hankinson, University of Texas David Konstan, Brown University Richard H. Kraut, Northwestern University, Evanston Alain de Libera, Collège de France Eleonore Stump, St. Louis University Allen Wood, Stanford University More information about this series at http://www.springer.com/series/6608 Ohad Nachtomy • Reed Winegar Editors Infinity in Early Modern Philosophy Editors Ohad Nachtomy Reed Winegar Philosophy Department Philosophy Department Bar-Ilan University Fordham University Ramat Gan, Israel Bronx, NY, USA ISSN 1879-8578 ISSN 2352-2585 (electronic) The New Synthese Historical Library ISBN 978-3-319-94555-2 ISBN 978-3-319-94556-9 (eBook) https://doi.org/10.1007/978-3-319-94556-9 Library of Congress Control Number: 2018950456 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. 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Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Acknowledgments This book was published with the support of the Israel Science Foundation (grants # 302/16 and 47/18). Ohad Nachtomy wishes to acknowledge the assistance of Barnaby Hutchins and Noam Hoffer. Reed Winegar wishes to acknowledge the assistance of Nicholas Sooy and Christopher Meyers, the support of a Fordham University Faculty Fellowship, and the support of a VolkswagenStiftung/Mellon Postdoctoral Fellowship in the Humanities. We are both extremely grateful to Liat Lavi for overseeing the whole project and putting everything in place. v Contents 1 Introduction: Infinity in Early Modern Philosophy . . . . . . . . . . . . . . 1 Ohad Nachtomy and Reed Winegar 2 Descartes’s ens summe perfectum et infinitum and its Scholastic Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Igor Agostini 3 The Ontic and the Iterative: Descartes on the Infinite and the Indefinite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Anat Schechtman 4 Descartes on the Infinity of Space vs. Time . . . . . . . . . . . . . . . . . . . . . 45 Geoffrey Gorham 5 “A Substance Consisting of an Infinity of Attributes”: Spinoza on the Infinity of Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Yitzhak Y. Melamed 6 Infinity in Spinoza’s Therapy of the Passions . . . . . . . . . . . . . . . . . . . 77 Sanja Särman 7 The Road to Finite Modes in Spinoza’s Ethics . . . . . . . . . . . . . . . . . . . 97 Noa Shein 8 All the Forms of Matter: Leibniz, Regis and the World’s Infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Mogens Lærke 9 Leibniz’s Early Encounters with Descartes, Galileo, and Spinoza on Infinity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Ohad Nachtomy vii viii Contents 10 Leibniz’s Syncategorematic Actual Infinite . . . . . . . . . . . . . . . . . . . . . 155 Richard T. W. Arthur 11 The Infinite Given Magnitude and Other Myths About Space and Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Paul Guyer Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Contributors Igor Agostini Department of Humanistic Studies, University of Salento, Lecce, Italy Richard T. W. Arthur Philosophy Department, McMaster University, Hamilton, Canada Geoffrey Gorham Philosophy Department, Macalester College, Saint Paul, MN, USA Paul Guyer Philosophy Department, Brown University, Providence, RI, USA Mogens Lærke CNRS, IHRIM (UMR 5317), ENS de Lyon, Lyon, France Yitzhak  Y.  Melamed Philosophy Department, Johns Hopkins University, Baltimore, MD, USA Ohad Nachtomy Philosophy Department, Bar-Ilan University, Ramat Gan, Israel Sanja  Särman Philosophy Department, Hong Kong University, Hong Kong, China Anat Schechtman Philosophy Department, University of Wisconsin-Madison, Madison, WI, USA Noa Shein Philosophy Department, Ben-Gurion University of the Negev, Beer- Sheva, Israel Reed Winegar Philosophy Department, Fordham University, Bronx, NY, USA ix Chapter 1 Introduction: Infinity in Early Modern Philosophy Ohad Nachtomy and Reed Winegar In his Pensées, Blaise Pascal gives vivid voice to both the wonder and anxiety that many early modern thinkers felt towards infinity. Contemplating our place between the infinite expanse of space and the infinite divisibility of matter, Pascal writes: What is a man in the infinite? But to show him another prodigy equally astonishing, let him examine the most delicate things he knows. Let a mite be given him, with its minute body and parts incomparably more minute, limbs with their joints, veins in the limbs, blood in the veins, humours in the blood, drops in the humours, vapours in the drops. Dividing these last things again, let him exhaust his powers and his conceptions, and let the last object at which he can arrive be now that of our discourse. Perhaps he will think that here is the smallest point in nature. I will let him see therein a new abyss. I will paint for him not only the visible universe, but also everything he is capable of conceiving of nature’s immensity in the womb of this impercep- tible atom. Let him see therein an infinity of worlds, each of which has its firmament, its planets, its earth, in the same proportion as in the visible world; in this earth of animals, and ultimately of mites, in which he will find again all that the first had, finding still in these others the same thing without end and without cessation. Let him lose himself in wonders as amazing in their littleness as the others in their vastness. For who will not be astounded at the fact that our body, which a little while ago was imperceptible in the universe, itself imperceptible in the bosom of the whole, is now a colossus, a world, or rather a whole, in respect of the final smallness which we cannot reach? He who regards himself in this light will be afraid of himself, and observing himself suspended in the mass given him by nature between those two abysses of the Infinite and Nothing, of which he is equally removed, will tremble at the sight of these marvels; and I think that, as his curiosity changes into admira- tion, he will be more disposed to contemplate them in silence than to examine them with presumption. O. Nachtomy (*) Philosophy Department, Bar-Ilan University, Ramat Gan, Israel e-mail: [email protected] R. Winegar Philosophy Department, Fordham University, Bronx, NY, USA e-mail: [email protected] © Springer International Publishing AG, part of Springer Nature 2018 1 O. Nachtomy, R. Winegar (eds.), Infinity in Early Modern Philosophy, The New Synthese Historical Library 76, https://doi.org/10.1007/978-3-319-94556-9_1