Table Of Content

Spinoza’s Epistemology through a Geometrical Lens Matthew Homan Spinoza’s Epistemology through a Geometrical Lens “Each chapter of Spinoza’s Epistemology through a Geometrical Lens makes an important contribution to our understanding of Spinoza’s philosophy. Homan develops a fascinating interpretation of Spinoza’s views about the ontology of mathematics, which he applies in surprising and insightful ways to address a range of difficult interpretive and philosophical problems. The overarching picture is inspiring. Homan’s Spinoza is a metaphysical realist, an optimist about the limits of human knowledge, and a friend to scientific inquiry.” —John Grey, Department of Philosophy, Michigan State University, USA Matthew Homan Spinoza’s Epistemology through a Geometrical Lens Matthew Homan Philosophy and Religion Christopher Newport University Newport News, VA, USA ISBN 978-3-030-76738-9 ISBN 978-3-030-76739-6 (eBook) https://doi.org/10.1007/978-3-030-76739-6 © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed 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. This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland [W]hen Spinoza speaks of intuitive knowledge and says: This kind of knowing proceeds from an adequate idea of the formal essence of certain attributes of God to the adequate knowledge of the essence of things, these few words give me the courage to devote my whole life to the examination of things…of whose formal essences I can hope to form an adequate idea. –Johann Wolfgang von Goethe (1786)1 1 Briefwechsel zwischen Goethe und F. H. Jacobi, ed. M. Jacobi (Leipzig: Wiedmann’sche Buchhandlung, 1846), 105–6. A cknowledgments I am grateful to a number of people who in one way or another helped me to bring this book project to fruition. Sanem Soyarslan, Karolina Hübner, and Christopher Martin graciously provided helpful feedback on chapter drafts. John Grey reviewed the manuscript for Palgrave and his judicious suggestions undoubtedly elicited improvements. Thanks to Edwin Curley and Brian McInnis for assistance on questions of text and translation; Graham Schweig for his advice; Eric Schliesser for his encouragement; and Phil Getz and Tikoji Rao for their editorial support. Many of the ideas expressed in this book can be traced back over ten years to my doctoral research, and I was fortunate to have Ursula Goldenbaum as my advisor during that germinal stage. She devoted countless hours to sharing her knowledge and insight with me, and to pointing me in the right direction. Her remarkable generosity as a teacher, mentor, and friend both then and since has been invaluable. My deepest thanks, finally, to Ashley Brewer, who cheerfully retrieves books for me from her library, supports every- thing I do, and fills my life with love and happiness. vii c ontents 1 Introduction 1 1.1 The Question of Mathematization 6 1.2 Outline of Chapters 15 1.3 A Note on Texts 18 References 19 2 Mathematics and Methodology: Spinoza Contra Skepticism 23 2.1 The Dogmatic Response 25 2.2 Mathematical Ideas qua Epistemic Exemplars: Problems for the Dogmatic Interpretation 30 2.3 Attaining the Idea of God: The Cartesian Response 34 2.3.1 Textual Evidence for the Cartesian Interpretation 37 2.4 The Cartesio-Dogmatic Response 39 2.5 Objections and Replies 42 References 48 3 Realism and Antirealism About Mathematical Entities 51 3.1 Figures as Beings of Reason 52 3.1.1 Figures as (Imaginative) Universals 54 3.1.2 Figures as a Form of Measure 58 3.1.3 Figures as Non-beings 61 3.1.4 G enetically Conceived Figures 63 3.2 Reductio ad Acosmism: The Case Against Antirealism 66 ix x CoNTENTS 3.3 Figure and Finite Bodies: The Case for Realism 70 3.3.1 Descartes and the Ontological Status of Figures 70 3.3.2 Spinoza’s Theory of Corporeal Individuals and Figure 73 3.3.3 What Are Figures in Spinoza? 78 3.4 True Ideas of Number? 82 References 84 4 R eason and Imagination in Spinozan Science 87 4.1 Reason and Spinozan Science 89 4.1.1 C ommon Notions as Foundations of Reason and Laws of Nature 91 4.2 Imagination in Spinozan Science and Issues of Adequacy 98 4.2.1 F rom the Historia Naturae to Common Notions 100 4.2.2 D escending to Particulars 106 4.3 Peculiar Common Notions 111 References 121 5 G eometry and Spinozan Science 123 5.1 Spinoza on the Geometry of Optical Lenses 125 5.2 Response to an(other) Objection from Letter 12 136 5.2.1 T he Commensurability Response 142 5.3 Letters 80–83 and the Incompleteness of Spinozan Science 144 References 149 6 S pinoza’s Notions of Essence 153 6.1 Common Essence, Species Essence, and Individual Essence 154 6.2 Formal Essence, Actual Essence, and Existence 163 6.2.1 Formal Essences and Existence 164 6.2.2 Actual Essences and Existence 170 6.2.3 E2p8 Reconsidered 175 References 179 7 Intuitive Knowledge: The Perfection of Reason 181 7.1 Preliminary Analysis of the Principal Texts 184 7.2 The Content of Intuitive Knowledge: The Common Essence Interpretation 191 CoNTENTS xi 7.3 Beyond the Common Essence Interpretation 197 7.3.1 A Geometrical Alternative to the Fourth Proportional Example: The Isoperimetric Problem 198 7.3.2 The Isoperimetric Example and Spinoza’s Definition of Intuitive Knowledge 201 7.4 The Difference Between Reason and Intuitive Knowledge: A Method Interpretation 208 7.4.1 Can Conatus Save the Content Interpretation? 213 7.5 Amor Dei Intellectualis and the Supremacy of Intuitive Knowledge 217 7.6 Intuitive Knowledge in Spinozan Science 224 References 224 8 Conclusion 227 8.1 Spinoza’s Epistemic Outlook 228 8.2 Spinoza Vis-à-Vis Descartes (and Galileo) 232 References 238 References 239 Index 249 A bbreviAtions Works by Descartes AT Oeuvres de Descartes. 11 vols. Edited by C. Adam and P. Tannery. Paris: J. Vrin, 1996. CSM The Philosophical Writings of Descartes. Vols. 1–2. Translated and edited by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press, 1984–85. CSMK The Philosophical Writings of Descartes. Vol. 3. Translated and edited by John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny. Cambridge: Cambridge University Press, 1991. DM Discourse on Method, Optics, Geometry, and Meteorology. Revised Edition. Translated by Paul J. olscamp. Indianapolis, IN: Hackett Publishing Company, 2001. Works by Spinoza CM Cogitata Metaphysica (Metaphysical Thoughts). Cited by part and chapter. Curley The Collected Works of Spinoza. 2 vols. Edited and Translated by Edwin Curley. Princeton, NJ: Princeton University Press, 1985, 2016. Cited by volume and page. DPP Renati des Cartes Principiorum Philosophiae Pars I & Pars II (Descartes’ Principles of Philosophy) xiii