Space, Imagination and the Cosmos from Antiquity to the Early Modern Period [1st ed.] 978-3-030-02764-3, 978-3-030-02765-0

Table of contents :
Front Matter ....Pages i-ix
Space, Imagination and the Cosmos, from Antiquity to the Early Modern Period: Introduction (Frederik A. Bakker, Delphine Bellis, Carla Rita Palmerino)....Pages 1-9
Aristotle’s Account of Place in Physics 4: Some Puzzles and Some Reactions (Keimpe Algra)....Pages 11-39
The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe (Frederik A. Bakker)....Pages 41-67
Space and Movement in Medieval Thought: The Angelological Shift (Tiziana Suarez-Nani)....Pages 69-89
Mathematical and Metaphysical Space in the Early Fourteenth Century (William O. Duba)....Pages 91-106
Space, Imagination, and Numbers in John Wyclif’s Mathematical Theology (Aurélien Robert)....Pages 107-131
Francisco Suárez and Francesco Patrizi: Metaphysical Investigations on Place and Space (Olivier Ribordy)....Pages 133-156
Giordano Bruno’s Concept of Space: Cosmological and Theological Aspects (Miguel Á. Granada)....Pages 157-178
Libert Froidmont’s Conception and Imagination of Space in Three Early Works: Peregrinatio cœlestis (1616), De cometa (1618), Meteorologica (1627) (Isabelle Pantin)....Pages 179-199
Questioning Fludd, Kepler and Galileo: Mersenne’s Harmonious Universe (Natacha Fabbri)....Pages 201-232
Imaginary Spaces and Cosmological Issues in Gassendi’s Philosophy (Delphine Bellis)....Pages 233-260
Space, Imagination and the Cosmos in the Leibniz-Clarke Correspondence (Carla Rita Palmerino)....Pages 261-283
Correction to: The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe (Frederik A. Bakker)....Pages C1-C1
Back Matter ....Pages 285-291

Citation preview

Studies in History and Philosophy of Science 48

Frederik A. Bakker Delphine Bellis Carla Rita Palmerino Editors

Space, Imagination and the Cosmos from Antiquity to the Early Modern Period

Studies in History and Philosophy of Science Volume 48

Series Editor Stephen Gaukroger, University of Sydney, Australia Advisory Board Rachel Ankeny, University of Adelaide, Australia Peter Anstey, University of Sydney, Sydney, Australia Steven French, University of Leeds, UK Ofer Gal, University of Sydney, Australia Clemency Montelle, University of Canterbury, New Zealand Nicholas Rasmussen, University of New South Wales, Australia John Schuster, University of Sydney/Campion College, Australia Koen Vermeir, Centre National de la Recherche Scientifique, Paris, France Richard Yeo, Griffith University, Australia

More information about this series at http://www.springer.com/series/5671

Frederik A. Bakker  •  Delphine Bellis Carla Rita Palmerino Editors

Space, Imagination and the Cosmos from Antiquity to the Early Modern Period

Editors Frederik A. Bakker Center for the History of Philosophy and Science Radboud University Nijmegen, The Netherlands

Delphine Bellis Department of Philosophy Paul Valéry University Montpellier, France

Carla Rita Palmerino Center for the History of Philosophy and Science Radboud University Nijmegen, The Netherlands

ISSN 0929-6425     ISSN 2215-1958 (electronic) Studies in History and Philosophy of Science ISBN 978-3-030-02764-3    ISBN 978-3-030-02765-0 (eBook) https://doi.org/10.1007/978-3-030-02765-0 Library of Congress Control Number: 2018965221 © Springer Nature Switzerland AG 2018, corrected publication 2019 Chapter 3 is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). For further details see license information in the chapter. This work is subject to copyright. All rights are reserved 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, 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. 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 volume derives from an international conference organized by Frederik Bakker, Delphine Bellis, and Carla Rita Palmerino and held at Radboud University, Nijmegen, on June 9–10, 2016. The event was funded by the Netherlands Organisation for Scientific Research (NWO) through Delphine Bellis’ Veni grant (275-20-042) and by the International Office of Radboud University. We would also like to acknowledge the financial support we received for the publication of this book through the translation subsidy fund of the Faculty of Philosophy, Theology and Religious Studies at Radboud University, as well as through the Research Foundation Flanders (FWO) with Delphine Bellis’ postdoctoral project (12O6516N). We would like to express our gratitude to Bill Duba for the translation into English of Olivier Ribordy’s chapter, to Hester van den Elzen for preparing the index, and to Anke Timmermann (A T Scriptorium) for the particular care and proficiency with which she conducted the copy-editing of the volume.

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Contents

1 Space, Imagination and the Cosmos, from Antiquity to the Early Modern Period: Introduction  ��������������������������������������������   1 Frederik A. Bakker, Delphine Bellis, and Carla Rita Palmerino 2 Aristotle’s Account of Place in Physics 4: Some Puzzles and Some Reactions ����������������������������������������������������������  11 Keimpe Algra 3 The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe ����������������������������������������������������������  41 Frederik A. Bakker 4 Space and Movement in Medieval Thought: The Angelological Shift  ����������������������������������������������������������������������������  69 Tiziana Suarez-Nani 5 Mathematical and Metaphysical Space in the Early Fourteenth Century  ������������������������������������������������������������  91 William O. Duba 6 Space, Imagination, and Numbers in John Wyclif’s Mathematical Theology ���������������������������������������������������������������������������� 107 Aurélien Robert 7 Francisco Suárez and Francesco Patrizi: Metaphysical Investigations on Place and Space  ���������������������������������� 133 Olivier Ribordy 8 Giordano Bruno’s Concept of Space: Cosmological and Theological Aspects ���������������������������������������������������� 157 Miguel Á. Granada

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9 Libert Froidmont’s Conception and Imagination of Space in Three Early Works: Peregrinatio cœlestis (1616), De cometa (1618), Meteorologica (1627) �������������������������������������������������� 179 Isabelle Pantin 10 Questioning Fludd, Kepler and Galileo: Mersenne’s Harmonious Universe ���������������������������������������������������������� 201 Natacha Fabbri 11 Imaginary Spaces and Cosmological Issues in Gassendi’s Philosophy �������������������������������������������������������������������������� 233 Delphine Bellis 12 Space, Imagination and the Cosmos in the Leibniz-Clarke Correspondence  ���������������������������������������������������� 261 Carla Rita Palmerino  orrection to: The End of Epicurean Infinity: C Critical Reflections on the Epicurean Infinite Universe �������������������������������� C1 Index  ������������������������������������������������������������������������������������������������������������������ 285

Contributors

Keimpe Algra  University of Utrecht, Utrecht, The Netherlands Frederik A. Bakker  Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands Delphine  Bellis  Department of Philosophy, Paul Valéry University, Montpellier, France William O. Duba  Institut d’Études Médiévales, Université de Fribourg, Fribourg, Switzerland Natacha  Fabbri  Galileo Museum, Institute and Museum for the History of Science, Florence, Italy Miguel Ángel Granada  University of Barcelona, Barcelona, Spain Carla Rita Palmerino  Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands Isabelle  Pantin  Ecole Normale Supérieure  – PSL Research University, Paris, France Olivier Ribordy  University of Fribourg, Fribourg, Switzerland Aurélien  Robert  Centre d’Études Supérieures de la Renaissance, CNRS, Université de Tours, Tours, France Tiziana Suarez-Nani  University of Fribourg, Fribourg, Switzerland

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Chapter 1

Space, Imagination and the Cosmos, from Antiquity to the Early Modern Period: Introduction Frederik A. Bakker, Delphine Bellis, and Carla Rita Palmerino

Abstract  In this introduction, we explain our choice to approach the topic of space from a cosmological perspective, that is, by studying the conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos, and the role that imagination played in those conceptions. We compare our approach with those of Alexandre Koyré and Edward Grant, and we present the two important issues this book intends to shed light on, namely the continuity and discontinuity between ancient, medieval, and early modern conceptions of space and the cosmos; and the role that metaphysical, cosmological, and theological considerations played in the elaboration of new theories of space in the course of history. This chapter also presents the main, recurring themes of this book: the relation between place and space; the notion of imaginary spaces; the role played by thought experiments in discussions concerning the nature of space and the structure of the cosmos; the impact of the condemnation of 1277 on subsequent theories of space; and the relation between God’s immensity and the infinity of space. Since antiquity space has been the object of metaphysical and physical enquiry. If space is the framework in which whatever exists is located, in what sense can space itself then be said to exist? Is it a substance or an accident? Does it exist independently of the objects contained in it? Can a part of space be emptied of matter? And are space and time isomorphic magnitudes? These questions have also had a bearing on cosmological speculations. Issues such as the origin and structure of the world, the infinity or finiteness of the universe, or the possibility of a plurality of worlds, could not be dealt with without addressing the question of the nature of space. As

F. A. Bakker (*) · C. R. Palmerino Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands e-mail: [email protected]; [email protected] D. Bellis Department of Philosophy, Paul Valéry University, Montpellier, France e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_1

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Milič Čapek insightfully noticed, a concept (like Aristotle’s) of the universe as enclosed within boundaries marked the limits of the universe also as being “the limits of space, not in space.”1 In this book, we approach the topic of space from a cosmological perspective, by studying the conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos, and we examine the role of imagination in those conceptions.2 Indeed, the acts of conceiving of space as being independent of body, extending indefinitely or infinitely beyond the limits of the cosmos or beyond our perception of the cosmos, and of contemplating the relations space could have with divine immensity, often entailed specific cognitive operations involving, in one way or another, imagination. With contributions on periods from antiquity to the early eighteenth century, this book intends to shed light on two important issues: 1. The first one is the continuity and discontinuity between ancient, medieval, and early modern conceptions of space and of the cosmos. In his groundbreaking study, From the Closed World to the Infinite Universe, Alexandre Koyré focused on the link that, according to him, existed between the destruction of the ancient cosmos initiated by Renaissance astronomers and the “geometrization of space,” that is “the substitution of the homogeneous and abstract space of Euclidean geometry for the qualitatively differentiated and concrete world-space conception of pre-Galilean physics.”3 As one of the first proponents of the idea of the Scientific Revolution Koyré found it important to stress that early modern cosmology constituted an essential break with ancient and medieval representations of the world. Admittedly, Koyré acknowledged that the Epicureans had already advocated the conception of an infinite universe, but claimed that their theories did not play a major role in the forging of the Scientific Revolution. Although persuasively argued, Koyré’s view does not do justice to the scientific and philosophical lines of influence that ran from antiquity to the early modern period. To take but one example, it is indicative of Koyré’s biased approach that he downplayed the importance of Pierre Gassendi (1592–1655) for the history of the theories of space and the cosmos. It turns out, however, that Gassendi, who explicitly acknowledged his debt towards Epicureanism and other ancient sources, played a crucial role in promoting the idea of a cosmos deprived of any boundary, and of space as an entity independent from all other beings. Even if some research has been done to reassess Koyré’s picture, an important part of existing scholarship still isolates the early modern period from its ancient and medieval background.4 By bringing together contributions on ancient, medieval,  Čapek 1976, xxi.  For a broader approach in terms of disciplines see Vermeir and Regier 2016, whose edited volume embraces not only cosmological approaches to space, but also perceptual, optical, geographical, and chemical uses of spatial concepts. 3  Koyré 1957, viii. 4  See for example Mamiani 1979; Peterschmitt 2013; Miller 2014. For an approach that covers the period from the 12th to the 16th centuries, and a closer approximation to the aims of this book, see Suarez-Nani, Ribordy and Petagine 2017. See also Grant 1981, although he focuses on Aristotelian 1 2

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and early modern philosophy and science this book intends to produce a historically more accurate picture of the variety of philosophical and scientific theories of space in the period under consideration.5 2. The second issue addressed in this volume is the role which metaphysical, cosmological, and theological considerations played in the elaboration of new theories of space throughout history. In his fundamental work, Much Ado about Nothing, Edward Grant stressed the remarkable continuity between scholastic and non-scholastic theories of space, and argued that “the concepts and arguments that were instrumental in the historical development of theories of space and the vacuum […] form a remarkably cohesive and independent tradition that was virtually immune to social, political, economic, educational and religious change.”6 One of our aims is to put this interpretation to the test. As several chapters in this volume document, natural philosophers addressing cosmological questions often saw themselves forced to reshape their metaphysical conception of space, as well as the ontological categories into which space could fit.7 Conversely, metaphysical and theological concerns deeply influenced the way in which both scholastic and non-scholastic natural philosophers dealt with cosmological issues.8 Take for example the concept of an infinite, extra-cosmic void space that, as Grant notes, the scholastics identified with God’s immensity.9 In our view this concept was appropriated and modified by early modern authors not in spite of, but thanks to its theological underpinnings. Amos Funkenstein has already insisted on the intimate connection between physical and theological arguments by stressing the emergence of a specific type of secular theology in the seventeenth century. Central to this theology was the issue of God’s omnipresence, which became “an almost physical problem for some.”10 As Funkenstein points out, “continuity and innovation” are not “mutually exclusive predicates.”11 Concepts inherited from antiquity or the Middle Ages (like the Stoic extra-cosmic void or the scholastic imaginary spaces) could be appropriated and reshaped in order to produce new conceptions of space and the cosmos. We consider Funkenstein’s approach particularly fruitful, especially insofar as it emphasizes and scholastic influences in the early modern period and somewhat neglects the import of other traditions such as Epicureanism. Albert Einstein, in his foreword to Max Jammer’s Concepts of Space, insists on the lineage between ancient atomist theories and Newton’s absolute space: Jammer 1954, xv. See also Čapek 1976, xx, xxiii. 5  Although its scope is broader, as it is not solely focused on space, Machamer and Turnbull 1976 can be seen as an attempt, albeit somewhat tentative, to address related topics, in terms of a longterm integrated history and philosophy of science. 6  Grant 1981, xii. 7  On a mostly metaphysical approach to the topic in the early modern period, see Peterschmitt 2013. 8  This was already noted by Max Jammer, although his approach centered on the relations between the concept of space and investigations in physics: Jammer 1954, vi, 2, 25–50. 9  Grant 1981, xi. 10  Quotation from Funkenstein 1986, 10. On God’s omnipresence see ibid., 23–116. 11  Ibid., 14.

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the specific role that imagination came to play in speculations which were at the same time cosmological, philosophical, and theological. However, we do not share Funkenstein’s view that medieval speculations on space and God’s immensity, as well as medieval imaginary experiments related to the creation of possible worlds in extra-cosmic space, were of a purely theological nature.12 As we hope to show in this volume, it was not only in the seventeenth century, but also in the ancient and medieval period, that theological, metaphysical, physical, and cosmological considerations converged to produce reflections on space. In his book Representing Space in the Scientific Revolution David M. Miller, while adopting a part of Koyré’s framework of the Scientific Revolution, pleads for a shift in research from a metaphysics of space to an epistemology of space.13 He embraces an interpretative approach centered on physical theories from Copernicus to Newton, and on the implicit representative framework they involve, rather than on the philosophical speculations bearing on the ontology of space. His claim is that the period from Copernicus to Newton is characterized by a crucial shift in the scientific representations of space, from a circular, center-oriented, anisotropic space to a rectilinear, isotropic space with a self-parallel orientation. Miller thus advocates a new focus on representations and conceptions of space that constitute the explicit or implicit background of early modern scientific theories. We believe that such an approach, which tightly links the history of science with the conceptual analysis of the notion of space, is particularly fruitful and can be extended to a wider historical scale. However, isolating scientific practices and theories from their philosophical context does not do justice to the actual intertwinement of science and philosophy which runs throughout the history of Western thought, at least up to the eighteenth century. Our approach therefore consists in tackling cosmological issues as an indissolubly scientific, theological, and philosophical unit. As a consequence, the various contributions to this book not only deal with an explicit metaphysics of space, but also address the conceptual function that space played in scientific and theological reflections. In this introduction we shall not provide a summary of the individual chapters, as they are all preceded by an abstract. We shall rather try to shed light on a number of specific topics, apart from the two main themes discussed above, which link the various contributions to this book. An issue which is addressed in most chapters is the relation between place, conceived as the location of individual substances, and space. From Keimpe Algra’s chapter we learn that there were three rival conceptions of place in antiquity. According to the first view, which goes back to Plato’s Timaeus, place can be identified with the extension of the located body. The second conception is found in Aristotle’s Physics 4, 1–5, where place is defined as the “first immobile limit of the surrounding body.” The third view was defended by Epicurus and the Stoics, ­according to whom place must be conceived as an independent three-dimensional 12 13

 See, for example, ibid., 63.  Miller 2014, 1–2, 19–20.

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portion of space, coextensive with the emplaced body. Most ancient commentators endorsed Aristotle’s position and stressed that the notion of a self-subsistent three-­ dimensional extension which is neither an accident nor a substance was ontologically untenable. There were, however, also commentators like Philoponus who, “in the face of the strong arguments in favour of the existence of space as a threedimensional extension,” concluded that “there is something wrong with the Aristotelian ontology, in particular with the idea that a quantity cannot subsist by itself” (Algra p. 24). In the medieval period Aristotle’s treatment of place also gave rise to interesting discussions. The chapters by Aurélien Robert, William Duba, and Tiziana Suarez-­ Nani show that fourteenth-century philosophers had various reasons to depart from Aristotle’s notion of place. Robert’s article draws attention to the connection between the theory of place and atomism. It shows that Wyclif, like other fourteenth-­ century atomists, identified place with a three-dimensional space composed of surfaces, lines and points. According to Robert, this theory was based on a Neopythagorean interpretation of Plato’s theory of place in the Timaeus. Duba’s chapter explains how fourteenth-century philosophers dealt with a paradoxical consequence of Aristotle’s notion of place, namely the fact that it is possible for a thing (e.g. a boat) to remain at rest while the surrounding body (e.g. the water of a river) moves. John Duns Scotus, Peter Auriol and Nicholas Bonet were not satisfied with Aristotle’s own solution to the problem of mobile place (sketched out in section 6 of Algra’s article) and proposed alternative views that relied on a distinction between a physical, a metaphysical, and a mathematical meaning of place. Suarez-Nani’s chapter documents that medieval theories of place and space were strongly dependent on metaphysical and theological reflections. Fourteenth-century thinkers found the Aristotelian notion of place inadequate to account for the localization of immaterial substances, and conceived of place as a “mathematical position” (Henry of Ghent) or as a “mathematical quantity” (John Duns Scotus), rather than as a physical property (Suarez-Nani p. 76). Early modern scholastics such as Francisco Suárez also dealt with the localization of immaterial substances. As Olivier Ribordy explains, Suárez rejected Aristotle’s definition of place in Physics IV in favor of a notion of ubi as an intrinsic mode which could be used to account for the localization of both corporeal and spiritual creatures. The notion of ubi intrinsecus made it also possible to assign a place to the universe, which according to Aristotle’s definition is located nowhere, as there is no body surrounding it. Ribordy’s chapter also deals with Francesco Patrizi, whose account of space and place bears interesting similarities with that of Giordano Bruno (discussed in Miguel Ángel Granada’s article) and Pierre Gassendi (which is the object of Delphine Bellis’ contribution). Patrizi and Bruno, both influenced by Philoponus, conceived of place as a three-­ dimensional physical quantity capable of receiving bodies. Moreover, both Patrizi and Bruno took issue with Aristotle’s ontology, according to which a three-­ dimensional extension can only be an attribute of corporeal bodies. Bruno argued that space “is incorporeal, but has dimensions,” whereas Patrizi defined space as a “corporeal non-body” and “incorporeal body.” It is well known that Patrizi’s ­conception of space as a three-dimensional extension which transcends the catego-

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ries of substance and accident strongly influenced Pierre Gassendi. Less well-known is the fact that Gassendi also drew inspiration from scholastic theories of space. As Delphine Bellis’ chapter shows, it was thanks to a re-elaboration of the scholastic notion of ‘imaginary space’ that Gassendi came to regard space as an “incorporeal entity,” thereby removing “the ontological confusion between space and body that still pervaded Patrizi’s theory” (Bellis p.  246). Bellis speaks of “re-elaboration” because Gassendi identified imaginary space with the three-dimensional extra-­ cosmic void, whereas scholastic authors such as Suárez and the Conimbricenses regarded it as a non-dimensional, virtual place capable of being filled by bodies (Bellis p. 233). From Isabelle Pantin’s, Natacha Fabbri’s and Carla Rita Palmerino’s chapters we learn that the expression ‘imaginary space’ also figures, albeit with different meanings, in Libert Froidmont’s Peregrinatio caelestis (1616), Marin Mersenne’s Harmonie universelle (1636–1637) and in the Leibniz-Clarke Correspondence (1715–1716). When Froidmont speaks of light elements spreading through imaginary spaces it is not clear, according to Pantin, whether he wants to endorse, or rather reject, the Stoic notion of an infinite extra-cosmic void. Mersenne maintains, following Duns Scotus, that an ‘imaginary space’ would survive if God ceased to conserve bodies. The existence of an extra-cosmic void space is one of the many points of disagreement between Leibniz and Clarke. While Leibniz takes the adjective ‘imaginary’ to mean ‘non-existent,’ Clarke stresses that the ancients use the adjective ‘imaginary’ to refer to an extramundane space which is real, but not accessible to our knowledge. As several chapters in this volume document, extra-cosmic space was often made the theater of thought experiments. The most famous and influential example is that of the man at the edge of the universe who tries to extend his hand. This scenario, which was originally invoked by the Pythagorean philosopher Archytas to deny the finitude of the universe, reappears time and again in the history of ancient, medieval, and early modern philosophy.14 Frederik Bakker explains how Lucretius, in his De rerum natura, proposed a modified version of Archytas’ thought experiment in order to prove that the universe is unbounded. The De rerum natura was, in turn, a source of inspiration for Giordano Bruno. As Granada recalls, in the introductory epistle of De l’infinito, Bruno used the Lucretian thought experiment to argue for the existence of an extra-cosmic space filled with other worlds. The scenario of the man at the edge of the universe also plays an important role in Locke’s Essay Concerning Human Understanding, where it is used to criticize the Cartesian identification of matter and extension. Palmerino explores why Leibniz in his New Essays, which were written in response to Locke’s Essay, chose not to deal with this famous thought experiment. A substantial part of Palmerino’s article is devoted to another thought experiment which, as Algra’s chapter reveals, was first discussed by the Stoic Cleomedes. In his Caelestia Cleomedes imagined that the whole cosmos moved in an empty space. Such a scenario, which was of course incompatible with the principles of Aristotle’s cosmology, reappears in a number of fourteenth-century 14

 Ierodiakonou 2011.

