This electronic thesis or dissertation has been downloaded from the King’s Research Portal at https://kclpure.kcl.ac.uk/portal/ Simplicity and Substantiality The Development of ‘Simple Substance’ as a Key Notion in Leibniz’s Philosophy Tropper, Sarah Awarding institution: King's College London The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without proper acknowledgement. END USER LICENCE AGREEMENT Unless another licence is stated on the immediately following page this work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ You are free to copy, distribute and transmit the work Under the following conditions: Attribution: You must attribute the work in the manner specified by the author (but not in any way that suggests that they endorse you or your use of the work). 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PhD Thesis in Philosophy 2015 Sarah Tropper King’s College London 1 To Maria Rosa Antognazza for providing a never-ending thread through various labyrinths. 2 Table of Contents Abstract .................................................................................................................................................... 4 Acknowledgements ............................................................................................................................... 5 Abbreviations .......................................................................................................................................... 7 Introduction ............................................................................................................................................ 9 1. Background: Some Scholastic Heritage and Leibniz’s Early Formative Years ............ 18 1.1. Scholastic Legacy: A Thomistic Explanatory Framework ......................................... 18 1.2. Leibniz’s Early Years ....................................................................................................... 28 1.2.1. Fundamental Principles of Substantiality ................................................... 28 1.2.2. Continuum and Cohesion ............................................................................. 44 2. To Arnauld: Complete Concepts and the Unity of Substance ......................................... 52 2.1. The Logical Strand: Complete Concepts and Individual Substances ...................... 53 2.2. The Problem of Extension and the Unity of Substance in the Mid-1680s ............. 60 3. The Metaphysics of Simple Substance ..................................................................................... 71 3.1. Simple Substances and Substantial Forms ................................................................... 71 3.2. To De Volder .................................................................................................................... 86 3.3. To Des Bosses ................................................................................................................ 106 3.4. Simplicity from 1690 to Des Bosses ........................................................................... 115 4. The Dynamics of Substance ...................................................................................................... 118 4.1. Primitive Active and Passive Force (The Metaphysics of Physics) ........................ 124 4.2. Derivative Active and Passive Force (Physics and its Objects) .............................. 134 4.3. Forces and their Relation to Simplicity ....................................................................... 136 5. Theological Considerations ....................................................................................................... 141 5.1. Is God a Monad? The Hierarchy of Substances and Degrees of Perfection ........ 141 5.2. Metaphysical Evil ........................................................................................................... 151 6. Simple Substances as Points and not as Parts ...................................................................... 156 6.1. The Analogy with Mathematics and its Boundaries ................................................. 156 6.2. Mereology: The Constitution of Wholes and their Parts ......................................... 163 Concluding Remarks ........................................................................................................................ 170 Bibliography ......................................................................................................................................... 173 3 Abstract In this thesis, I will argue that there are various considerations which drove Leibniz to the adoption of simplicity as a fundamental criterion for substantiality. ‘Simplicity’ seems to be a deceivingly obvious term, but on closer inspection it turns out to be nonetheless in need of further explanation. Leibniz’s definition as that which is ‘without parts’ does not lead us to an understanding unless it is clearly set out what ‘being a part’ entails and whether simplicity goes beyond indivisibility. The reconstruction of such considerations will be of help in carving out a more determinate content of this notion as it features in Leibniz’s metaphysical system, and will explain how it came to be assigned a core function in his philosophy. Various undertakings throughout his lifetime about activity, unity, indivisibility and impredicability finally culminate in the notion of simplicity. Within this overall development, several different areas of science and philosophy have taken influence on Leibniz’s considerations. There is, obviously, an overreaching metaphysical strand, which tries to account for a notion of substance that is in accordance with the requirements from other, more specific strands. Some demands derive from Leibniz’s reflections on physics, most importantly the notion of force, and from logical considerations concerning the concept of substance. Equally important are theological considerations concerning the simplicity of God, and thus the hierarchy of monads and their similarity with God. Part of the answer as to what to regard and not to regard as partless, i.e. simple, can also be found in Leibniz’s mathematical writings. First and foremost it is mereology that occupies itself with the notions of parts and wholes and will thus give clues as to how to understand the terms explicitly involved in the definition of ‘simplicity’. But Leibniz also frequently feels the need to resort to mathematics and the notions of ‘point’ and ‘function’ in order to illuminate the notion of a simple substance. Bringing all these strands together will finally give a clearer picture of what it means to be a Leibnizian simple substance. 4 Acknowledgements I am deeply indebted to my supervisors, Maria Rosa Antognazza, who has carefully read and commented on many drafts of this thesis and without whose input and the occasionally required motivational words, this thesis would probably have never been finished. The equally careful reading of this thesis combined with his profound knowledge of all things early modern (and otherwise) made my second supervisor, Jasper Reid, an indispensible contributor to the thoughts presented in it. I would not be writing a thesis at all without the tremendous support of my family, especially my parents, who have encouraged me to pursue in my life whatever makes me happy. I hope they are satisfied with this thesis as the outcome of their encouragement and with who I have become. My sister Elisabeth has always been a tower of strength in my life and supplied me continuously with a place to on the occasional breaks I needed from Leibniz. My grandmother passed away during the process of writing this thesis. All I can hope for is that she would have been proud, had she seen this. The pursuit a PhD would be a far lonelier endeavour without the presence of caring fellow students. The Philosophy Department at King’s College is particular well- stocked with such individuals. I want to thank in particular for their tremendous support, for keeping me supplied with coffee, sweets and kind words throughout these years, and for being in general absolutely wonderful human beings: Michael Campbell, Mike Coxhead, Paul Doody, Alexander Douglas, Owen Englefield, Giulia Felappi, Alex Franklin, John Heron, Chris Machut, Clare Moriarty, Peter Ridley, Paola Romero, Saloni de Souza, Peter Sutton, Caspar Wilson, Jennifer Wright, and John Wright. I am certain that I have forgotten to name a lot of people who have made essential contributions to my time at King’s being such a wonderful time. Thank you all! In order to pursue a PhD at King’s, I have left behind a wonderful department in Graz, which provided me throughout my stay in London with a welcoming place to go back to once in a while and the