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philosophical works. As Algra, Duba, Bellis, and Palmerino recall, the medieval revival of the thought experiment is a consequence of the famous condemnation promulgated in 1277 by the bishop of Paris Étienne Tempier, which prohibited Parisian professors from teaching that God could not move the heavens in a straight line. Palmerino’s article documents how the Newtonian theologian Samuel Clarke used this medieval thought experiment to challenge Leibniz’s theory of space. Incidentally, the condemnation of 1277, just as the reaction of Church authorities to heliocentrism which is mentioned in Pantin’s and Bellis’ chapters, provides a good example of how a historical episode could influence the way in which natural philosophers dealt with cosmological issues. A thought experiment discussed in other chapters of the book consists of imagining what would happen if God annihilated the created bodies or ceased to conserve them. Aurélien Robert recalls that the Council of Constance condemned Wyclif for holding, among other things, that “God cannot annihilate, diminish or increase the world,”15 whereas Bellis provides details of a number of medieval, late scholastic and early modern authors who discussed the scenario of the annihilatio mundi. Interestingly most of these authors agreed that the annihilation of the world would lead to the formation of a vacuum of some sort, but disagreed as to whether the world was created in a pre-existing space. As Delphine Bellis points out, most fourteenth-­century philosophers argued, in accordance with the condemnation of 1277, that the existence of a void space was not a necessary precondition for the creation of the world. Fabbri’s chapter reveals that a similar position was endorsed by Marin Mersenne who, following Duns Scotus, denied the existence of an empty space prior to the creation of bodies, while claiming that an ‘imaginary space’ would survive if God ceased to conserve bodies. Patrizi, Gassendi and Roberval, by contrast, invoked the annihilatio mundi thought experiment in support of the view that space is an independent three-dimensional extension which exists prior to the creation of the world (see Ribordy for Patrizi, Bellis and Fabbri for Roberval, and Bellis for Gassendi). The influence of the condemnation of 1277 on theories of space was not limited to the two cases mentioned above. Tempier’s decree prohibited the teaching of the theory that angels were not located in space, or that they were located only by their operation. As Suarez-Nani explains, many authors writing in the wake of the condemnation “conceived the relationship to physical place as a necessary and intrinsic condition of all creatures, both material and immaterial” (Suarez-Nani pp. 74–75). Also very influential was the article of the condemnation which stated that God could create as many worlds as he pleased. While most thirteenth-century natural philosophers endorsed Aristotle’s proof of the unicity of our world, authors writing after the condemnation regarded the existence of a plurality of worlds as possible according to God’s absolute power (de potentia Dei absoluta). But this view had, of course, ancient roots: as Bakker shows, the ancient atomists – first Democritus and later Epicurus and his followers – already maintained that the infinite expanse of ­extra-­cosmic space also contains an infinity of atoms, which in turn gives rise to an 15

 [Councils] 1973, 426.

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infinite number of worlds. The step from infinite atoms to infinite worlds was justified with reference to the so-called principle of plenitude: given the infinity of time and space, everything that is possible (like a world) will be actualized, and not just once, but an infinite number of times. However, while for most authors writing after the condemnation of 1277 the plurality of worlds was only a possibility, and necessary to avoid limiting God’s power, for Bruno it was a reality: defending the infinity of space and invoking the principle of plenitude as well as God’s infinite goodness, Bruno concluded that infinite space not only contains an infinity of worlds but is, in fact, always and everywhere completely filled with informed matter (Granada pp.  163–164). As Fabbri explains, this view was criticized by Mersenne, who adopted a voluntaristic stance: God could have created an infinite universe, but this does not mean that he should have created it (Fabbri p. 213). A similar position was also adopted by Gassendi; while accepting the Epicurean argument for the infinity of space, and admitting that “the infinity of worlds could not be excluded on purely logical or physical grounds,” (Bellis p. 239) for theological reasons he preferred to adhere to the uniqueness of our world (Bellis pp. 239 and 244). The tension between an intellectualist and a voluntarist stance is particularly evident in the correspondence between Leibniz and Clarke. When Leibniz invokes the principle of sufficient reason to argue in favor of the indefiniteness of the world, Clarke retorts that ­sufficient reason is sometimes nothing else than God’s will, and that divine wisdom may have good reasons for limiting the quantity of created matter (Palmerino pp. 262–263 and 265). Finally there is the issue of the relation between God’s immensity and the infinity of space. In her article Suarez-Nani relates that the fourteenth-century philosopher John of Ripa “introduced a radical distinction between God’s immensity and spatial infinity that began to haunt natural philosophy” (Suarez-Nani pp.  71–72). Ripa’s stance was analyzed at length by Paul Vignaux, who is mentioned in Suarez-Nani’s article, and by Edward Grant. In his Much Ado about Nothing Edward Grant notices that “to identify imaginary, infinite space with God’s immensity and also to assign dimensionality to that space would have implied that God Himself was an actual extended, corporeal being.” Grants observes that this stance, which was adopted by Spinoza and Newton, “would have been completely unacceptable in medieval and early modern scholasticism.”16 This explains, in Grant’s view, why those medieval authors who identified God’s immensity with infinite space, thereby denying the creation of space, described the latter as non-dimensional. Elsewhere in his book Grant observes that “the medieval fear that void space would be interpreted as an eternal, uncreated positive entity independent of God was realized in the metaphysics of Giordano Bruno,” who regarded infinite space “as coeternal with but wholly independent of God.”17 Granada’s article explicitly challenges Grant’s interpretation and shows that Bruno anticipated Spinoza in conflating God, extension, matter, and space. With this volume we do not intend to cover all dimensions of the relations between spatiality, cosmology, and the imagination involved in their conception. 16 17

 Grant 1981, 164.  Ibid., 191.

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However, we hope to have offered some results which can be gained through a longue-durée approach in combination with scrupulous and close textual analysis, and thereby to foster similar collaborative work on space between scholars specialized in different periods of the history of philosophy and science.

References Čapek, Milič, ed. 1976. The Concepts of Space and Time: Their Structure and their Development. Dordrecht: D. Reidel. [Councils]. 1973. Conciliorum oecumenicorum decreta, ed. Giuseppe Alberigo et  al., 3rd ed. Bologna: Istituto per le scienze religiose. Funkenstein, Amos. 1986. Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century. Princeton: Princeton University Press. Grant, Edward. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Ierodiakonou, Katerina. 2011. Remarks on The History of an Ancient Thought Experiment. In Thought Experiments in Methodological and Historical Contexts, ed. Katerina Ierodiakonou and Sophie Roux, 35–49. Leiden: Brill. Jammer, Max. 1954. Concepts of Space: The History of Theories of Space in Physics. Cambridge, MA: Harvard University Press. Koyré, Alexandre. 1957. From the Closed World to the Infinite Universe. Baltimore: The Johns Hopkins Press. Machamer, Peter K., and Robert G.  Turnbull, eds. 1976. Motion and Time: Space and Matter. Columbus: Ohio State University Press. Mamiani, Maurizio. 1979. Teorie dello spazio da Descartes a Newton. Milan: Franco Angeli. Miller, David Marshall. 2014. Representing Space in the Scientific Revolution. Cambridge: Cambridge University Press. Peterschmitt, Luc, ed. 2013. Espace et métaphysique de Gassendi à Kant: Anthologie. Paris: Hermann. Suarez-Nani, Tiziana, Olivier Ribordy, and Antonio Petagine, eds. 2017. Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe–XVIe siècles). Barcelona: Fédération Internationale des Instituts d’Études Médiévales. Vermeir, Koen, and Jonathan Regier, eds. 2016. Boundaries, Extents and Circulations: Space and Spatiality in Early Modern Natural Philosophy. Dordrecht: Springer.

Chapter 2

Aristotle’s Account of Place in Physics 4: Some Puzzles and Some Reactions Keimpe Algra

Abstract  This contribution focuses on Aristotle’s account of place (not: space) as it is developed in Physics 4, 1–5, a difficult text which has proved to be both influential and a source of problems and discussions in the ancient and medieval Aristotelian tradition. The article starts out by briefly positioning this account within the Corpus Aristotelicum, within the later ancient and medieval Aristotelian tradition, and within the tradition of theories of place and space in general. It goes on to examine the argument of Phys. 4, 1–5, showing that proper attention to Aristotle’s dialectical procedure is crucial for a correct understanding and evaluation of the various claims that we find scattered throughout his text. It then zooms in on the most important questions, problems and loose ends with which Aristotle’s theory confronted his commentators (ancient, medieval and modern): the puzzling arguments for the rejection of the rival conception of place as an independent three-­ dimensional extension (and of the void); the supposed role of Aristotelian places in the explanation of motion; the supposed role of Aristotelian natural places in the explanation of natural motion; the problem of the required immobility of Aristotelian places; and the problem of the emplacement of the heavens.

2.1  Introduction: Aristotle’s Account in Context This paper offers a synthesizing discussion of Aristotle’s ‘classic’ account of place, as the “first immobile limit of the surrounding body,” as it is worked out in Physics 4, 1–5, and of the main problems with which this account has saddled its interpreters in antiquity and beyond.1 In passing, we will also be able to cast occasional  Although this paper offers a fresh, synthesizing perspective, it covers a number of items which I have discussed, sometimes at greater length and in more detail, in earlier publications as well. Inevitably, therefore, there will be some overlap (from slight to considerable) with my earlier work, in particular with Algra 1995 in Sections 2.1 and 2.5, and with Algra 2014 in Sections 2.3, 2.4, 2.6 and 2.7.

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glances at how this text relates to some other parts of the Physics (in particular the discussion of the void in Physics 4, 6–9 and the discussion of the dynamics of natural motion in Physics 8), as well as to some other texts from the Corpus Aristotelicum (most notably the Categories). Aristotle’s account of place in Physics 4 has had a long and varied reception history. It started with the early Peripatetics Eudemus of Rhodes and Theophrastus of Eresus. Eudemus’ Physics basically appears to have been a paraphrasing commentary that preserved the sequence of subjects of Aristotle’s work, whereas Theophrastus’ similarly entitled treatise was more of an independent work.2 From the fragments of these two works, preserved by Simplicius, it appears that they both critically discussed Aristotle’s account of place, albeit without straightforwardly rejecting it. Strato of Lampsacus, however, who succeeded Theophrastus as head of the Lyceum, did in fact reject it and opted instead for the conception of place as a three-dimensional extension.3 Sympathy for the latter conception can also be detected in the testimonies on the work of the first century BC Peripatetic Xenarchus of Seleucia, whom we know to have defused Peripatetic arguments against the Stoic conception of the (extracosmic) void.4 Aristotle’s conception of place was further discussed and criticized by other philosophers in the Hellenistic and early Imperial periods, perhaps most notably by the sceptic Sextus Empiricus at the end of the second century AD.5 The account of Physics 4, 1–5 first became ‘classical’ in later antiquity when the Corpus Aristotelicum, of which the Physics was a prominent part, had become canonized and integrated into the standard philosophical curriculum. In order to be able to function in such a context the Physics, like other difficult Aristotelian texts, had to be opened up and explained in exegetical paraphrases (Themistius) and commentaries (Alexander of Aphrodisias, Simplicius, Philoponus).6 The same goes for the subsequent practice of the study of Aristotle in the medieval Islamic world: we still 2  On the character of Eudemus’ work, see Gottschalk 2002 and Sharples 2002. On Theophrastus’ work and the nature of his Aristotelianism, see Gottschalk 1998 and Sharples 1998. Their reactions to Aristotle’s theory of place are discussed in more detail in Algra 2014, 25–29 (Eudemus) and 29–38 (Theophrastus). 3  On Strato in general see the edition by Sharples (2011) and the studies collected in Desclos and Fortenbaugh 2011. On his theory of space and void, see Algra 2014, 38–42. 4  On the evidence on Xenarchus on the void, see Algra 2014, 42–47. For the Stoic conception of extracosmic void see Section 3.2 of Bakker’s Chapter 3 in this volume. 5  On the discussion of place in Sextus Empiricus, also in relation to the text of Physics 4, see Algra, 2015. 6  English translations of the commentaries on Physics 4 by Themistius, Simplicius and Philoponus are available in Richard Sorabji’s invaluable series Ancient Commentators on Aristotle. For Themistius, see Todd 2003; for Philoponus, see Furley and Wildberg 1991 and Algra and Van Ophuijsen 2012; for Simplicius, see Urmson 1992 and Urmson and Siorvanes 1992. Alexander’s commentary is no longer extant. Fragments are discussed and a reconstruction attempted in Rashed 2011. On the later ancient commentary tradition, in general and in relation to the school practice, see Sorabji 1990. Some of the most important passages on (Aristotle’s conception of) place from the ancient commentary tradition have been conveniently collected and translated, with brief introductions, in Sorabji 2004, 226–243. Much of this material has been discussed at greater length in Sorabji 1988, esp. 125–218.

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have commentaries on the Physics by, among others, Ibn Bajja (Avempace) and Ibn Rushd (Averroes). It goes for the world of Latin late medieval scholasticism as well, where the Physics was discussed in commentaries and series of quaestiones by Thomas Aquinas, John Buridan, William Ockham and others.7 Part of the ancient reception of Aristotle’s conception of place had been critical – apart from Strato and Xenarchus, already referred to, we should in particular mention John Philoponus (sixth century AD), who offered a sustained critique in the so-called Corollary on Place, inserted in his commentary on Physics 4, while the commentary of his near-­ contemporary Simplicius is quite critical as well.8 On the whole, however, the Arabic and Latin commentators in the Middle Ages basically appear to have attempted to defend Aristotle’s account of place and to work out solutions for the problems it raised. Its strong presence in the late scholastic tradition may partly explain its rather surprising reappearance, in the guise of the concept of locus externus, in Descartes’ Principia Philosophiae (II, 14), published in 1644.9 Also in more recent times Aristotle’s theory of place has kept attracting the attention of philosophers. Henri Bergson, for example, devoted his dissertation to it.10 In a more recent and much more ambitious monograph on the subject Ben Morison put up a lively defense and even claimed that the theory is “of enduring philosophical interest.”11 Those who are into postmodern feminist interpretations may enjoy the ‘total makeover’ offered by Luce Irigaray (“The female sex organ is neither matter nor form but vessel” – and so on).12 Back to Aristotle’s text. In so far as the account of Phys. 4, 1–5 is about the location of individual substances rather than about a system of such locations, it presents us with a theory of place rather than space.13 If we count out the specific metaphysical conceptions of space or place defended in late antiquity  – in which place or space figures as a channel, so to speak, through which being, order and unity are conveyed to the physical world in a process of emanation from higher principles – and confine ourselves to conceptions of physical place, we may see that in antiquity as well as in the Middle Ages and the early modern period, such conceptions basi-

 For the reception of the Physics in the Arabic world, see Lettink 1994. For the Latin medieval tradition of interpreting Aristotle’s account of place (and his critical account of the void that follows), see Grant 1981a, b. 8  A translation of Philoponus commentary on Physics 4, 1-5 is available in Algra and Van Ophuijsen 2012. The philosophically more significant Corollary on Place has been translated separately by Furley and Wildberg 1991. On the relation between the Corollary and the commentary proper, see Algra 2012. Simplicius’s Corollary on Place is available in translation in Urmson and Siorvanes 1992. 9  Text quoted and discussed in Algra 1995, 17, n15. 10  Bergson 1889, a shortish and mainly paraphrasing study. 11  Morison 2002. “Enduring philosophical interest” is a quote from the somewhat over-excited blurb text. 12  The quotation is from Irigaray 1998, 48 (English translation of a chapter from her 1983 Éthique de la différence sexuelle). 13  On concepts of place versus concepts of space see see Algra 1995, 20–21. 7

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cally came in three types.14 Place could be identified with matter, or the extension of the emplaced body itself (a view that can be found in Plato’s Timaeus, certainly as it was read by Aristotle15; another instance is Descartes’ notion of locus internus); or with an independent extension (or part of space) coextensive with the located body, in which bodies are located and through which they can move (Epicurus, Newton); or place could be defined in terms of a body’s surroundings, either by identifying it as a surrounding something (as in the case of Aristotle: a surrounding surface) or by defining it as the relation between the emplaced thing and its surroundings (a view suggested as an alternative to Aristotle’s by his pupil Theophrastus, and famously defended by Leibniz in his correspondence with Clarke). Unlike modern physics, early modern and pre-modern physics was still to a considerable extent moored in common sense ways of thinking and speaking about reality. And indeed, all three main conceptions of place just outlined are in their own way rooted in the way spatial concepts are used in ordinary thinking and speaking. We may be said to use the first, when we say that a thing ‘occupies so and so much room.’ After all, we are, then, in fact focusing on the thing’s own extension, the extension of its matter, and not necessarily implying that the room ‘occupied’ exists in its own right. We use the second when we are talking about things moving ‘through space’ (their place then being the part of space they occupy at any given moment). And we use the third conception, defining location in terms of surroundings, when we say that a fish is swimming ‘in’ the water or that I am presently ‘in’ the city of Utrecht. Aristotle acknowledges as much when he claims that the difficulty of arriving at a coherent theory of place is precisely due to the fact that the phainomena from which physics should take its start  – and which for Aristotle famously include the ways in which we ordinarily speak and think about reality – point in different directions.16 He does so right at the start of his account: Text 1. The question what place is, is beset with difficulties. For it does not appear as the same thing, according as we consider the matter on the basis of the various available data (Phys. 4, 208a32-34).17  This threefold typology is further worked out, with references to the relevant texts, in Algra 1995, 15–22. What I here call ‘metaphysical’ conceptions of place or space can be found in the works of some Neoplatonists of late antiquity: Iamblichus, Proclus, Syrianus, Damascius, Simplicius. They all somehow connect place or space with form, causation and creation (dêmiourgia). This is consistent with the Neoplatonic tendency to claim that the lower hypostases are somehow ‘in’ the higher and formative ones. Thus Iamblichus can claim that place is a power that “sustains bodies and holds them apart, raising up those that have fallen [i.e. disintegrated into prime matter, KA] and uniting those that are scattered, filling them up and surrounding them on every side” (Iamblichus ap. Simplicium In Phys. 640, 2–6). On these theories, see Sambursky 1982, 11–29; Sorabji 1988, 202–215, with comments in Algra 1992, 157–162. 15  Cf. Phys. 4, 209b11-13: “That is why Plato in the Timaeus says that matter and space (χώρα) are the same thing.” On ancient and modern interpretations of the receptacle of the Timaeus as either space or matter (or both), and on Aristotle’s critique, see Algra 1995, 72–120. 16  On Aristotle’s (dialectical) method in his Physics, see the seminal paper by Owen 1961; a more detailed discussion in Algra 1995, 153–181. 17  Translations throughout this paper are my own, unless otherwise indicated. Of course I have benefitted from consulting existing standard translations, such as Hussey 1983 and Waterfield and Bostock 1996 for Aristotle’s Physics. 14

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He is even more explicit in chapter 4, in a passage in which we recognize our three main conceptions of place, with the identification of place as form added as a fourth possibility (I have numbered the four candidates (i)–(iv))18: Text 2. Place seems to be something profound and difficult to grasp, both because the notions of (i) matter and (ii) form present themselves together with it (παρεμφαίνεσθαι), and because of the fact that change of position of a moving body occurs within a surrounding body which is at rest; for [from this] it appears to be possible (ἐνδέχεσθαι γὰρ φαίνεται) that there is (iii) an extension in between which is something other than the magnitudes which move. Air, too, contributes to this suggestion, by appearing to be incorporeal; place seems (φαίνεται) to be not only (iv) the limits of the vessel, but also (iii) that which is in between, which is considered as being void (Phys. 4, 212a7-30).

According to the methodology laid out in the first chapter of Physics 1, the philosopher, in his search for the principles of nature, should start out with “what is more intelligible to us,” i.e. the phainomena, in order to arrive at these principles, which are what is “more intelligible in itself.”.19 However, in the present case, or so Aristotle claims, the phainomena at first sight seem to lead us to different conclusions. The notions of matter and form are somehow intricately bound up (παρεμφαίνεσθαι) with our experience of place. In addition, our experience of moving objects  – especially things moving through air  – seems to suggest that place exists as a three-dimensional extension independent of the extension of the emplaced bodies. So prima facie one might be inclined, on the basis of the phainomena, to identify place with matter, form, or an independent three-dimensional extension. As a matter of fact, the latter conception was apparently at first sight so appealing that we even find Aristotle using it himself elsewhere, in less technical (or not strictly physical) contexts within the Corpus Aristotelicum.20 In the Categories, for example, place is presented as a continuous three-dimensional extension, ‘doubling,’ so to speak, the continuous extension of the emplaced body: Text 3. Place belongs to the quantities which are continuous. For the parts of a body which join together at a common boundary occupy a certain place. Therefore also the parts of place which are occupied by the several parts of the body join together at the same boundary at which the several parts of the body do. Therefore also place is seen to be continuous. For its parts join together at one common boundary (Cat. 5a8-14).

That Aristotle is here presenting place in this way is probably due to the fact that in the Categories (a treatise dealing with the way in which we generally name things) he tends to be speaking “in accordance with widespread usage” (secundum famositatem), to quote John Buridan quoting Averroes.21 Physics 4, 1–5 however, is the  On the reason why Aristotle thinks (perhaps, at first sight, surprisingly) that we might be tempted to identify place with form, see below, p. 26 ff. 19  Phys. 4, 184a16-18. See above, n16. 20  See also below, text 7. 21  The quotation is from Buridan’s Questiones super octo Physicorum libros Aristotelis, Paris 1509 (first printed edition), f. lxxiii rb. Some modern scholars have suggested that the Categories presents us with an early view, and that Aristotle had changed his mind on the subject of place by the time he was writing the Physics. This possibility cannot be excluded, but is less likely, since (i) the underlying conception of place in Cat. does not appear to be very coherent anyway, and (ii) the 18

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text in which he delivers his fullest philosophical discussion of all issues to do with place, and in such a context he seems to see it as the philosopher’s task to disentangle the various conceptions that are around and to show which one can be coherently maintained after a careful dialectical investigation. And it is here (Phys. 4, 212a20) that he thus arrives at his ‘considered view’ of place as “the first immobile surface of the surrounding body.” The intrinsic difficulty of the subject is not the only problem with which Aristotle confronts his reader. There is also the difficulty of his own presentation: the text of Phys. 4, 1–5 is not as smooth and well organized as we might have wished it to be. It is patchy and at times crabbed and obscure. It is a text which was meant for, or which at least reflects, Aristotle’s classroom practice, where it could be elucidated by the viva vox of the teacher. Nevertheless, it is not an unintelligible text, as I will try to show in Section 2.2 of this paper, which offers an overview of its contents, and the way they cohere. Finally, and most importantly, the conception of place Aristotle ends up with is puzzling, and has in fact puzzled commentators, in various respects. Sometimes the puzzlement merely occurs if we look at things from a non-Aristotelian point of view and (partly) disappears once we take the larger context of Aristotle’s physics and ontology into account. In other cases we are dealing with problems which should also bother an Aristotelian, but which Aristotle appears not to have solved or even recognized in the Physics or anywhere else in what remains of the Corpus Aristotelicum. In the present paper I will address what I think are the five most prominent puzzling features, which all left their traces in later ancient, medieval and even modern discussions of Aristotle’s theory: the strange arguments for rejecting the rival theory of place as a three-dimensional extension (Section 2.3), the way in which Aristotelian places are supposed to figure in the explanation of locomotion (Section 2.4), the role of natural place in the explanation of the natural motion of the elements (Section 2.5), the problem of securing the required immobility of place (Section 2.6), and the problem of the emplacement of the heavens (Section 2.7). By going through these difficulties, and through some possible solutions, we will get a better grasp of Aristotle’s theory, and will be in a better position to understand the way in which it was received in antiquity and in the Middle Ages. For, as Simplicius already noted at the beginning of his own systematic Corollary on Place (a rich and very informative excursus appended to his discussion of Phys. 4, 1–5), Aristotle’s account contains “many difficulties and offered many lines of examination to those who came after him.”22

conception of place as three-dimensional extension also recurs in non-technical contexts in a later work such as the Meteorology; see below, text 7. On this, on the relation between the two treatises and their respective conceptions of place in general, and on some later interpretations of the differences, see Algra 1995, 121–153. 22  Simplicius In Phys. 601, 1–3. Here, and in the rest of this contribution, references to the texts of Themistius, Philoponus and Simplicius use the page and line numbers of the standard editions in the series Commentaria in Aristotelem Graeca (CAG).

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2.2  The argument of Physics 4, 1–5 Physics 4, 1–5 covers various items that are all connected to the subject of place: various possible conceptions of place, an intricate analysis of what it means to be ‘in’ something, a discussion of Zeno’s paradox of place, a discussion of proper and derived (or ‘incidental’) senses of moving and a separate discussion of the way in which the heavens with their eternal circular motion exhibit locomotion and can be said to be in a place. However it does not explicitly connect these little mini-­treatises in a linear account that is easy to follow. Still, behind this patchy ‘surface structure’ there is an argumentative or dialectical ‘deep structure’ which Aristotle himself lays out in the following passage (of course the numbering of the various items in this ‘dialectical programme’ is mine): Text 4. We must try to make our inquiry in such a way that (i) the ‘what-it-is’ is provided, (ii) the aporiai are solved, (iii) the apparent facts about place are accounted for, and, finally, (iv) so that the reason for the difficulty and for the problems around it are clear. Any discussion which achieves all this, on any topic, has succeeded admirably (Phys. 4, 211a3-11).

The passage is from chapter 4, and it is indeed there and in chapter 5 that Aristotle actually can be seen to assemble his own theory, albeit with the help of the findings of the slightly more aporetic chapters 1, 2 and 3. We can also see that he practices what he preaches: Ad (i): A definition is provided, in chapter 4, first at 212a6 (“the limit of the surrounding body,” τὸ πέρας τοῦ περιέχοντος σώματος), and then again, with the requirement of immobility added, at 212a20 (“the first immobile limit of what surrounds,” τὸ τοῦ περιέχοντος πέρας ἀκίνητον πρῶτον). Ad (ii): In the second half of chapter 5 a number of aporiai that had been set out in the first three chapters – such as Zeno’s paradox of place – are shown to be soluble for Aristotle’s own conception of place or not to apply to it (while it seems to be assumed, though not explicitly stated, that they cannot be solved for, and thus in fact demolish, the rival conceptions). Ad (iii): The apparent facts are accounted for – that is, evidently not all apparent facts, for as we saw in the previous section, the apparent facts (phainomena) seem to support various different conceptions. In fact, it is presumably because the first list of phainomena offered in chapter 1 contains various ways of speaking and thinking about place that are on closer scrutiny untenable (e.g. the assumption that there is such a thing as the void), that we are given a fresh list in the opening section of chapter 4: the properties which appear truly to belong to place in its own right (ὅσα δοκεῖ ἀληθῶς καθ’ αὑτὸ ὑπάρχειν αὐτῷ, 210b32-34). Ad (iv): Finally, Aristotle manages to indicate the reason for the difficulties, also in chapter 4, at 212a7-30, the passage quoted above as text 2. In sum, the conception of place which can account for the list of true phainomena, and for which the relevant aporiai can be solved or shown to be harmless, will be the winner, which can and will be accurately defined, whereas it will be shown at the same time why the rejected candidates could have been thought of as candidates in

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the first place. With this general, unifying programme in mind we may now walk through the text as a whole. Chapter 1 starts out by setting out a number of apparent facts (phainomena) concerning the existence of place, framed as a number of possible reasons for assuming that place exists. But, as we saw, Aristotle does not think we are required to accept all of these phainomena as true or even plausible. And indeed, a brief glance at the list shows that it contains various ways of thinking and speaking about place that will turn out to be wrong: the idea that place has three dimensions, the idea that there is such a thing as void, the idea that place seems to be (ontologically) prior to all things, as Hesiod is here said to have thought. This should be taken as a warning that, if this same context contains the claim that the natural motions of the elements show us that place “has a certain dunamis” (208b10-11), we should not too readily take this at face value as something to which Aristotle is in the end firmly committed himself. I will discuss the question of the exact role of place in the explanation of natural motion below, in Section 2.5, and will there return to the question of how this phrase should be interpreted. Aristotle goes on (Phys. 4, 209a2-209a31) to list a number of aporiai on the nature of place, which he claims may make us doubt in the end not just what place is but even whether it exists at all. Some of these aporiai merely apply to the notion of place as a three-dimensional extension. For example: (i) how can place be three-dimensional, yet not be a body (209a4-7); ( ii) if bodies have a three-dimensional extension as their place, then surfaces, lines and points must have underlying places too, which seems absurd (209a7-12). Neither of these two aporiai will be solved, and hence they will continue to count against the rival conception (as will be made explicit for (i) in chapter 4). Other aporiai may be taken to apply to Aristotle’s own conception of place as well, for example: (iii) even if place is taken to have a certain dunamis, it is nevertheless not one of the four causes (209a18-22); (iv) Zeno’s paradox: if everything that exists is in a place, place itself, if existent, will be in a place as well, and so on ad infinitum (209a23-25). Some of the aporiai, such as (iv), are explicitly solved in the rest of Aristotle’s account in Physics 4, others are not, or not very clearly and explicitly. Aporia (iii), for example, left some uncertainty in the later Aristotelian tradition about the precise role of (natural) place in natural motion. As noted, this will be the subject of Section 2.5 of this paper. Chapter 2 (Phys. 4, 209a31-210a13) turns to the nature of place, by working out two basic intuitions: place as a three-dimensional extension, and place as a surrounding container, and explores and criticizes two definitions of place to which these intuitions might be thought to give rise, viz. the identification of place as form (surrounder) or as matter (extension). Aristotle’s most important objection to these definitions is that both form and matter are intimately bound up with the substance

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to which they belong, whereas the place of a substance should be separate.23 Later on, in chapter 4, he will accordingly add two further candidates for consideration: an independent surrounding container (the limit of the surrounding body) and an independent three-dimensional extension, so that we then have four candidates. Here, in chapter 2, the elimination of two of these four candidates (matter and form) is already being prepared. Chapter 3 has as its most important element a discussion of the different senses of ‘being in,’ which is brought to bear upon the solution of Zeno’s paradox of place. Interestingly, the first premise of this paradox – which in chapter 1 (209a23-25) had been rendered as “everything that exists is in a place” – is now (210b22-23) rewritten as “everything that exists is in something.” Aristotle gives no explicit reason for this reformulation, but various remarks in the context of Phys. 4, 1–5 suggest that he thinks that the premise “everything that exists, is in a place” can only be accepted as true if we take “everything that exists” to refer to (mobile) physical substances.24 And in that form the paradox loses its force against all the conceptions of place he discusses, for none of these takes place itself as a physical substance or a mobile body. However, in the form in which it has now been rephrased, the paradox can be defused only for his own conception of place as a surface (which he has at this point of the discussion not yet proven to be right), because such a place is indeed ‘in something else’ (viz. in the substance of which it is the surface), though in a non-­ local sense of ‘in’  – i.e. in the sense (outlined by Aristotle in what preceded) in which a property is in a thing. No such defense is possible, we may realize (although this is not spelled out explicitly), for the most important rival conception of place as an independent three-dimensional extension. Aristotle appears to have regarded the text of what we nowadays demarcate as chapters 1, 2 and 3 as primarily aporetic.25 Chapter 4 returns to the main question – “but what actually is place?” – and seems to make a fresh constructive start. In a kind of prefatory section (210b32-211b5) we are presented, as we saw, with a revised list of characteristics that seem to “genuinely belong to place” (210b33-34)– i.e. presumably characteristics that do not involve the difficulties discussed in the previous chapters.26 Aristotle then states his ‘research programme’ on place (quoted  A second, related objection is: “how could a thing move to its own place, if its place was its matter or its form” (210a2-3); presumably the idea is that, if a thing’s form or matter were its place, it would always by definition be in its own place. A third objection (210a5-9) is that form and matter move along with the thing of which they are the form and matter, which would mean that place itself would be moving, and thus changing place. 24  See 208b28: “every perceptible body is in a place;” 209a26 “every body is in a place;” 212b28 “only a movable body is in a place, not everything.” 25  He concludes chapter 2 by claiming that “we have now reviewed the arguments which force us to conclude that place exists, and also those which make it difficult to know what it is,” and chapter 3 by saying that “that concludes our discussion of the difficulties.” 26  They are, briefly: (i) that place is the first thing surrounding that which is in place; (ii) that it is separate from the emplaced object; (iii) that it is neither larger nor smaller than the emplaced object; (iv) that it can be left behind by the object and is separable; (v) that it exhibits the directions ‘above’ and ‘below;’ (vi) [that it helps to explain] that each body should naturally move to its own 23

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as text 4 above), which, as we saw, gives the argumentative ‘deep structure’ underlying chapters 4 and 5. He goes on by squarely linking the notion of place to the notion of locomotion, and appends some rather disjointed notes on real versus incidental motion and on the difference between being in a place and being in a whole. In the central section of chapter 4 (211b5-212a7) he then sets out his fourfold division of possible conceptions of place and eliminates three of the four candidates (form, independent three-dimensional extension, matter; 211b9-212a2). Hence place must be the fourth and only remaining candidate: the limit of the surrounding body (τὸ πέρας τοῦ περιέχοντος σώματος, 212a6). Aristotle next (212a7-30) discusses the cause of the difficulty of the subject (our text 2, quoted above) and goes on to elucidate the difference between a vessel and a place, by claiming that a vessel is a mobile place and place an immobile vessel, thus adding immobility as a further requirement for the correct conception of place, partly with the help of an example – a boat on a river – which has puzzled most subsequent commentators. The river example and the problem of immobility will be discussed below, in Section 2.6. The chapter ends with some rather sketchy notes (212a21-30) that may serve to show that the resulting final definition of place (i.e., with the feature of immobility added, the “first immobile limit of that which contains” (212a20)) fits a number of the characteristics that belong to place according to the common conception of it: (i) that the cosmos has an ‘above’ and a ‘below;’ (ii) that place is like a vessel and a surrounder; (iii) that place is together with the object – after all, on this view “the limits are together with what is limited.”27 Chapter 5, finally, roughly consists of two parts. The first part (212a31–212b22) deals with the question whether and to what extent the heavens and the cosmos as a whole are in a place; this as well is a section of which both the wording and the implications have puzzled commentators over the centuries. I will discuss the relevant problems below, in Section 2.7. The second part of the chapter (212b22– 213a11) then finally shows that the (or rather: some) puzzles that were raised with respect to place can be solved on Aristotle’s theory, and that the phenomenon of natural motion in connection with natural places can be accounted for, although the latter section is very sketchy and leaves much to be explained (I will briefly revert to it in my discussion of the question of natural place and natural motion below, in Section 2.5). From this overview of the contents of Physics 4, 1–5 it will already transpire that this text does provide us with a general idea of how Aristotle works and of the main arguments that support his conclusions. However, there are many loose ends as well: not all the aporiai that are brought up are explicitly discussed and solved, some arguments are rather baffling in their brevity, important aspects of the arguplace. Note, by the way that strictly speaking (i) has by this time not yet been established (the rival conception of place as a separate three-dimensional extension is only eliminated in the course of chapter 4). This illustrates what has been noted in the text above, viz. that the argument in Phys. 4, 1–5 is not ‘linear.’ 27  Of course, as we saw, the common conception of place is not confined to the idea of place as a ‘vessel and surrounder.’ But Aristotle seems to be referring back to the revised list of phainomena presented at the beginning of this chapter (and by now the rival conception of place as threedimensional extension has indeed been eliminated).

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ment and of the theory are left implicit. Moreover, although Aristotle seems to think that he has successfully eliminated the three possible rival theories by showing how they lead to inconsistencies and irresolvable puzzles, questions can be raised about the coherence and usefulness of his own theory as well. His own pupil Theophrastus already produced a list of five puzzles generated by the conception of place defended in Physics 4, 1–5, and later commentators repeat these puzzles and add others of their own making.28 The interpretative and conceptual problems raised by Aristotle’s text will be the subject of the remaining sections of this paper.

2.3  P  lace as Three-Dimensional Extension: A Puzzling Rejection By the time Sextus Empiricus was writing his sceptical account of physical theories of place, at the end of the second century AD, there were only two main options around: Aristotle’s conception of place as a surrounding surface, or the conception of place as an independent three-dimensional extension, versions of which had in the meantime been endorsed by Epicurus and the Stoics. Also for Aristotle himself the conception of place as three-dimensional extension constituted the most formidable rival view.29 Where form and matter could be rather easily disqualified as suitable candidates for the identification of place, the conception of place as a three-­ dimensional extension was one which had a more solid foundation in ordinary thinking and speaking, and which possibly for that very reason even figured in Aristotle’s own Categories, as we saw. In Physics 4 he intends to prove that, from the strict point of view of philosophical physics, ordinary thinking and speaking are wrong in this respect. Given that there is this much at stake, the arguments adduced are surprisingly obscure and puzzling. This was in fact what triggered Philoponus’ insertion of a separate excursus (now known as his Corollary on Place) right in the middle of his commentary on chapter 4. It starts out with a refutation of Aristotle’s arguments (In Phys. 557, 12–563, 25) before turning to its main task: offering a vindication of the rival conception of place as extension. Let us first have a closer look at the two arguments Aristotle applies in chapter 4. They can be paraphrased as follows: (i) On this conception of place, there would be an infinity of places in the same spot (ἐν τῷ αὐτῷ ἄπειροι ἂν ἦσαν τόποι, 211b20-21), for in a continuous emplaced body we can distinguish an infinity of parts which will all have their own places, so that we have an infinity of juxtaposed (and, we may presume, in fact also overlapping) three-dimensional places ‘in the same spot;’ and  Theophrastus ap. Simplicium In Phys. 604, 5-11 (= Theophrastus fr. 146 FHSG). On Theophrastus’ position and the interpretation of these aporiai, see Algra 2014, 29-38. 29  Averroes (Ibn Rushd) in his Short Commentary suggests that the main rival views of place as either a surrounding surface or an extension should be presented as alternatives in a hypotheticodisjunctive argument. See Lettink 1994, 313. 28

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(ii) On this conception of place, place will be moving (ἅμα δὲ καὶ ὅ τόπος ἔσται μεταβάλλων, 211b23). Later on in the same book, in the course of his discussion of the void (which of course is supposed to be the kind of self-subsistent three-dimensional extension we are here discussing) in chapter 8, Aristotle uses another argument to reach the absurd conclusion of an infinity (or at least: an indefinite number) of places ‘in the same spot.’ This time he no longer seems to be thinking of a process of dividing, but rather of a process of doubling the three-dimensional extension which can go on ad infinitum: (iii) “What will be the difference between the body of the cube and the void and place which are equal to it? And if two things can behave like this, why cannot any number of things coincide?” (216b9-11). Arguments (i)–(iii) thus represent a threefold reductio ad absurdum of the view that place is an independent three-dimensional extension. But do the alleged absurd consequences really follow? In the case of (i) it is not prima facie clear what precisely the supposed absurdity consists in. That a continuous three-dimensional place can be divided in a potentially infinite number of parts should not be particularly objectionable, given that the same operation can be performed on the emplaced body – in fact the possibility of infinite potential divisibility is part and parcel of Aristotle’s own theory of infinity and the continuum as set out in Physics 3.30 What seems to be suggested, therefore, is rather that the conception of place as a three-­ dimensional extension would involve an actual infinity of overlapping or nested places. That, however, is simply not true. The rival view would at most involve the idea that the (only potentially infinite number of) parts of a continuous substance, however specified, would occupy (a potential infinity of) correspondingly specified parts of one and the same absolute extension, not that an actual infinity of places ‘co-exist.’ But perhaps the supposed absurdity should not primarily be located in the element of infinity, but rather in the very idea of parts of a continuous substance having a place of their own. After all, in Aristotle’s own theory the parts of continuous substances do not move in their own right (but only incidentally, κατὰ συμβεβηκός), and accordingly do not have a place in their own right: they move with the substance of which they are part, and accordingly their place is the place of this substance as a whole (211a17-22 and 211a29-34). Parts of a continuous substance, in other words, are not the sort of things to be emplaced in any proper sense. However, apart from the fact that it is in principle perfectly legitimate not to share this part of Aristotle’s substance ontology and to think, by contrast, that a theory of place would do well to be able to account for the emplacement of continuous parts of substances, it is just not true that the rival conception of place as extension necessarily involves the idea that such parts have places of their own. This is in fact shown by the example of 30  On which see his discussion in Physics 3, with the excellent introduction in Hussey 1983, xviii-xxvi.

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Philoponus’ own theory of place, which combines the conception of place as a self-­ subsistent three-dimensional extension with a world view that for the rest preserves Aristotle’s substance ontology, including the concomitant idea that what may count as a place is only the extension occupied by a whole, separate, substance.31 A place, for Philoponus, accordingly is a part of space occupied by a substance. So apart from not involving the idea of an infinity of places of parts (except in the harmless sense of a potential infinity), the rival conception of place here discussed by Aristotle does not even necessarily involve the whole idea of places of parts to begin with. We may conclude that argument (i) fails to produce the required absurd consequences, however we choose to construct it. The argument behind (ii) appears to rest on a misleading or mistaken interpretation of the words “some kind of extension between the limits” (διάστημά τι τὸ μεταξὺ τῶν ἐσχάτων, 211b7-8), as if this ‘extension between the limits’ is part of the vessel, wedged in between its limits and thus moving along with it when the vessel moves. However, the view criticized here by Aristotle implies no such thing, since it looks upon this extension as self-subsistent, or as we might say: absolute. As Philoponus puts it in his Corrolary on Place: Text 5. For the jar that moves does not move the internal extension that receives the water along with it, but rather the whole thing changes its whole place. For the void is immovable (Philoponus, In Phys. 562, 3-6).

On the rival view of place as extension, in other words, the notion of a moving place makes no sense at all, let alone that it can be presented as one of its implications. If we now turn to (iii), we may note, for a start, that it actually presupposes Aristotle’s conviction that there is only one kind of three-dimensional extension, viz. the extension of substances themselves. As he puts it in the context of chapter 4, “what is in between a place is whatever body it may be, but not the extension of a body” (σῶμα γὰρ τὸ μεταξὺ τοῦ τόπου τὸ τυχόν, ἀλλ᾿ οὐ διάστημα σώματος, Phys. 4, 212b26-27). Once you admit, or so the argument seems to go, that this extension can be ‘doubled’ by conceiving of a second separate extension, you can go on repeating this move, so that you will end up with a (potential) infinity of coinciding extensions, a conclusion which is supposedly absurd. In his Corollary (e.g. at In Phys. 561, 27–562, 3) Philoponus defuses this argument as well. First of all, he argues, the idea of a plurality of coinciding extensions or dimensions is not logically absurd at all, as long as these extensions are not the extensions of bodies, for you cannot have more than one body in the same place. Secondly, however, in physical reality you will as a matter of fact always find two, and no more than two, coinciding extensions: the extension that is intrinsic to body (substance) plus the extension of place (which is in its own nature void). Philoponus was not the first to be dissatisfied with Aristotle’s arguments here. As we noted, in the third century BC the third head of the Lyceum, Strato of Lampsacus, had simply swapped Aristotle’s conception for the rival conception of place as extension, and in the first century BC the Peripatetic Xenarchus of Seleucia appears 31

 See e.g. In Phys. 577, 32-578, 4; and Algra 2012, 9.

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to have been prepared to do so as well. However, Sextus Empiricus’ accounts of place in PH 3, 119–135 and M 10, 1–36, written down in the late second century AD, show us that the late Hellenistic arsenal of sceptical (and in this case: originally Peripatetic) arguments from which he could draw still used versions of Aristotle’s unsatisfactory arguments against the conception of place as a three-dimensional extension. So there were still people who took these arguments seriously. In general, the at first sight slightly surprising fact that so many other commentators in antiquity and in the medieval tradition were prepared to follow Aristotle in rejecting this rival conception of place (and to accept his arguments) may well be largely due to the fact that in the end this conception simply could not be integrated within an Aristotelian ontology (and ultimately this may well have been the idea behind (iii)). Being self-subsistent such a place or space could not be considered as an accident, i.e. a quantity; but neither could it be seen as a substance in the sense of a combination of form and matter. It is not a point, by the way, which Aristotle explicitly makes in Phys. 4, although it is probably implied in one of the aporiai in chapter 1, which claims that it is unclear what genus we should ascribe to place: it has three dimensions but is not a body (209a4-6). Philoponus acknowledges the underlying ontological problem in his Corollary, but argues that, in the face of the strong arguments in favour of the existence of space as a three-dimensional extension, we should rather conclude that there is something wrong with the Aristotelian ontology, in particular with the idea that a quantity cannot subsist by itself (In Phys. 578, 5–579, 17).

2.4  Place and the Explanation of Motion The explanation of motion, or change of place in general (which includes the quantitative changes of expansion and contraction), is explicitly adduced as the raison d’être for the discussion of place within the context of the Physics.32 On closer view, however, it is less clear how it is actually supposed to function in the context of the explanation of locomotion. There are at least two problems. First, Aristotle’s theory of place appears to be primarily a theory of the location of static bodies, whereas it is not easy to use his conception of place to describe the trajectory of bodies in motion. In fact, using Aristotle’s conception of place, we should describe a body in motion as traversing an infinity of instantaneous two-dimensional places. In his Corollary on Place Philoponus takes Aristotle to task for the element of two-dimensionality: Text 6. If place is the boundary of the container and is not some different extension between the boundaries over and above the bodies that come to be in it, then clearly during my motion from Athens to Thebes the parts of air that yield up their own place to me (for motion is a change of places and a continuous exchange) yield up nothing but surfaces. But  See Phys. 3, 200b20: “Change seems to be impossible without place and void and time, and in any case place, void and time are pervasive and common to all kinds of change, so for both these reasons we shall obviously have to look into each of them” (transl. Waterfield).

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when surfaces alone are put together, even an infinite number of them, coinciding with each other they make the whole no bigger. So how can the moving body move forwards? (Philoponus, In Phys. 567, 12–18).

It is perhaps no coincidence that in contexts like these, where we are describing the trajectory of a moving body, Aristotle sometimes consciously or unconsciously resorts to the very concept of place as a three-dimensional extension which in Physics 4, 1–5 he rejects for theoretical reasons33: Text 7. […] the celestial element is eternal and the spatial path (τόπος) through which it moves is endless, though always complete, while the terrestrial bodies each have their distinct and limited regions (τόπους) (Meteor. 1, 339a25-28).

In spite of all this, we may note that the problem signaled by Philoponus will in actual practice not have counted as fatal among ‘mainstream’ Aristotelians. Being able to serve to indicate the location of static substances may well have been what most Aristotelians expected from the theory of place, even within the context of a theory of locomotion. After all, Aristotle and Aristotelians were used to analysing changes, including locomotion, first and foremost in terms of their starting point and end point. True, Aristotle claimed that change (whether of form, size or place) is observed to proceed “from opposite to opposite and what is in between” (Cael. 4, 310a24-25), but the focus of the analysis was in general on the ‘from opposite to opposite’ part. Think, for example, of the general analysis of change in Phys. 1 (esp. chapters 1 and 5) as a process occurring between opposites. Within such a general descriptive framework Aristotle’s conception of place sufficed to describe the situation at the outset as well as the situation at the end of a process of locomotion. Or did it? Here we seem to encounter a second problem, next to the one that a succession of two-dimensional surfaces does not make for a three-dimensional trajectory. As Richard Sorabji has well brought out, the surrounding surfaces in the course of such a trajectory are instantaneous.34 Hence, a boat moving through water should be taken to traverse a series of instantaneous limits, so that strictly speaking it could never return to a place, for once a place is left it no longer exists. In principle this may not count as an odd result, if we recall the explicit claim (Phys. 4, ­212a29-­30) that “place is together with the object, for the limits are together with what is limited” (ἅμα τῷ πράγματι ὁ τόπος· ἅμα γὰρ τῳ πεπερασμένῳ τὰ πέρατα).35 However, it does appear to be an odd result, if we take account of another requirement also introduced by Aristotle, namely that place should be something that can be left behind, like a vessel: “the place where the thing is can be left by it, and is therefore separable from it” (Phys. 4, 211a3).36 For then the problem is simply this:  Cf. Philoponus In Phys. 567, 8-29. On unorthodox conceptions of place in the Corpus Aristotelicum see Algra 1995, 182–188. 34  Sorabji 1988, 190. 35  Here again, we may note, the focus seems to be on place as a ‘locator’ of static substances. 36  One may compare the earlier claims that place is “different from all the things that by replacement come to be in it,” and something “which they alternately leave and enter” (Phys. 4, 208b1-8), and the fact that Aristotle more than once describes place as a kind of vessel that can be filled, but also left behind (212a14-15). 33

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in what sense does Aristotle’s theory allow us specify the place I occupied this morning while standing in the garden, or of the place where I will be tonight while having dinner, if the relevant surrounding surfaces exist no longer or not yet? Aristotle’s pupil Eudemus of Rhodes appears to have been sensitive to this problem: Text 8. Eudemus says that a further cause of the difficulty of the problem of place is that [the notion of] place is not easy to grasp, because it altogether escapes us when the body in it is removed, and it is not possible to apprehend it in itself, but, if at all, in combination with something else, like the sounds of the so-called consonants. For with ‘a’ added the sound of ‘b’ and ‘c’ becomes clear (Simplicius In Phys. 523, 22–28; Eudemus fr. 73 Wehrli).

The early-twelfth-century Arabic commentator Ibn Bajja (Avempace) argued, along the same lines, that place exists as long as the body that is in it exists, and that if a body is removed from its place and no other body replaces it, the place “breaks down.”37 For the rest, however, there is not much evidence that this problem greatly bothered ancient or medieval commentators. And, once again, as long as we expect Aristotelian places to provide the location of individual static (non-moving) substances, they will do fine. The problem merely arises as soon as we want to endow place with a certain stability and see it as something that can be left and re-filled, indeed like a vessel. Perhaps we should conclude that Aristotle’s suggestion that place served as some kind of ‘vessel’ (ἀγγεῖον) was in this respect not a particularly fortunate one after all.

2.5  Natural Place and the Explanation of Natural Motion It is clear that for Aristotle in Physics 4, 1–5 the phenomenon of the natural motions of the elements is something which any theory of place should help account for. Yet his statements on the issue do not all unambiguously point in the same direction, and this has given rise to divergent interpretations, both in the ancient and medieval commentary tradition and among modern exegetes. In particular, it has proved difficult to square two of Aristotle’s statements, both made in chapter 1: (i) place appears to have some sort of power (208b8-11; part of the initial list of phainomena); and (ii) place is not one of the four causes (209a18-22; part of the initial list of aporiai). Simplicius (In Phys. 533, 31–32) claims that the problem has been passed over by previous commentators. This may well have been the case because they saw that Aristotle, especially if we also take into account what he says about the dynamics of natural motion in Physics 8, provides enough indications that (i) is not to be taken at face value, whereas (ii) is to be taken very seriously. This, at any rate is how 37

 Lettink 1994, 303.

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Simplicius himself and Philoponus saw things, and it is also what I am going to argue in this section. Some medieval and modern readers, by contrast, have ignored or explained away (ii) and interpreted (i) in the sense that Aristotle saw natural place as the formal, final or even moving cause of natural motion.38 Quite apart from the fact that Aristotle nowhere says such a thing, it is doubtful whether it would make any philosophical sense. For in what sense can we imagine a surface working as a cause? As a final cause? But, to quote John Philoponus: Text 9. It is quite ridiculous to say that place has any power in its own right; it is not through desire of a surface that things desire that station in the order that they have been given by the creator (Philoponus, In Phys. 581, 17–21).

Moreover, as both Simplicius (In Phys. 533, 26–30) and Philoponus (text 15 below) point out, a final cause is something the changing object strives to become, and in that sense it is internal to the changing object, whereas place, even an object’s natural place, is not what the object strives itself to become: it remains external to it. Should we then assume that place is a formal or a moving cause? But a formal cause and a moving cause are supposed to precede, or at least to be contemporaneous, with the change they cause, whereas as we have just seen, during the trajectory of natural motion the eventual natural place in an important sense does not yet exist. Fortunately, it turns out that if we give due attention to all the pointers in the text of Physics 4 and if we adduce the account of the dynamics of natural motion provided in Physics 8, we can reconstruct a much more plausible position on Aristotle’s part concerning the role of place in the explanation of natural motion. So let us have a closer look. As I have indicated in Section 2.2 of this paper, (i) need not be taken at face value (since Aristotle is not automatically committed to the truth of the phainomena he mentions in chapter 1). Moreover the cautious phrasing (ἔχει τινὰ δύναμιν) should make us pause before being prepared to ascribe to place any kind of full-blown causal status. Next, (ii) cannot be simply dismissed or played down as “merely a part of a puzzle or aporia,”39 for it is nowhere countered or defused. Then again, it is surely significant that Aristotle nowhere explicitly speaks of place as a cause. The most plausible way to take these statements together, therefore, would be to regard (i) as describing a phainomenon that might seem to be the case, but that in the end will turn out to need to be explained in different terms: place does play a role in the explanation of natural motion, though not as a cause. Indeed, three further passages in Aristotle’s dialectical discussion of place in Phys. 4, 1–5 may be adduced to support an interpretation which denies to place any causal status.  Just some examples: Bonaventura Sent. II, dist. 14, pars I, art. III, qu. 2 thinks of place as a moving cause in speaking of “the force of the place that attracts and of the place that expels” (virtus loci attrahentis et virtus loci expellentis). Thomas Aquinas De physico auditu, liber IV, lectio I, objects to such a view by claiming that place rather attracts like a final cause (sicut finis dicitur attrahere). Some modern scholars have taken natural place in Aristotle to figure as a formal cause (Pierre Duhem); others see it as a final cause (Michael Wolff, Richard Sorabji). For references and further discussion, see Algra 1995, 195–221, esp. 196–197 and 219–221. 39  Thus Sorabji 1988, 187, n6. 38

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First of all, as part of his attempt, in chapter 3, to show that place cannot be matter or form, Aristotle uses the following argument: Text 10. Further, how could a body be carried to its own place, if place was the matter or the form? It is impossible that that which has no reference to motion or the distinction of above and below can be place. So place must be looked for among things which have these characteristics (Phys. 4, 210a2-5).

We define locomotion with reference to place, not with reference to matter or form. And to explain what it is for a body to move to its own (i.e. its natural) place, we need to be able to differentiate places in terms of ‘above’ and ‘below,’ but there is no such differentiation to be discerned in form or matter. This passage thus clearly confirms that natural place cannot be identified as a formal or material cause. Next, at the beginning of chapter 4, where Aristotle offers his revised list of phainomena as “the things that are supposed truly to belong to it,” he makes clear that the need to be able to differentiate places in terms of ‘above’ and ‘below’ is among these phainomena: Text 11 We assume […] that all place admits of the distinction of above and below, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes the place either above or below (Phys. 4, 211a3-6).

The suggestion is not that natural place helps to explain natural motion as a cause, but that a proper theory of place is able to account for the difference between places that are ‘above’ (where the light elements naturally are or move to) and those that are ‘below’ (where the heavy elements are or move to). Finally, after having established, in chapter 4, his own account of place as the first immobile limit of the surrounding body, Aristotle explicitly returns to the phenomenon of natural motion in order to show how his own conception of place is able to account for it: Text 12. Also, it can be explained that each kind of body should be carried to its own place (φέρεται […] εὐλόγως). For a body which is next in the series and in contact (not by compulsion) is akin, and bodies which are united do not affect each other, while those which are in contact interact on each other. Nor is it inexplicable that each should remain naturally in its proper place (μένει […] οὐκ ἀλόγως). For parts do, and that which is in a place has the same relation to its place as a separable part to its whole […] (Phys. 4, 212b29-35).

The details of the analogy between places and parts need not concern us here.40 What is important in the present context is that, once again, there is no hint that place has any causal status. Instead, we get the more modest suggestion that the Aristotelian concept of place as a surrounding surface allows us to make sense (note the use of the terms εὐλόγως and of οὐκ ἀλόγως) of our talking about bodies moving to their own, or their natural, place. It is precisely because the natural motion or rest of the elements is in one way or another dependent on the bodies that are surrounding them, that Aristotle’s concept of place as the limit of the surrounding body allows for meaningful talk about natural motion. Or, as we might put it, Aristotelian places are not isotropic: it makes a difference whether a body is contained by the 40

 More details in Algra 1995, 205–206 and 216–217.

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limit of the right body (its natural place) or by the limit of the wrong body (a non-­ natural place). That this is one of the reasons why according to Aristotle his own theory is to be preferred over its most important rival theory (place as independent three-dimensional extension) is further shown by a passage in chapter 8, where the void is being discussed: Text 13. How can there be such a thing as natural motion, if there are no distinctions within that which is void and infinite? For since it is infinite, there is no above or below or centre; since it is void, there is no distinction between above and below (Phys. 4, 215a6-9).

The isotropic void-space of the atomists, it is suggested, makes all talk about natural motion and natural places meaningless. Of course this leaves us with the question what, then, is the cause of the natural motion of the elements, if it is not their natural place. Aristotle’s answer does not come in the context of his discussion of place, but only in book 8 of the Physics (with some further relevant information being provided in some passages in book 4 of the On the Heavens), where he describes the dynamics of natural motion. I will here not go into the details, but will briefly present the theory there outlined.41 The elements, as inanimate natural objects, have an inner tendency, or nisus, to move (or rather, as Aristotle puts it: “a principle of motion, not of moving something else or causing motion, but of suffering it,” κινήσεως ἄρχην, οὐδὲ τοῦ κινεῖν, οὐδὲ τοῦ ποιεῖν, ἀλλὰ τοῦ πάσχειν, 255b30-31) which is activated when they are generated in unnatural surroundings, for example when the sun through its heat turns water into air and thus generates air in a place that is suitable for water. This means that there are two main factors involved: the external cause which triggers the whole process by generating the changed substance and the inner tendency of this new substance to be somewhere, namely in its natural place. The external generator actualizes the potentiality to acquire a new substantial form (the potentiality of water to become air, and thus light). Along with this new form two further, secondary, potentialities (in the categories quantity and ‘where’) will be actualized: unless prevented the new mass will expand (quantity) and it will tend to move to a new place, thus actualizing its lightness. In Aristotle’s own words: Text 14. The actuality of lightness consists in the light thing being somewhere (που), namely high up: when it is in the contrary place it is being impeded. The case is similar with regard to quantity and quality. But, be it noted, this is the question we are trying to answer: how can we account for the motion of the light things and heavy things to their proper places? The reason for it is that they have a natural tendency to go in a certain direction (πέφυκεν ποι); and this is what it is to be light or heavy, the former being determined by an upward, the latter by a downward tendency (Phys. 8, 255b11-17).

So it is a thing’s being somewhere, as the actuality of its lightness or heaviness, that constitutes the goal, and thus the final cause of its natural motion, which in turn is a concomitant (a secondary actualization) of a substantial change (with the original external generator acting as the moving cause that sets the whole process going). It  For a fuller discussion of the dynamics of natural motion (including the relevant passages in the On the Heavens), see Algra 1995, 195–221.

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is important to note what some commentators have missed: ‘being somewhere’ is not the same thing as ‘place.’ We need to get the ‘semantics of natural motion’ right. A light or heavy thing’s ‘being somewhere’ in the sense of being in its natural place is an attribute of the heavy or light thing itself, and as such following upon the actualization of the thing’s new substantial form, just as this change of form may involve a change of size. Place, by contrast, is external to the thing itself. As Philoponus puts it, Text 15. Also otherwise, final causes are seen to be present in the things of which they are the ends, but place is different from all the things that are in it, having no share in the emplaced object (Philoponus, In Phys. 509, 30–510, 2).

We can now see Aristotle’s position more clearly. The claim in chapter 1 of Physics 4 that place appears to ‘have a certain power’ should not be taken literally. At any rate, place itself is not a cause, whether final or otherwise. But we still do need the concept of place to specify the ‘somewhere’ in the element’s ‘being somewhere’ that is the final cause of its natural motion. And since, as we saw, in the case of natural place this ‘being somewhere’ essentially means ‘having the right surroundings’ (being in its surroundings as a part in a whole), Aristotle’ conception of place (as the surface of the surrounding body) is better equipped, or so he believes, to describe this process than any other conception of place, including the concept of an isotropic empty space defended by the atomists. Some commentators, such as Simplicius and Philoponus, did in fact recognize that this was Aristotle’s considered view.42 We may surmise that later interpretations went astray mainly for two reasons. First, they failed to appreciate the different force of the various claims in Phys. 4, in particular of the claims (i) and (ii) as outlined above, against the background of its overall dialectical programme of sifting out phainomena and bringing in aporiai. Secondly, in interpreting book 4 of the Physics they may not have paid sufficient attention to the details of the relevant discussion in Physics 8. It is only after reading Phys. 8 that we can fully appreciate how the concept of natural place is to play an important role in the explanation of natural motion without this in any way implying that natural places are causes.

2.6  The Problem of the Immobility of Place At some point in the middle of his account in chapter 4 Aristotle adds the requirement that place should be immobile (βούλεται δ’ ἀκίνητος εἶναι ὁ τόπος, 212a18), so he qualifies his definition of place accordingly: it is not just the limit of the surrounding body, but the first (or nearest) immobile limit of the surrounding body. In  For Simplicius, see In Phys. 533-22-25 where it is argued that “if place is not the same as being in a place […] and the goal of bodies, if anything, is to be in a particular place, then place [itself] is not the final cause.” On Philoponus’ similar position see the reconstruction in Algra 2012, 7–9. On similar qualifications in Averroes and even in Thomas Aquinas, see Algra 1995, 219–220, with n67 and n68.

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the same context he adds that a thing located in a mobile container is in a vessel rather than in a place. So a vessel is a mobile place and a place is an immobile vessel. We have seen above (Section 2.4) that the vessel analogy suggests a stability which Aristotelian places actually lack. We are now faced with a disanalogy between vessels and places – unlike vessels, places are said to be immobile – which raises problems of its own. In principle the requirement that place should be immobile seems to make sense: after all, places are supposed to figure as an immobile frame of reference against which the change of position of moving bodies can be measured. However, for a theory that defines place in terms of a thing’s surroundings it is not so obvious how this can work, for in most circumstances a thing’s surroundings consist of mobile substances. Even in the case of the layers of the elements we see that water and air are mobile and in fact moving; the same goes for fire, and for the aether of the heavenly bodies. This is why, faced with the immobility criterion for Aristotelian places, Simplicius (In Phys. 604, 3) rhetorically asks: “where, then is such a place to be found and what things are properly in place?” Aristotle adds to the difficulty by providing a rather obscure example: a boat in a river. Presumably what he has in mind is a boat flowing along with the current of the river. He claims that in such a case the boat is in the flowing water as in a vessel (with respect to which, we may add, it does not move), whereas its immobile place is ‘the whole river’ (with respect to which, we may add, it does move): Text 16. Just as a vessel is a mobile place, so place is an immobile vessel. That is why, when something is in motion inside a moving object (imagine a boat on a river), it uses its surroundings as a vessel rather than as a place. But place is meant to be immobile. For that reason rather the whole river is the place (ὁ πᾶς μᾶλλον ποταμὸς τόπος), because taken as a whole it is immobile (ἀκίηντος ὁ πᾶς) (Phys. 4, 212a14-20).

This passage was much debated by ancient and medieval commentators and various interpretations were put forward.43 Some commentators took the claim about ‘the whole river’ being the place to refer to the immobile river banks (as opposed to the mobile, flowing water). But that would be to violate one of the criteria for place which Aristotle had set up himself, viz. that it should be contiguous (πρῶτον πέρας) and of the same size (“neither larger nor smaller,” 211a2). In order to save both the contiguity and the immobility of Aristotelian place (qua surface of the surrounding body) some later medieval commentators introduced a distinction between material place (the actual surface of the immediately surrounding body, which may be mobile) and formal place (the surrounding surface, considered in abstracto, and with its immobility defined in terms of its location in relation to the outer sphere of the heavens).44 A modern variant of this theory is presented by Ben Morison.45 Whereas the medieval commentators specified the relevant immobile surface as the surface of the immediately containing substance, but taken in abstracto, Morison specifies it as 43  For an overview of the problems and solutions, see Grant 1981b; Sorabji 1988, 190; Algra 1995, 222–230. 44  On the concepts of formal and material place in the medieval discussions, see Grant 1981b, 63–72. 45  See Morison 2002, 155–161.

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the containing surface taken as the surface of a larger surrounding entity, or of a group of entities, and in the end – and this is crucial – even as the surface of the surrounding cosmos or universe as a whole. And the cosmos as a whole is immobile; indeed it could not even move, because there is nothing outside it. Now it is not easy to derive this interpretation from what Aristotle actually says: “rather the whole river is the place.”46 Moreover, the role which this interpretation accords to the immobility of the cosmos as a whole seems questionable. For the immobility of the cosmos as a whole does not appear to be the kind of immobility we are looking for. We are discussing intra-cosmic motion and rest, so we need an immobile reference point within the cosmos which allows us to determine whether a particular body is moving or at rest. This is what Aristotle makes clear in the passage immediately following on the river example and the statement of the immobility requirement. For there he goes on to talk about the centre of the world and the inner limit of the sphere of the heavens as ‘above’ and ‘below’ in the basic, or ‘absolute’ sense, because they are both at rest. It is with respect to these two items that we can determine the natural rest or natural motion of the elements. Eudemus explicitly works out this line of thought by specifying that we define immobile places with reference to the heavenly sphere which is immobile in the relevant, intra-cosmic, sense: Text 17. Having said that place must be the limit, in so far as it surrounds, of the surrounding body which was immobile he [i.e. Eudemus] added: “For that which moves is like a vessel, and that is why we determine places in relation to the heavens. For they do not change place, except in their parts” (Simplicius In Phys. 595, 5–8; part of Eudemus fr. 80 Wehrli).

No sign here of the supposed relevance of the immobility of the cosmos as a whole in this connection. In fact, we may well ask what this relevance could possibly have been. Imagine a situation where the cosmos is surrounded by an infinite empty space and where – as imagined by the Stoic Cleomedes and in medieval thought experiments  – it moves or is moved so that it exhibits a rectilinear translation through this space.47 Would that change the way in which we define mobile versus  Morison, appears to support his interpretation by offering a different translation of the words ὁ πᾶς μᾶλλον ποταμὸς τόπος. He takes them to mean: “rather the whole river is a place,” i.e one of the possible ways of identifying the surrounding surface, next, for example, to the identification of this surface as the limit of the surrounding universe. In this reading, in other words, the eventual identification of the surrounding surface as the surface of the surrounding immobile universe is thus at least implied. However, the fact that the noun τόπος here occurs without the article is perfectly normal Greek idiom for nouns in a predicate position. It does not indicate that Aristotle is talking about ‘a place’ rather than ‘the place.’ Indeed the equivalent of ‘a place’ would probably have been something like τόπος τις. The context seems to suggest that we are being told that it is not the immediately surrounding water, but the river as a whole that is said to be the place of the boat. 47  See Cleomedes Cael. 1, 1, 39–43 Todd. More or less the same thought experiment was referred to in the 49th proposition of the famous Parisian condemnation of 1277 issued by bishop Étienne Tempier (which argued against those (Aristotelians) who claimed that God could not shift the world) and it was taken up by philosophers such as Thomas Bradwardine, John de Ripa and 46

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immobile substances within the cosmos? Wouldn’t we still regard the centre and the periphery as fixed reference points for determining intra-cosmic motion and rest? Conversely, of what use would the immobility of the cosmos as a whole be, for the purpose of locating things within the cosmos, if we imagine it as containing no fixed elements, but consisting of substances which all move helter-skelter all the time? It appears, in other words, that the search for immobile places would in principle not be thwarted by any supposed motion of the cosmos as a whole, whereas it would indeed be thwarted if we had no immobile reference points within the cosmos. So it appears that the immobility of the universe is of no help in securing the required immobility of places. On the basis of these considerations I do not think it very likely that Aristotle’s claim that “rather the whole river is the place” refers to the surrounding surface of the boat-sized hole in the cosmos, as Morison suggests. One would rather expect it to refer to the surface of the surrounding river, taken in abstracto, i.e. as a geographic entity, following the interpretation of the earlier mentioned medieval commentators (an interpretation which has been taken up some time ago in a slightly different way by Myles Burnyeat).48 This surface, we may surmise, derives its immobility from the immobility of the river qua geographical entity, which has a fixed position on the immobile earth, which in turn has a fixed position with respect to the heavenly spheres. Nevertheless, even this solution cannot be smoothly extracted from Aristotle’s text. It presupposes a rather specific unpacking of the roughshod phrase “the whole river is the place.” In addition, it still presupposes a distinction between the surface qua surface of the surrounding water and the surface qua surface of the surrounding immobile river as a geographical entity – a distinction which is not provided in the context of these particular passages, nor indeed elsewhere in Phys 4. Consequently, we need not be surprised that the problem of the immobility of place remained on the agenda in the later ancient and medieval commentary traditions, starting with Theophrastus, who included the fact that “place will be in motion” among the aporiai raised by Aristotle’s conception of place as a surrounding surface (Simplicius In Phys. 604, 5–11; Theophrastus fr. 146 FHSG).

2.7  The Emplacement of the Heavens Two further aporiai raised by Theophrastus in the same context concern the fact that on Aristotle’s theory not every body will be in a place – not the sphere of the fixed stars – and that also the heavens (ouranos) as a whole will not be in a place. These aporiai are related to the text of the first part of chapter 5 of Phys 4, which deals Nicolas Oresme. See Grant 1979, 230–232. In these contexts, the thought experiment was actually used to prove that there is, or can be, an extra-cosmic void space. As Palmerino’s Chapter 12 in this volume documents, this thought experiment plays a central role in the Leibniz-Clarke Correspondence. 48  Burnyeat 1984, 230, n15.

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with the subject of the emplacement of the (outer sphere of the) heavens (212b8-­ 21), and which is extremely condensed and difficult. Aristotle appears to claim that the ouranos is not in a place as a whole, but that it has places for its parts in so far as they move and contain each other (hence, they somehow act as each other’s places). The very fact that Aristotle designates his subject as ‘the ouranos’ does not make matters easier. After all, in Aristotle, even in this single context, the word ouranos can refer either to (1) the whole cosmos (as a synonym of ‘the universe’ or to pan), or to (2) the outer sphere of the heavens, or to (3) the heavens as a whole. Interpretations of what Aristotle says (and especially of what he means by ‘the parts’ of the ouranos) naturally differ according as one opts for (1), (2) or (3).49 Simplicius (In Phys. 594, 35–37) actually complains that “it is clear that he was calling either the whole universe or the whole of that which revolves ‘the heavens,’ but he created much unclarity in the passage before us by meaning sometimes ‘the heavens’ and sometimes ‘the universe’.” But let us leave the problem of the lack of clarity in the presentation for what it is and move on to the underlying conceptual problems. Whether the referent of the word ouranos is the outer sphere, or the heavens as a whole, or the cosmos as a whole, it is said not to be in a place. One could argue that these three entities all do indeed lack a container, so that they are not ‘in something’ in the required sense and that they exhibit no locomotion apart from rotation, so that it is hardly a problem if we have to conclude that they are not in a place. We have evidence that this was the interpretation opted for by Alexander of Aphrodisias, in his now lost commentary. He added that it is not impossible for something to exist without being in a place, because being in a place is not an essential property (belonging to the definition) of a body.50 We may note that this might be a way to take up Aristotle’s repeated suggestion that not everything that exists, but only mobile substances, are in a place.51 The additional claim to make would then be that the ouranos is not a mobile substance in the relevant sense, because it exhibits no rectilinear motion, whereas its rotation of its parts does not count as locomotion properly speaking and thus does not need places as a frame of reference.52 However, in chapter 5 Aristotle seems reluctant to take this line. Despite everything, he now seems so much swayed by the “universally accepted” (208a39) idea that that all existing things are somewhere as to want to show that the ouranos for sure does have a place, even if only in a derivative sense, and he also appears intent on maintaining the idea that its rotation, or the rotation of its parts involves places. And indeed, how could rotation be explained without invoking some conception of place?  The translation by Waterfield and Bostock 1996, for example opts for (1) and takes the whole of 212a31–b22 to be about the (place of the) universe. Hussey 1983, 119 rather assumes that Aristotle is moving between the various senses of ouranos, as indeed does Philoponus in the various sections of his commentary, on which see Algra and Van Ophuijsen 2012, 118, n201, n202, n203. 50  This is how Averroes describes Alexander’s position in his Long Commentary, as paraphrased by Lettink 1994, 308. 51  On which see above, n24. 52  This additional claim was indeed made by Alexander, on which see below, the text to n56. 49

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Accordingly, his own solution in the obscure first part of chapter 5 seems to come down to two claims: (i) the ouranos, in whatever meaning of the word we have in mind here, is indeed in place, but only incidentally, in virtue of the fact that its parts are in place; and (ii) the kind of locomotion involved is rotation; this involves the idea that its parts exchange places without the ouranos as a whole doing so. So the ouranos is said not to exhibit locomotion in its own right; only its parts change place. And thus the ouranos is not in place in its own right, but only incidentally, in virtue of the fact that its parts, presumably all of them, are in place. But does this work? In particular – and here we are back at the problem we started with – what is the ouranos in this connection and what, accordingly, are the parts that are moving and emplaced? The commentary tradition comes up with two ways in which this could be worked out, each of them equally unsatisfactory. One option is to take this passage to be about the heavens as a whole, in which case the reference to the ‘parts’ and their respective motions is taken to be to the nested spheres. The problem with this is that it does not leave us with a place which can serve as the measure of rotation; for during its rotation each inner sphere remains in the same outer sphere. Secondly we are left anyway with the problem of the outermost sphere, which on this interpretation should still be taken not to be in a place at all, for it has nothing to surround it from outside, unless we take it to be located, exceptionally, not in a concave surrounding surface, but in the convex surface of the inner sphere of Saturn, as Themistius appears to have suggested.53 Some Arabic commentators extended this solution from the sphere of the fixed stars to all celestial spheres. Thus Ibn Bajja (Avempace), basically followed by Ibn Rushd (Averroes), claims that a surrounding surface on the outside figures as the place for bodies exhibiting rectilinear motion, whereas bodies that exhibit rotation (i.e. the heavenly spheres) have as their place a surrounding surface on the inside.54 Philoponus knows Themistius’ solution, but objects that such a place for the sphere of the fixed stars (the outer surface of the sphere of Saturn) would not be of equal size (as demanded by Aristotle’s own constraints on the theory, 211a1-2). The second option mentioned in the commentary tradition is to take the passage to be about the outer sphere, i.e. the sphere of the fixed stars, alone, and to take the reference to the parts, which in so far as they are surrounded by each other s­upposedly are emplaced, to be to the continuous parts of this outer sphere itself.55 The problem with his interpretation is that on Aristotle’s own line of thought, and as we noted above in Section 2.3, the parts of a continuous whole are not in a place, properly speaking. Moreover, in the process of the rotation of the outer sphere these parts do not in fact change place rela Cf. Themistius In Phys. 121, 1–5.  For the arguments, see Lettink 1994, 297 (Ibn Bajja) and 309–310 (Ibn Rushd). 55  See, for example, Philoponus In Phys. 594, 5–10; Simplicius In Phys. 593, 13–15 with reference to Alexander of Aphrodisias. 53 54

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tively to each other: they rotate along with each other. As such they, or their surfaces, can hardly constitute the places that measure the rotation of the sphere. Once again, a possible way out for an Aristotelian might be to claim that locomotion as such is restricted to the kind of rectilinear motion that we witness in the sublunary world, and that only substances in that region are the sort of things that need places to explain their motions. In that case the fact that the outer sphere and the heavens as a whole are not in place, although they rotate, could be seen as no longer problematic, provided that rotation would no longer be treated as a subspecies of locomotion, but as a separate species of change in its own right (next to locomotion, qualitative change etc.), one which does not require a place to start from, nor a place to move into. And this indeed appears to have been the option chosen by Alexander of Aphrodisias.56 However, as Simplicius notes in the first part of his Corollary, there are many passages where Aristotle emphatically does claim that rotation is in fact one of the subspecies of locomotion or kinêsis kata topon.57 So he would have to revise that aspect of his theory to be able to take Alexander’s line of approach. All in all, then, the first part of chapter 5 appears to reveal that Aristotle did not manage to really sort out some rather crucial aspects of his theory of place: whether and to what extent we should be committed to the truth of the first premises of Zeno’s paradox of place, what should be considered to be the sort of things that need places, and whether or not rotation is a species of locomotion that requires places to measure it. In his Corollary on Place Philoponus has this to say on the attempts by the commentators to save this part of Aristotle’s account: Text 18. Hence, when they try to explain how the sphere of fixed stars could move in place when it is not in place, they throw everything into confusion rather than saying anything clear and persuasive. For they cannot deny that the sphere moves in place, because they cannot even make up a story about what {other} kind of motion it would have. However, they cannot explain what is the place in respect of which it moves, but like people playing dice they throw out first one account, then another, and through them all they destroy their original assumptions and agreements. For by concealing the weakness of his account with obscurity, Aristotle licensed those who want to change their stories however they wish (Philoponus, In Phys. 565, 12–21).

Even Aristotle’s staunch defender Ben Morison has to conclude that the problem of the emplacement of the ouranos is “a problem which is recognized and tackled by Aristotle, but unsatisfactorily.”58

2.8  Conclusions Physics 4, 1–5, as we have seen, is a difficult text in many respects, and the conception of place which it eventually works out is not in all respects a viable or very useful element in any theory of locomotion. In the present paper I have discussed  See Simplicius In Phys. 595, 20–21; see also 589, 5–8; 602, 31–35.  Simplicius In Phys. 603, 4–16. 58  Morison 2010, 85. 56 57

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five of the main exegetical or conceptual problems with which this text has confronted its later readers, starting with Aristotle’s pupils Eudemus and Theophrastus. These problems, as we saw, are not all of the same type, and in the end not all of the same weight and importance. The problem of the precise role of natural places in the explanation of the natural motion of light and heavy elements (discussed in Section 2.5) turns out not to be so much of a conceptual or philosophical problem after all, but rather a problem of presentation. One has to pull the pieces together, but the emerging picture makes sense, once we realize that the claim that place seems to have ‘a certain power’ need not be taken at face value, that Aristotle quite emphatically states that it is not one of the four causes, and that the dynamics of natural motion as sketched in Physics 8 isolates other causal factors (among which we find the element’s ‘being somewhere,’ not its place, labeled as a final cause). The problem of the unsatisfactory way in which the rival conception of place as three-dimensional extension is rejected (Section 2.3) and the problem of how places can figure in the explanation of locomotion (Section 2.4) arguably lose much of their edge, once we look at things from an Aristotelian perspective. Admittedly, the arguments against the conception of place as an independent three-dimensional extension do not work as they stand, but what seems to be the underlying problem – the inconceivability of such an extension within the context of Aristotle’s substance ontology (and the concomitant theory of the categories) – was a real one for Aristotle and many of his followers. We may also admit that Aristotelian places are hopeless if we want to explain the trajectory of a body moving from place A to place B. However, in many contexts the fact that the theory is able to identify place A at the beginning and place B at the end of the trajectory arguably lends it sufficient explanatory power for an Aristotelian. However, the problem of specifying the required immobility of Aristotelian places (Section 2.6), and the problem of clarifying whether and in what sense the outer sphere of the heavens, the heavens as whole, or the cosmos as a whole have a place, both represent aspects of the theory that Aristotle himself appears not to have thought through sufficiently. In everyday contexts we may for all practical purposes think it good enough to say that a boat moving along with the current in a river does not move with respect with the immediately surrounding water, but does move with respect to ‘the river as a whole.’ But once we want to translate this ‘the river as a whole’ in the more technical language of Aristotelian places as contiguous and immobile surfaces we run into problems and are forced to think up solutions (like the medieval ‘nominalist’ solution of taking these surfaces in abstracto) of which there is not a trace in the actual text of Physics 4, 1–5. When it comes to the problem of the emplacement of the ouranos (Section 2.7), in whatever sense of the word we take it, it appears that Aristotle has not managed to make clear to what extent precisely he is committed to the first premises of Zeno’s paradox, and that he has failed to make clear in what sense the parts of the ouranos are to be thought of as being in a place, in what sense its rotation is or is not a species of locomotion and in what sense the explanation of rotation requires a place of the type developed in Physics 4 at all. Perhaps all this could be resolved, for example along the lines suggested by Alexander, but no such resolution is forthcoming from chapter 5 of Physics 4.

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In spite of all this, it is fair to say that Physics 4, 1–5 is also an intriguing, rich and highly original text – the more so since it is the first in its kind. Right at the beginning of the account (208a34-36) Aristotle himself highlights this point by claiming that, apart from the inherent difficulty of the subject, a proper discussion is hampered by the fact that thinkers before him have neither shown any awareness of the problems inherent in thinking about place (οὐδὲν […] προηπορημένον), nor offered any good insights (οὐδὲν […] προηυπορημένον). Certainly, later on he is willing to admit that “although everyone assumes that there is such a thing as place, Plato is the only one who tried to say what it is” (209b15-16). But in Aristotle’s view Plato’s account in the Timaeus has not been successful in doing so because it remains fundamentally unclear, and from a purely physical point of view he is surely right.59 And so Aristotle’s Physics 4, 1–5 stands out, despite all its problematic features, as the first systematic discussion of various possible conceptions of place, of some of the problems inherent in thinking about place, and of new and necessary conceptual distinctions.

References Algra, Keimpe. 1992. Place in Context: On Theophrastus fr. 21 and 22 Wimmer. In Theophrastus: His Psychological, Doxographical and Scientific Writings, ed. William Fortenbaugh and Dimitri D. Gutas, 141–165. New Brunswick: Transaction Publishers. ———. 1995. Concepts of Space in Greek Thought. Leiden: Brill. ———. 2012. Introduction. In Philoponus On Aristotle Physics 4. 1-5, ed. Keimpe Algra and Johannes van Ophuijsen, 1–12. Bristol: Bristol Classical Press. ———. 2014. Aristotle’s Conception of Place and Its Reception in the Hellenistic Period. In Space in Hellenistic Philosophy, ed. Graziano Ranocchia, Christoph Helmig, and Christoph Horn, 11–52. Berlin: De Gruyter. ———. 2015. Place (M 10, 1–36). In Sextus Empiricus and Ancient Physics, ed. Keimpe Algra and Katerina Ierodiakonou, 184–216. Cambridge: Cambridge University Press. Algra, Keimpe, and Johannes van Ophuijsen. 2012. Philoponus On Aristotle Physics 4, 1–5. Bristol: Bristol Classical Press. Bergson, Henri. 1889. Quid Aristoteles de loco senserit. Paris: Alcan. Burnyeat, Myles. 1984. The Sceptic in His Place and Time. In Philosophy in History: Essays on the Historiography of Philosophy, ed. Richard Rorty, Jerome Schneewind, and Quentin Skinner, 225–254. Cambridge: Cambridge University Press. Desclos, Marie-Laurence, and William Fortenbaugh. 2011. Strato of Lampsacus: Text, Translation and Discussion. New Brunswick: Transaction Publishers.

 This is a subject not discussed in this paper. But the long and the short of it is that Aristotle thinks that (i) the Timaeus leaves it fundamentally unclear whether the ‘receptacle’ can be seen as a separable self-subsistent space in which phenomenal bodies are and move around in the strictly local sense of ‘being in,’ or rather an inseparable constituent factor of the world in which immanent qualities are, in the non local sense of ‘being in’ which we might call ‘inherence;’ and that (ii) its identification of space or place with matter is of no use in a physical context dealing with the locomotion of substances. For a vindication of Aristotle’s critique of the Timaeus and its ‘receptacle,’ with a discussion of the relevant texts, see Algra 1995, 110–117.

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Furley, David, and Christian Wildberg. 1991. Philoponus, Corollaries on Place and Void – With Simplicius, Against Philoponus on the Eternity of the World. London: Duckworth. Gottschalk, Hans. 1998. Theophrastus and the Peripatos. In Theophrastus: Reappraising the Sources, ed. Johannes van Ophuijsen and Marlein van Raalte, 281–299. New Brunswick: Transaction Publishers. ———. 2002. Eudemus and the Peripatos. In Eudemus of Rhodes, ed. Istvan Bodnár and William Fortenbaugh, 25–37. New Brunswick: Transaction Publishers. Grant, Edward. 1979. The Condemnation of 1277: God’s Absolute Power and Physical Thought in the Late Middle Ages. Viator 10: 211–244. ———. 1981a. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. ———. 1981b. The Medieval Doctrine of Place: Some Fundamental Problems and Solutions. In Studi sul XIV secolo in memoria di Anneliese Maier, ed. Alfonso Maierù and Agostino Paravicini Bagliani, 57–79. Rome: Edizioni di Storia e Letteratura. Hussey, Edward. 1983. Aristotle: Physics Books III and IV. Oxford: Clarendon Press. Irigaray, Luce. 1998. Place, Interval: A Reading of Aristotle, Physics IV. In Feminist readings of Aristotle, ed. Cynthia A. Freeland, 41–58. University Park: The Pennsylvania State University Press. Lettink, Paul. 1994. Aristotle’s Physics and its Reception in the Arabic World: With an Edition of the Unpublished Parts of Ibn Bajja’s Commentary on the Physics. Leiden: Brill. Morison, Ben. 2002. On Location: Aristotle’s Concept of Place. Oxford: Oxford University Press. ———. 2010. Did Theophrastus Reject Aristotle’s Account of Place? Phronesis 55 (1): 68–103. Owen, Gwyll. 1961. Tithenai ta phainomena. In Logic, Science and Dialectic, Collected Papers in Greek Philosophy, ed. Martha Nussbaum, 239–251. London: Duckworth. Rashed, Marwan. 2011. Alexandre d’Aphrodise: Commentaire perdue à la Physique d’Aristote (livres IV-VIII). Les scholies byzantines: Édition, traduction et commentaire. Berlin: De Gruyter. Sambursky, Shmuel. 1982. The Concept of Place in Late Neoplatonism. Jerusalem: The Israel Academy of Sciences and Humanities. Sharples, Robert. 1998. Theophrastus as Philosopher and Aristotelian. In Theophrastus: Reappraising the Sources, ed. Johannes van Ophuijsen and Marlein van Raalte, 267–281. New Brunswick: Transaction Publishers. ———. 2002. Eudemus’ Physics: Change, Place and Time. In Eudemus of Rhodes, ed. Istvan Bodnár and William Fortenbaugh, 107–126. New Brunswick: Transaction Publishers. ———. 2011. Strato of Lampsacus: The Sources, Texts and Translations. In Strato of Lampsacus: Text, Translation and Discussion, ed. Marie-Laurence Desclos and William Fortenbaugh, 5–231. New Brunswick: Transaction Publishers. Sorabji, Richard. 1988. Matter, Space and Motion. London: Duckworth. ———. 1990. The Ancient Commentators on Aristotle. In Aristotle Transformed, ed. Richard Sorabji, 1–30. London: Duckworth. ———. 2004. The Philosophy of the Commentators 200-600 AD: A Sourcebook, vol. 2, Physics. London: Duckworth. Todd, Robert. 2003. Themistius, On Aristotle’s Physics 4. London: Duckworth. Urmson, James O. 1992. Simplicius, On Aristotle’s Physics 4, 1–5 and 10–14. London: Duckworth. Urmson, James O., and Lucas Siorvanes. 1992. Simplicius, Corollaries on Place and Time. London: Duckworth. Waterfield, Robin, and David Bostock. 1996. Aristotle’s Physics. Oxford: Oxford University Press.

Chapter 3

The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe Frederik A. Bakker

Abstract  In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred from the infinity of space, because they believed that a limited amount of matter would inevitably be scattered through infinite space, and hence be unable to meet and form stable compounds. By contrast, the Stoics claimed that there was only a finite amount of matter in infinite space, which stayed together because of a general centripetal tendency. The Roman Epicurean poet Lucretius tried to defend the Epicurean conception of infinity against this Stoic alternative view, but not very convincingly. One might suspect, therefore, that the Epicureans’ adherence to the infinity of matter was not so much dictated by physical arguments as it was motivated by other, mostly theological and ethical, concerns. More specifically, the infinity of atoms and worlds was used as a premise in several arguments against divine intervention in the universe. The infinity of worlds was claimed to rule out divine intervention directly, while the infinity of atoms lent plausibility to the chance formation of worlds. Moreover, the infinity of atoms and worlds was used to ensure the truth of multiple explanations, which was presented by Epicurus as the only way to ward off divine intervention in the realm of celestial phenomena. However, it will be argued that in all of these arguments the infinity of matter is either unnecessary or insufficient for reaching the desired conclusion.

The original version of this chapter was revised. This chapter was considered as an Open Access chapter. A correction to this chapter can be found at https://doi.org/10.1007/978-3-03002765-0_13 F. A. Bakker (*) Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_3

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3.1  Introduction A prominent feature of ancient atomism that still captures the imagination is its endorsement of the infinity of the universe and, associated with it, the infinite number of worlds.1 Whereas most ancient philosophers argued for a single cosmos, either identified with a finite universe, as in Plato’s and Aristotle’s cosmologies, or placed in an infinite void, as in Stoic cosmology, the atomists made our cosmos a negligible and utterly unremarkable part of the infinite matter-filled universe.2 The infinity of the universe, in terms of space as well as bodies, was arrived at through rigorous argumentation, much of which may go back to the earlier atomists, but which has come down to us mainly through the works of Epicurus and Lucretius, who adopted and reinforced some of the earlier arguments.3 The centrality of this theory to Epicurean cosmology is clear from the prominent place given to it in Epicurus’ Letter to Herodotus (close to the beginning) and in Lucretius’ De rerum natura (in the final and concluding parts of books one and two). However, the dual infinity of matter and void, and the consequent infinite number of worlds, are not simply curious but otherwise sterile logical consequences of the basic tenets of Epicurean physics, but they also serve as the starting points for further inferences: the infinity of the universe is argued to rule out divine governance, to make the spontaneous formation of a cosmos not merely possible but inevitable, and to guarantee the simultaneous truth of multiple, mutually incompatible explanations. Moreover, all of these consequences relate directly or indirectly to the question of the gods’ involvement in the world. In this chapter I will investigate the infinity of the universe from both points of view. First, I will critically examine the Epicurean arguments for the infinity of space and bodies, as well as the way in which they deal with a rival view, and, second, I will look into some of the corollaries to the infinity of space and bodies, and the role these corollaries play in underpinning the Epicurean view of the gods, in order to see whether this role may serve as an additional motivation for the Epicureans’ insistence on the infinity of bodies and worlds.

 See e.g. Mash 1993, 204–210; Dick 1996, 12–13, Dowd 2015, 56, Traphagan 2015, 18; and Darling 2016, s.vv. ‘atomism,’ ‘Leucippus,’ ‘Democritus,’ ‘Metrodorus,’ ‘Epicurus’ and ‘Lucretius.’ 2  See e.g. Lucretius 6.649–652. Henceforth all references to Lucretius will follow the text and translation of Rouse and Smith 1992, unless otherwise specified. 3  For the Presocratic antecedents of these arguments see Furley 1989, 110–114; Avotins 1983; Asmis 1984, 261–267. 1

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3.2  Cosmological Arguments for the Infinity of the Universe Two Epicurean accounts for the infinity of the universe have come down to us. One is found in Epicurus’ Letter to Herodotus 41–42, and another, longer one in Lucretius’ De rerum natura 1.951–1113. In both accounts the arguments presuppose the Epicurean division of being into bodies and void. In order to clarify these two somewhat ambiguous concepts and to provide a background for the discussion of Epicurean infinity, I will start with a brief discussion of these two concepts.

3.2.1  Clarification of Concepts: Bodies and Void According to Epicurus the universe (τὸ πᾶν) consists of bodies and void (κενόν).4 The existence of bodies is directly attested by the evidence of the senses,5 but the existence of void, being inaccessible to sense perception, has to be inferred from other phenomena (Letter to Herodotus 40): And if there were not that which we term void and room and intangible nature, bodies would have nowhere to exist and nothing through which to move, as they are seen to move.6

In this statement void (κενόν) is connected with two other spatial concepts, room (χώρα) and intangible nature (ἀναφὴς φύσις). In the Letter to Herodotus Epicurus does not provide a definition for any of these three terms, but a later source, Sextus Empiricus, Against the Professors 10.2, provides the following testimony: According to Epicurus, of ‘intangible nature,’ as he calls it, one kind is named ‘void,’ another ‘place,’ and another ‘room,’ the names varying according to the different ways of looking at it, since the same nature when empty of all body is called ‘void,’ when occupied by a body is named ‘place,’ and when bodies roam through it becomes ‘room.’7

So, although Epicurus apparently did sometimes distinguish these spatial terms, in Letter to Herodotus 40 these distinctions are observed neither nominally  – for Epicurus presents the three terms as mere synonyms –,8 nor conceptually – for the 4  Epicurus, Letter to Herodotus 39. Henceforth all references to Epicurus’ letters will follow the text edition of Arrighetti 1973. See also Lucretius 1.419–20. 5  Epicurus, Letter to Herodotus 39. See also Lucretius 1.422–25. 6  Epicurus, Letter to Herodotus 40: εἰ μὴ ἦν ὃ κενὸν καὶ χώραν καὶ ἀναφῆ φύσιν ὀνομάζομεν, οὐκ ἂν εἶχε τὰ σώματα ὅπου ἦν οὐδὲ δι’ οὗ ἐκινεῖτο, καθάπερ φαίνεται κινούμενα. Translation in Bailey 1926, 23 (slightly modified). See also Lucretius 1.329–69. 7  Sextus Empiricus, Against the Professors 10.2: κατὰ τὸν Ἐπίκουρον τῆς ἀναφοῦς καλουμένης φύσεως τὸ μέν τι ὀνομάζεται κενόν, τὸ δὲ τόπος, τὸ δὲ χώρα, μεταλαμβανομένων κατὰ διαφόρους ἐπιβολὰς τῶν ὀνομάτων, ἐπείπερ ἡ αὐτὴ φύσις ἔρημος μὲν καθεστηκυῖα παντὸς σώματος κενὸν προσαγορεύεται, καταλαμβανομένη δὲ ὑπὸ σώματος τόπος καλεῖται, χωρούντων δὲ δι’ αὐτῆς σωμάτων χώρα γίνεται. Text in Long and Sedley 1987b, 22; translation in Long and Sedley 1987a, 28 (slightly modified). 8  Similarly Lucretius 1.334 “quapropter locus est intactus inane vacansque;” 1.954-955 “quod inane repertumst / seu locus ac spatium;” and 1.1074 “omnis enim locus ac spatium, quod in.”

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existence of void is inferred from the fact that bodies (1) need to be somewhere, which is place, and (2) need something to move through, which is room. This means that in Letter to Herodotus 40, and possibly also other passages, the term ‘void’ is used to denote not just empty space, but also occupied space (i.e. ‘place’) and the space through which bodies move (i.e. ‘room’). In other words, ‘void’ is used as a stand-in for the generic term ‘intangible nature,’ which may also be translated as ‘space.’9 Another ambiguity that must be addressed concerns the concept of body. Bodies, according to Epicurus (Letter to Herodotus 40–41), come in two kinds: compounds and atoms. Now, when Epicurus claims that the existence of bodies is attested by the evidence of the senses (see above), he must be thinking primarily of compounds, since atoms cannot be perceived (Letter to Herodotus 56). However, since in compound bodies there is always an admixture of void (Lucretius 1.358-369), conceptual purity requires that, in those contexts where bodies are opposed to void, we think primarily of atoms.

3.2.2  P  ositive Arguments for the Infinity of the Universe, Bodies and Void In section 41 of his Letter to Herodotus, Epicurus provides the following argument for the infinity of the universe: Moreover, the universe is boundless. For that which is bounded has an extreme point, and the extreme point is seen against something else, 10 so that, as it has no extreme point, it has no limit, and as it has no limit, it must be boundless and not bounded.11

The same view is also defended by Lucretius (1.951-1007), who offers no fewer than four arguments.12 In the first place (1.958-967), Lucretius argues, whatever is finite must have a boundary, but a boundary requires something external to bound it; however, since there is nothing external to the universe, the universe cannot have a  See Long and Sedley 1987a, 29–30; Algra 1995, 52–58. However, Inwood 1981, and more recently Konstan 2014, claim that Epicurus uses the term ‘void’ (τὸ κενόν) exclusively to refer to ‘empty space.’ (Concerning these two interpretations see also n18 below.) In this article I will follow the first-mentioned interpretation, which I find to be the more convincing of the two. My own conclusions concerning the Epicurean theory of infinity do not, however, essentially depend on this choice, and could also agree with the alternative interpretation. 10  Addition suggested by Usener 1887, xviii, on the basis of Cicero’s version of Epicurus’ argument in De divinatione 2.103; it is rejected by Bailey 1926, 22 and 184, but accepted by Arrighetti 1973, 39. 11  Epicurus, Letter to Herodotus 41: Ἀλλὰ μὴν καὶ τὸ πᾶν ἄπειρόν ἐστι· τὸ γὰρ πεπερασμένον ἄκρον ἔχει· τὸ δὲ ἄκρον παρ’ ἕτερόν τι θεωρεῖται· ὥστε οὐκ ἔχον ἄκρον πέρας οὐκ ἔχει· πέρας δὲ οὐκ ἔχον ἄπειρον ἂν εἴη καὶ οὐ πεπερασμένον. Translation in Bailey 1926, 23 (modified). 12  See Bailey 1947, vol. 2, 763–764; Asmis 1984, 262–264; Bakker 2016, 182–184. 9

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boundary, and hence must be infinite. Secondly (1.968-983), if the universe had a boundary and someone threw a spear towards it, the spear would either stop or continue: if it stops, there must be matter outside to obstruct it, but if it continues there must be empty space to receive it: in either case there must be something outside, and the boundary of the universe turns out to be no boundary at all; this result repeats itself wherever one assumes the presence of a boundary. As a consequence the universe cannot have a boundary, and is proved to be infinite. Thirdly (1.984-­ 997), if space were finite and bounded on all sides, all bodies would be heaped up at the ‘bottom,’ i.e. the lower boundary, by strength of their weight, and nothing further would happen, but this is not the case; therefore the universe must be infinite. Finally (1.998-1001), we see that everything that is bounded is always bounded by something else, but in the case of the universe there is nothing else to bound it; therefore the universe must be infinite. The first of Lucretius’ arguments basically repeats Epicurus’ argument from the Letter to Herodotus 41, and may go back to the earlier atomists: one version is presented and rejected by Aristotle in Physics 3.4, 203b20-22. The second argument is a famous thought experiment that goes back to the Pythagorean Archytas and was also used by the Stoics.13 Both these arguments, as well as the fourth, exploit the notion of limit, which seems to include the notion of a ‘beyond.’14 Lucretius’ third argument is of a different nature. Presupposing the Epicurean conception of downward motion as a motion along parallel lines from infinity to infinity,15 and hypothetically enclosing the universe in boundaries, Lucretius argues that the lower boundary, the ‘bottom,’ would obstruct this natural downward motion and cause matter to be compacted into one inert mass.16 However, at this point of the argument the Epicurean theory of parallel downward motion has not yet been proved: in fact, its proof depends upon the rejection of centripetal gravity in 1.1052-1093 (see the next section), which in turn presupposes the infinity of space  – the very thing Lucretius is arguing for here. In short: Lucretius’ third argument presents a petitio principii. The fourth argument seems to be nothing but a restatement of the first. A version of this argument is also used by the Stoic Cleomedes (1.1, 112–122).

 Archytas fr. A24 in Diels and Kranz 1951–1952; Stoics SVF II 535–536 (Here and elsewhere I use the standard abbreviation SVF for references to Arnim 1903–1905). For an analysis of the various ancient versions of this thought experiment, see Ierodiakonou 2011. For early modern versions of the thought experiment see Granada’s and Palmerino’s Chapters 8 and 12 in this volume. 14  Furley 1989, 111; Avotins 1983, 427; Asmis 1984, 262–263. 15  See Epicurus, Letter to Herodotus 60, with the comments on the same in Konstan 1972, and Lucretius 2.216-250, with the comments on the same in Bakker 2016, 214–216. 16  It might be argued that, were the existence of a centripetal downward motion assumed, the centre would provide a similar ‘bottom,’ and the same argument would apply (on which see p. 51 below). However, in the present context Lucretius is clearly thinking of external boundaries, and his identification of one of these external boundaries as the ‘bottom’ indicates that he is assuming the existence of a parallel downward motion. 13

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With the infinity of the universe proven, and given the fact that the universe consists of bodies and void, the question naturally arises how the infinity of the universe relates to each of its two components. In sections 41–42 of the Letter to Herodotus, Epicurus argues for the infinity of both bodies and void: Furthermore, the universe is boundless both in the number of the bodies and in the extent of the void. For if on the one hand the void were boundless, and the bodies limited in number, the bodies could not stay anywhere, but would be carried about and scattered through the infinite void, not having other bodies to support them and keep them in place by means of collisions. But if, on the other hand, the void were limited, the infinite bodies would not have a place to be in.17

Here too, ‘void’ seems to be used in the sense of ‘space,’ encompassing both that through which bodies move (i.e. ‘room’) and that where bodies are (i.e. ‘place’).18 However, this should not mislead us into thinking that bodies and space might be coextensive, with bodies (i.e. atoms) filling up every portion of space. Lucretius offers three arguments for the existence of actually empty space. Firstly, motion requires the existence of pockets of empty space, in order to provide a beginning of motion (1.335-345); secondly, the penetration of sound and cold into bodies, but also the dispersion of food through the living body require the existence of empty passageways (1.346-357), and thirdly, differences in specific weight must be due to differing amounts of empty space in (compound) bodies (1.358-369).19 When, therefore, the Epicureans state that both the extent of space and the number of bodies are infinite, what they have in mind is an infinite alternation of (atomic) bodies and (empty) space.20 In an expanded version of Epicurus’ argument for the infinite number of bodies Lucretius (1.1008-1051) specifies that our world is being maintained by external bodies, which constantly either replace atoms or beat them back into line.21

 Epicurus, Letter to Herodotus 41–42: Καὶ μὴν καὶ τῷ πλήθει τῶν σωμάτων ἄπειρόν ἐστι τὸ πᾶν καὶ τῷ μεγέθει τοῦ κενοῦ· εἴ τε γὰρ ἦν τὸ κενὸν ἄπειρον, τὰ δὲ σώματα ὡρισμένα, οὐθαμοῦ ἂν ἔμενε τὰ σώματα, Ἀλλ’ ἐφέρετο κατὰ τὸ ἄπειρον κενὸν διεσπαρμένα, οὐκ ἔχοντα τὰ ὑπερείδοντα καὶ στέλλοντα κατὰ τὰς Ἀνακοπάς· εἴ τε τὸ κενὸν ἦν ὡρισμένον, οὐκ ἂν εἶχε τὰ ἄπειρα σώματα ὅπου ἐνέστη. Translation in Bailey 1926, 23 (slightly modified). 18  According to Algra 1995, 56–57, ‘being in’ and ‘moving through’ imply that ‘void’ is here thought of as occupied, and therefore not empty. Konstan 2014, 90–91, retorts that ‘being in’ means ‘being surrounded by’ and ‘being separated by,’ and since bodies are always surrounded and separated by empty space (because otherwise they would not be able to move), the infinity of bodies implies an infinite amount of surrounding empty space. 19  Algra 1995, 57. 20  Cf. Lucretius 1.1008-1011 “Ipsa modum porro sibi rerum summa parare / ne possit, natura tenet, quae corpus inani / et quod inane autem est finiri corpore cogit, / ut sic alternis infinita omnia reddat.” Text from Rouse and Smith 1992, 82 and 84. 21  A similar argument is also found in fragment 67 (in Smith 1993, 259–260) of the Epicurean inscription of Diogenes of Oenoanda. 17

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3.2.3  Refutation of a Rival Theory At first sight the Epicurean argument for an infinite number of bodies seems quite plausible. However, the assumption it is based on – that in infinite space a limited number of bodies would not be able to find a stable foothold, and would therefore be dispersed throughout the void  – is not self-evident. While Epicurus simply assumes that this is true, Lucretius is aware of, and actively engages with, a rival theory that challenges precisely this implication. In 1.1052-1093, Lucretius warns Memmius, his addressee, to “avoid and keep afar” the view that, as some say, all things press towards the centre of the whole and that for this reason the nature of the world stands firm without any external blows, and […] cannot be set loose in any direction, because all presses towards the centre.22

If, as these unnamed rivals claim, all bodies have a natural tendency to move towards a central point, even a limited amount of bodies would be able to remain together and be safe from dispersal into the infinite void, without the need for external blows to keep the bodies in check, or to repair the losses. One could even argue – although Lucretius does not make this point – that the assumption of a general centripetal tendency of bodies would actually preclude their infinite number, because otherwise the world would experience continuous growth due to the incessant accrual of new atoms converging on the centre from the infinite stock of surrounding matter, which is not the case.23 Lucretius does not identify the proponents of this theory, and over the years various candidates have been proposed. The common, and in my opinion the most plausible, view is that Lucretius was thinking of the Stoics.24 Although several ancient philosophers and schools of philosophy endorsed some kind of centripetal gravity, only the Stoics deployed this theory in order to safeguard the integrity of a single and finite cosmos in infinite space, and only they extended this centripetal tendency to all bodies, heavy and light alike. Other proposed candidates, like Aristotle or the early Platonists, simply rejected extra-cosmic space, and therefore did not have to account for the coherence of the cosmos as such, or to counterbalance the centrifugal tendency of air and fire with a centripetal one.25 However, although Lucretius probably had the Stoics in mind, this does not necessarily mean that he understood

 Lucretius 1.1052–1055: “Illud in his rebus longe fuge credere, Memmi, / in medium summae quod dicunt omnia niti, / atque ideo mundi naturam stare sine ullis / ictibus externis, neque quoquam posse resolvi, / […] quod in medium sint omnia nixa.” Text and translation from Rouse and Smith 1992, 87–89. 23  Compare Aristotle, De caelo 1.8, 276a18-b21, where Aristotle argues that, if one assumes the universe to consist of the same elements having the same nature and potentialities everywhere, the universe must also have a single centre towards (or away from, or around) which all the elements would move; hence there can only be one world, because every part of matter in another world would take up position with respect to this single centre. 24  For a more extended argument see Bakker 2016, 191–202. 25  Aristotle was proposed by Furley 1989, 187–195, and the early Platonists by Sedley 1998, 78–82. 22

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or represented their theory correctly in every respect. The clearest ancient testimony as to the Stoic theory in question is preserved by Stobaeus: In the case of all things in the cosmos that have a hexis of their own the parts tend towards the centre of the whole thing. Similarly in the case of the cosmos itself; and it is in virtue of this fact that it is rightly said that all parts of the cosmos have a tendency to move towards the centre of the cosmos, most of all the things possessing weight. The same thing is responsible both for the immobility of the cosmos in the infinite void and for the earth’s immobility in the cosmos, as it is situated around the centre of it [viz. of the cosmos] in a state of equal balance. Still it is not unrestrictedly so that body has weight, but air and fire are weightless. However, also these elements tend towards the centre of the whole globe of the cosmos, although they find their relative position in the direction of the periphery of the cosmos. For by their own nature they are upward moving because they don’t have any share in weight.26

According to the Stoics, just as individual things within the cosmos are held together by a cohesive force or hexis, so the cosmos as a whole has a hexis, which causes all its parts to converge on its centre. This tendency is felt most strongly by the heaviest parts, which take up a more central position, but less by the weightless bodies, which therefore move towards, and settle at, the periphery. After describing the rival theory and mockingly highlighting some of its paradoxical corollaries – that on the underside of the earth gravity is directed upwards, and animals and humans stand upside down (1058–1067) – Lucretius proceeds with his refutation. His main arguments are, first (1070–1071), that the universe, being infinite, does not have a centre for the parts of the cosmos to move towards; second (1071–1080), that the centre, even if it existed, would be a spatial and hence incorporeal entity, and as such incapable of exerting any effect on bodies; and, third (1083–1093), that the rival theory is internally inconsistent in also claiming that air and fire tend away from the centre. Given that the rival theory stands in the way of a central Epicurean tenet, one would expect a particularly strong effort to refute it. In fact, however, Lucretius’ arguments seem to be rather weak. In order to demonstrate this I will now discuss Lucretius’ arguments one by one. I will start with the first and third arguments, whose inadequacy is the most obvious, and leave the second argument, which presents some difficulties, for last. Lucretius first argues that there is no centre, because the (infinite) universe can have no centre. This seems to be a good point. However, if we take a closer look at the Stoic theory as reported by Stobaeus (see above) and other sources, we see that

 Stobaeus, Eclogae Physicae 1.166, 2–22 (= Arius Didymus fr.23 / SVF I 99): Τῶν δ’ ἐν τῷ κόσμῳ πάντων τῶν κατ’ ἰδίαν ἕξιν συνεστώτων τὰ μέρη τὴν φορὰν ἔχειν εἰς τὸ τοῦ ὅλου μέσον, ὁμοίως δὲ καὶ αὐτοῦ τοῦ κόσμου· διόπερ ὀρθῶς λέγεσθαι πάντα τὰ μέρη τοῦ κόσμου ἐπὶ τὸ μέσον τοῦ κόσμου τὴν φορὰν ἔχειν, μάλιστα δὲ τὰ βάρος ἔχοντα. ταὐτὸν δ’ αἴτιον εἶναι καὶ τῆς τοῦ κόσμου μονῆς ἐν Ἀπείρῳ κενῷ καὶ τῆς γῆς παραπλησίως ἐν τῷ κόσμῳ, περὶ τὸ τούτου κέντρον καθιδρυμένης ἰσοκρατῶς. οὐ πάντως δὲ σῶμα βάρος ἔχειν, Ἀλλ’ Ἀβαρῆ εἶναι Ἀέρα καὶ πῦρ· τείνεσθαι δὲ καὶ ταῦτά πως ἐπὶ τὸ τῆς ὅλης σφαίρας τοῦ κόσμου μέσον, τὴν δὲ σύστασιν πρὸς τὴν περιφέρειαν αὐτοῦ ποιεῖσθαι. φύσει γὰρ Ἀνώφοιτα ταυτ’ εἶναι διὰ τὸ μηδενὸς μετέχειν βάρους. Text from Arnim 1903–1905, vol. 1, 27; translation in Algra 1988, 160. 26

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the centre in question is not the centre of the universe at all, but the centre of the (finite) cosmos.27 Lucretius’ first argument, then, simply turns out to be unfounded. Lucretius’ third argument consists in pointing out an internal inconsistency in his rivals’ position. In line 1052 Lucretius still reported that, according to the unnamed rivals, ‘all things press towards the centre of the whole’ (‘in medium summae […] omnia niti’) (my emphasis). Now, in lines 1083–1084, we are told that according to these same opponents ‘not all bodies press towards the centre’ (‘non omnia corpora […] in medium niti’) (my emphasis), but only those which make up earth and water, whereas air and fire are naturally centrifugal.28 We do not exactly know how the argument was developed because the relevant portion of Lucretius’ text is lost in a lacuna, but Bailey’s suggestion that Lucretius would have first charged his rivals with inconsistency, and then pointed out that their thesis of centrifugal air and fire undermines the very coherence of the cosmos which their original thesis was meant to safeguard, is quite plausible.29 However, if we compare Lucretius’ criticism with the actual statements of the Stoics, we can see both where it came from, and why it may not be justified. On the one hand, Stobaeus confirms that the Stoics did, in fact, make these two, apparently inconsistent, claims, asserting both that all the elements, including air and fire, show a tendency to move towards the centre, and that air and fire have a natural tendency to move upwards, i.e. away from the centre. On the other hand, however, Stobaeus’ testimony also shows that, in reality, these two claims are neither inconsistent with each other nor deserving of Lucretius’ criticism, since Stobaeus clearly states that the centrifugal tendency of air and fire is only secondary and subordinate to their centripetal tendency, and will not take them beyond the confines of the cosmos. On the basis of this and other testimonies some commentators ascribe to the Stoics a version of the ancient extrusion or buoyancy theory, according to which lighter bodies, such as those which make up air and fire, have a natural tendency to move downwards (i.e. towards the centre), but are extruded and forced upwards (i.e. away from the centre) against their nature by heavier ones, and hence they will not move beyond the sphere of these heavier elements, but instead position themselves at the periphery.30 Whether or not this interpretation is correct, it at least shows that it would be possible to resolve the apparent inconsistency in a way that the Epicureans could hardly object to, since they themselves endorsed a version of the buoyancy theory, albeit one that did not define

 See e.g. Plutarch, De Stoicorum repugnantiis 44, 1055a 1–2 (SVF II 550, 31–32), quoting Chrysippus: πιθανὸν πᾶσι τοῖς σώμασιν εἶναι τὴν πρώτην κατὰ φύσιν κίνησιν πρὸς τὸ τοῦ κόσμου μέσον; and Cleomedes 1.1, 91–92: νένευκε γὰρ {sc. ὁ κόσμος} ἐπὶ τὸ ἑαυτοῦ μέσον καὶ τοῦτο ἔχει κάτω, ὅπου νένευκεν. 28  Furley 1989, 189, claims without offering an argument that no such inconsistency is implied: ‘omnia’ in l. 1052 would refer only to bodies that are heavy, and coming from all sides, while ‘omnia corpora’ in l. 1083 would refer to all bodies, both heavy and light. Furley’s claim is supported by Sedley 1998, 79. See, however, Schmidt 1990, 213, and Bakker 2016, 197. 29  Bailey 1947, vol. 2, 787–788. 30  Sambursky 1959, 111; Wolff 1988, 507 et passim; Furley 1989, 192–193; idem 1999, 444–445. For arguments against the attribution of this theory to the Stoics see Bakker 2016, 197–198. 27

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upwards and downwards in centrifocal,31 but in parallel terms. Thus Lucretius’ third argument is dissipated, too. This brings us to Lucretius’ second argument. In lines 1.1074-1080 we read: For all place and space, which we call void, must yield a passage through middle or not-­ middle equally to weights, wherever their movements tend. Nor is there any place in which bodies, when they have come thither, can lose the force of weight and stand still in the void; nor again must that which is void ever give support for anything, but, as its nature craves, it must proceed to give place.32

Here Lucretius points out that, even if it existed, the centre, being a place and hence incorporeal, would not be able to affect bodies in the way the anonymous rivals want it to. This seems to be a legitimate point.33 The Stoics indeed held that a centre was a place or a limit, and that places and limits as such were incorporeal.34 They also held that incorporeal entities were incapable of producing effects in bodies.35 On these matters Stoics and Epicureans could, in fact, see eye to eye.36 Consequently, the centre would not be able to attract bodies to itself or to check their motion. Here, too, however, a closer look at our sources reveals that Lucretius may not quite have captured the Stoic theory. Indeed, although the precise interpretation of the relevant testimonies is disputed, it seems clear that the Stoics did not assign some miraculous power of attraction to the centre, but rather considered the centripetal motion to be the resultant effect of a cohesive force that somehow draws all the parts of the cosmos to each other.37 In other words, the centripetal tendency of bodies is not attributable to the incorporeal centre, but to the corporeal whole to which the

 For the buoyancy theory see Epicurus fr. 276 (in Usener 1887, 196–197) and Lucretius 2.184– 215, with the comments on the same in Bakker 2016, 211–213. ‘Centrifocal’ is a term coined by Furley 1989, 15, 234–235, to describe systems in which ‘up’ and ‘down’ are defined in relation to a centre; for the contrast between centrifocal and parallel dynamics see Bakker 2016, 177–179. 32  Lucretius 1.1074–1080: “omnis enim locus ac spatium, quod inane vocamus, / per medium, per non medium, concedere debet  /  aeque ponderibus, motus quacumque feruntur.  /  nec quisquam locus est, quo corpora cum venere, / ponderis amissa vi possint stare in inani; / nec quod inane autem est ulli subsistere debet, / quin, sua quod natura petit, concedere pergat.” Text and translation from Rouse and Smith 1992, 88–91. 33  A similar point against the Stoic theory is made by Plutarch in De facie in orbe lunae 7, 924b 4–8 and 11, 926a 10 – b 7. 34  On the centre as a place see Plutarch, De facie 6, 923e 5 and 926a 2; on the centre being a limit see ibid. 10, 925e 10–11 and 11, 926b 9 (cf. Aristotle, De caelo 2.13, 293a 33). On the incorporeal nature of place see SVF II 331; on that of limits see SVF II 487 and 488. 35  SVF I 89; II 336, 340, 341, 343, 363, 387: only corporeal things can produce an effect. 36  On place/space/void being incapable of affecting bodies in Epicurean cosmology see e.g. Lucretius 1.437-439, 443 and 2.235-237. Cf. also Sextus Empiricus, Against the Professors 10.221-222 and the scholion to Epicurus, Letter to Herodotus 43. 37  Sambursky 1959, 111–113; Wolff 1988, 505–507; Furley 1989, 8, 192; 1999, 443–448. Another indication that the centripetal tendency was merely a resultant is provided by the later Stoic Cleomedes (1.1, 164–172), who claims that only in spherical bodies the inward tendency of their parts is always directed towards the centre; in oblong bodies, on the other hand, the focus of each part’s motion does not necessarily coincide with the centre of the whole. 31

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individual bodies belong, whence it is communicated to the individual bodies themselves. As a matter of fact, Lucretius even seems to hint at this possibility, perhaps unwittingly, when writing, at 1.1077-1078: “Nor is there any place in which bodies, when they have come thither, can lose the force of weight and stand still in the void.” In these lines he seems to envisage, and reject, the thesis that upon reaching the centre bodies would actively lay down their weight and come to a standstill. Although this account comes closer to the Stoics’ actual theory, Lucretius’ words still betray an Epicurean bias: according to the Stoic theory bodies would stop at the centre not because they lose their weight, but rather because upon reaching the centre their downward or centripetal tendency, which is weight, is fulfilled or actualized. For the Epicureans, on the other hand, downward motion is motion along parallel lines from infinity to infinity, a motion which can neither be ‘laid down,’ nor be checked by the resistance of some immaterial ‘centre.’38 At this point, however, Lucretius has not yet established the Epicurean theory of weight and downward motion, nor would he have been able to, before the Stoic alternative was fully refuted. Moreover, it is not clear on what grounds the Stoic theory is rejected. Evidently the Epicureans could not accept the Stoic theory of centripetal gravity tout court, as this requires a complete contiguity of bodies – Stoics and Epicureans alike rejected the possibility of action at a distance –39 that is at odds with the Epicurean duality of atoms and void. Yet there does not seem to be a cogent reason why bodies could not have an inbuilt tendency to move towards a specific point. After all, the Epicureans themselves endorsed the view that weight is a tendency to move in a certain direction, albeit a motion along parallel lines, and not along lines converging to a single point.40 In reaction against this view Lucretius could have repeated his earlier argument of 1.984-997.41 There he had argued that if the universe had a bottom, all matter would be heaped up there to form one compact and inert mass, putting an end to all activity and change.42 Now, on the assumption of a centripetal downward motion, the ‘centre’ would provide just such a ‘bottom,’ so that the same conclusion would apply. However, I do not believe such a conclusion would be warranted, as it does not seem to take into account a crucial aspect of the Epicurean theory of atomic motion. According to the Epicureans (including Lucretius) the atoms are in constant motion, and when their motion is checked they will simply rebound and continue to move in the opposite direction43: accordingly, even with the assumption of an ­absolute ‘bottom,’ no complete cessation of activity and change would result. Anyway, Lucretius does not invoke this argument against the rival theory.

 For the Epicureans’ endorsement of a parallel downward motion see n15 above.  For the Stoics see Sambursky 1962, 102–103; Long 1986, 160; Wolff 1988, 507, 522. For the Epicureans see Furley 1989, 12, 78; O’Keefe 2005, 80–81. 40  See Konstan 2014, 96. 41  See also Bakker 2016, 208–209. 42  See p. 45 above. 43  Epicurus, Letter to Herodotus 43–44; idem fr. 280 (in Usener 1887, 199); Lucretius 2.80–88. 38 39

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What is more, later on in the De rerum natura, he seems to actually endorse the centrifocal theory that he just rejected. In 5.449-508 Lucretius describes the coming-­ into-­being of our cosmos in terms that strongly suggest that a centripetal gravity is at work.44 In lines 449–454, for instance, we read: For in plain fact firstly all the bodies of earth, because they were heavy and entangled, came together in the centre and all took the lowest place; and the more entangled they came together, the more they squeezed out those particles which could make sea, stars, sun, and moon and the walls of the great world[.]45

The entire process starts with earthy particles moving towards, and settling in, the centre, or “the lowest place,” “because they were heavy and entangled.” As they settle and become even more entangled they squeeze out all the lighter stuffs that will eventually make up the sea, the heavenly bodies and the outer boundary of the cosmos. Later on we learn how in this way ether, which is the lightest element, takes up the highest and outermost region of the cosmos, “fencing in all the rest with greedy embrace,”46 and how the other elements and the individual heavenly bodies take up intermediate positions in proportion to their relative weights. Nowhere in this passage we are told why heavy bodies should move to the centre; Lucretius simply assumes that they do, as if it were natural for them to do so. However, if heavy bodies naturally move towards the centre, but also by definition tend downwards, then ‘to the centre’ and ‘downwards’ must be the same thing, as indeed Lucretius seems to imply, and as was definitely the case in Stoic cosmology.47 In other words, Lucretius’ cosmogony assumes a theory of centripetal gravity that is virtually indistinguishable from the rival theory he rejected earlier. As it turns out, then, none of Lucretius’ three arguments against centripetal gravity seems cogent. Two arguments are simply misguided, while another can be easily circumvented and is, in fact, contradicted by Lucretius himself.

3.2.4  The Status of Lucretius 1.1052-1093 and 5.449-508 In the preceding section we encountered two mutually inconsistent Lucretian passages. In the first of these (1.1052-1093) Lucretius refutes a rival theory that may be attributed to the Stoics. Now, since it is generally assumed that Epicurus himself did not yet engage the Stoics, who had then only recently come into the picture,  For a more extensive discussion of this passage see Bakker 2016, 223–235.  Lucretius 5.449–454: “Quippe etenim primum terrai corpora quaeque,  /  propterea quod erant gravia et perplexa, coibant / in medio atque imas capiebant omnia sedes; / quae quanto magis inter se perplexa coibant, / tam magis expressere ea quae mare sidera solem / lunamque efficerent et magni moenia mundi.” Text and translation (slightly modified) from Rouse and Smith 1992, 412–413. 46  Lucretius 5.457-470 and 498-501. 47  See e.g. Cicero, De natura deorum 2.84, reporting the Stoic view: “in medium locum mundi, qui est infimus.” 44 45

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Lucretius’ anti-Stoic polemic must postdate Epicurus.48 In that case Lucretius’ refutation can be seen as a defence of the orthodox Epicurean position against a challenge that Epicurus himself will not have been aware of. That the passage should be a later addition to Epicurus’ argumentation even seems to be borne out by the order of Lucretius’ account: without any prior reference to the Stoic alternative Lucretius first emphatically concludes that “there is need of an infinite quantity of matter on all sides,”49 and only then sets out to refute the rival theory which threatens to undermine this conclusion. The second passage (5.449-508), by contrast, is hard to reconcile with the orthodox Epicurean view. Whereas Epicurus himself endorses a parallel conception of downward motion, to which Lucretius generally also subscribes, this passage assumes a centripetal downward tendency. Moreover, the account finds no parallel in any other known Epicurean writing. The only parallel passage is found in Aëtius’ Placita 1.4, where a very similar theory is reported without attribution.50 Yet the explicit reference to atoms and to the non-providential nature of the world’s coming-­ into-­being make it clear that the account must be atomistic. Moreover, certain details – weight difference rather than a vortex as the formative principle, and the tenuous rather than heavy nature of the heavenly bodies – clearly place the account on the Epicurean rather than the Democritean side.51 In fact, the theory is Epicurean in every respect other than the assumption of a centripetal instead of parallel gravity. And yet, precisely this assumption makes the theory anomalous within the framework of orthodox Epicurean cosmology, and virtually irreconcilable with the infinity of atoms and worlds.

3.2.5  Provisional Conclusion While in the Letter to Herodotus Epicurus could still confidently claim to have proved, once and for all, the joint infinity of space and bodies, the subsequent appearance of an alternative theory which allowed for a finite amount of matter to remain together in infinite space posed a challenge which later Epicureans had to meet. In Lucretius’ De rerum natura we find an attempt to refute this rival theory and reestablish the orthodox Epicurean position, which in the rest of his work is simply taken for granted. As we have seen, however, Lucretius’ refutation is not entirely convincing. The question arises, therefore, why Lucretius, like most other Epicureans, chose to stick to the orthodox view. An answer may be found in the important consequences of this view, especially with respect to Epicurean theology.  For the early Epicureans’ lack of engagement with Stoic philosophy see Sedley 1998, 73, and especially Kechagia 2010. 49  Lucretius 1.1051: “infinita opus est vis undique materiai.” Text and translation from Rouse and Smith 1992, 86–87. 50  For a comparison of Lucretius’ and Aëtius’ cosmogonical accounts, see Bakker 2016, 224–227. 51  Spoerri 1959, 8–29; Bakker 2016, 226–227. 48

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3.3  Theological Consequences of the Infinity of the Universe The infinity of the universe and its two component parts appears to have some remarkable consequences. Firstly, it spawns an infinity of other worlds beside the one we inhabit; secondly, it makes the spontaneous coming-into-being of a world not merely possible but necessary; and, finally, it allows for the simultaneous truth of multiple, even mutually incompatible, explanations. What is more, all these corollaries have been argued by Epicurus himself or by his modern interpreters to be crucial, in one way or another, to the Epicurean mission to free the world from divine intervention. If it can be shown that they are, indeed, crucial, this might explain why the Epicureans were so committed to the infinity of the universe, and had to defend this view against rival theories. In the following part I will discuss each of these corollaries of the infinity of space and bodies, with special attention to their theological aspects. First, however, it will be expedient to give some account of the Epicurean concept of divinity, to serve as a background for the following discussion of infinity.

3.3.1  The Epicurean Concept of Divinity The most important thing to know about the gods, according to Epicurus, is that they are not involved in the creation and administration of the world or any of its parts in any way. This does not mean that they do not exist, for we do have a preconception of them – a preconceived notion resulting from repeated impressions, such as occur to us in dreams.52 This preconception not only tells us that the gods exist, but also that they are immortal and blissful.53 And since, being perfectly blissful, the gods have neither need nor care for anything besides themselves, any involvement on their part in the creation and governance of the world or any part thereof must be rejected.54 In addition to this conceptual proof of the gods’ inactivity with respect to the world, the Epicureans also had a store of empirical arguments to bolster their view. Since the opposite view was often supported by some form of the argument from design, in which the observation of functional and orderly structures in the world led to the assumption of a grand design and hence a designer god, the Epicureans could simply point to the many instances of disorderly and useless, or even harmful, things and phenomena in order to disprove the idea of such a grand design.55 To the  Cicero, De natura deorum 1.43–44; Epicurus, Letter to Menoeceus 123–124. For gods appearing in dreams see Lucretius 5.1169-1171 53  Cicero, De natura deorum 1.45; Epicurus, Letter to Menoeceus 123–124. Cf. Lucretius 5.1175-1182. 54  Epicurus, Letter to Herodotus 76 and 81; idem, Letter to Pythocles, 97; Cicero, De natura deorum 1.51-53; Lucretius 5.156-173 55  Lucretius 5.195-234. Cf. Diogenes of Oenoanda “Theological Physics-sequence” (= NF 167 + NF 126/127 + fr. 20 + NF 182), cols. XIV-XVI, in Hammerstaedt and Smith 2014, 263–270. 52

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Epicureans it was evident, therefore, that the gods neither created nor took care of the world or any of its parts or inhabitants. It is with this view of the gods in mind that we will now look into some corollaries of the infinity of bodies and space.

3.3.2  Infinite Worlds and the Demiurge One consequence of the infinity of atoms is the existence of not just a plurality, but even an infinity of worlds. In Letter to Herodotus 45, Epicurus writes: Furthermore, there are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number, as was proved already, are borne on far out into space. For those atoms, which are of such nature that a world could be created out of them or made by them, have not been used up either on one world or on a limited number of worlds, nor again on all the worlds which are alike, or on those which are different from these. So that there nowhere exists an obstacle to the infinite number of the worlds.56

In this passage Epicurus seems to take on Plato, who in Timaeus 32c-d states that the composition of our world used up all the elements, leaving nothing outside, and in Timaeus 55c-d, conceding that there might be more than one world – say, five – still emphatically rejects the notion that there might be infinitely many.57 Epicurus’ statement is repeated by Lucretius, De rerum natura 2.1048-1066, who then adds the following argument: Besides, when abundant matter is ready, when space is to hand, and no thing and no cause hinders, things must assuredly be done and completed. And if there is at this moment both so great store of seeds as all the time of living existence could not suffice to tell, and if the same power and the same nature abides, able to throw the seeds of things together in any place in the same way as they have been thrown together into this place, then you are bound to confess that there are other worlds in other regions and different races of men and generations of wild beasts.58

If the atoms were able to form a cosmos in this part of the universe they must have been able to do so elsewhere, and given the infinity of the universe, a possibility

56  Epicurus, Letter to Herodotus 45: Ἀλλὰ μὴν καὶ κόσμοι ἄπειροί εἰσιν, οἵ θ’ ὅμοιοι τούτῳ καὶ Ἀνόμοιοι. αἵ τε γὰρ ἄτομοι ἄπειροι οὖσαι, ὡς ἄρτι Ἀπεδείχθη, φέρονται καὶ πορρώτατω· οὐ γὰρ κατανήλωνται αἱ τοιαῦται ἄτομοι, ἐξ ὧν ἂν γένοιτο κόσμος ἢ ὑφ’ ὧν ἂν ποιηθείη, οὔτ’ εἰς ἕνα οὔτ’ εἰς πεπερασμένους, οὔθ’ ὅσοι τοιοῦτοι οὔθ’ ὅσοι διάφοροι τούτοις. ὥστε οὐδὲν τὸ ἐμποδοστατῆσόν ἐστι πρὸς τὴν Ἀπειρίαν τῶν κόσμων. Translation in Bailey 1926, 25. 57  See also Plato, Timaeus 31a–b. 58  Lucretius 2.1067-1076: “Praeterea cum materies est multa parata, / cum locus est praesto, nec res nec causa moratur / ulla, geri debent nimirum et confieri res. / nunc et seminibus si tanta est copia quantam  /  enumerare aetas animantum non queat omnis,  /  visque eadem et natura manet, quae semina rerum / conicere in loca quaeque queat simili ratione / atque huc sunt coniecta, necesse est confiteare / esse alios aliis terrarum in partibus orbis / et varias hominum gentis et saecla ferarum.” Text and translation in Rouse and Smith 1992, 178–179.

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cannot fail to be realised, and not once, but infinitely many times. Hence there must be an infinity of worlds. Lucretius’ conclusion rests upon the application of two principles: the principle of uniformity, which assumes that the same circumstances obtain always and everywhere,59 and a version of the so-called principle of plenitude, which states that whatever can be done, will be done at some time or place.60 Having concluded that there are infinitely many worlds, Lucretius proceeds to use this conclusion as a premise in his argument against the notion of a divinely governed universe: If you hold fast to these convictions, nature is seen to be free at once and rid of proud masters, herself doing all by herself of her own accord, without the help of the gods. For I appeal to the holy hearts of the gods, which in tranquil peace pass untroubled days and a life serene: who is strong enough to rule the sum of the immeasurable, who to hold in hand and control the mighty bridle of the unfathomable? who to turn about all the heavens at one time and warm the fruitful worlds with ethereal fires, or to be present in all places and at all times[.]61

Lucretius’ conclusion takes the form of a series of rhetorical questions which invite the answer ‘nobody’: nobody is strong enough to rule and control an infinite number of worlds, and nobody is able to be present always and everywhere throughout the infinite expanse of time and space. However, as James Warren notes, this is not a particularly strong argument.62 Several responses come to mind that would avoid Lucretius’ desired conclusion that infinite worlds rule out divine intervention. It might be suggested, for instance, that each world is governed individually by its own god. In Lucretius’ defence, David Sedley points out that even those of Lucretius’ opponents who were willing to assume a plurality of gods still assumed a single overall command by a supreme deity, and would thus, after all, be subject to Lucretius’ implied criticism.63  See e.g. Darling 2016, 416, and Mash 1993, 209, who explicitly identifies ‘uniformitarianism’ as one of the assumptions underlying the Lucretian argument. 60  The ‘Principle of Plenitude’ was first described by Lovejoy 1936, 52 et passim. For the attribution of this principle to the ancient atomists see e.g. Dick 1996, 12–13; Fowler 2002, 368–369; Sedley 2007, 138; 2013, ch. 4 (ad 5.416-770); Darling 2016, 329; and Bakker 2016, 21–24, 28–31, 74, 210. Versions of Lucretius’ argument – e.g. Drake’s Equation – are still invoked today by those arguing for the likely existence of extra-terrestrial life and intelligence: see e.g. Mash 1993, and Darling 2016, 329. For Bruno’s application of the principle see Section 8.2 of Granada’s Chapter 8 in this volume. 61  Lucretius 2.1090–1099: “Quae bene cognita si teneas, natura videtur / libera continuo, dominis privata superbis, / ipsa sua per se sponte omnia dis agere expers. / nam pro sancta deum tranquilla pectora pace, / quae placidum degunt aevom vitamque serenam, / quis regere immensi summam, quis habere profundi / indu manu validas potis est moderanter habenas, / quis pariter caelos omnis convertere et omnis / ignibus aetheriis terras suffire feracis, / omnibus inve locis esse omni tempore praesto.” Text and translation in Rouse and Smith 1992, 178–181. 62  Warren 2004, 363–364. See also Sedley’s critical response in Sedley 2007, 148–149. 63  Sedley 2007, 149 n33, cites Xenophon, Memorabilia 4.3.13, where “he who organizes and holds together the whole world” (my translation) is singled out over the other gods. One might also think 59

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One might also respond that god is, in fact, strong enough to rule the infinite. In Lucretius’ defence, David Sedley points out that this would imply an infinitely extended god, a view which the Epicureans attributed to certain Presocratic philosophers, and which they strongly opposed, on the grounds that this would make it impossible for god to experience sensation, due to the lack of bodily extremities to sense with.64 Perhaps, however, we do not even need to suppose that such a criticism was implied. Lucretius’ most obvious opponents in the present context are not the Presocratics, but thinkers like Plato and the Stoics, who equated infinity with indeterminacy and imperfection, which have no place in divine creation65; and who therefore emphasized the limited and finite nature of the created world.66 It was not until the third century A.D. that, among Neoplatonists and Christians, infinity began to be seen as perfection and a fitting attribute for a god.67 In short, Lucretius’ argument is aimed at thinkers who not only believe in a divine involvement with the universe, but also think that this involvement needs to be a unified and limited affair. Although, at first sight, this assumption seems to rescue Lucretius’ anti-­ interventionist argument from such responses as were suggested above, it actually undermines his argument even further. Lucretius’ argument is based on the infinity of worlds, a theory which in turn relies, among other things, on the application of the principle of uniformity  – the assumption that the same circumstances apply everywhere. The validity of this assumption may be obvious if one adopts the Epicurean view of a universe filled with atoms that all obey the same physical laws, and hence may be assumed to produce the same effects everywhere. If, on the other hand, one adopts the theory that the world is created by a supreme deity, and that this act of creation is necessarily both unique and limited, it is clear that this result cannot be applied universally: even in an infinite universe filled with infinite matter the creation of one cosmos in no way implies the creation of another, let alone of an of Plato’s Timaeus 40a–d, where the lesser, created gods are said to partake in the creation of the world at the Demiurge’s behest. In fact, several centuries after Epicurus, in the second century AD, the Platonist Plutarch, conceding that there might, in fact, be more than one world (though not infinitely many), suggests that while each world might be governed by its own supreme deity, all the worlds together would still be subject to the single rule and reason of one divine overlord (Plutarch, De defectu oraculorum 29, 425f2 – 426b1). 64  Sedley 2007, 149, citing the Epicurean arguments reported by Cicero in De natura deorum 1.26–28. 65  On Plato see Clarke 1994, 70–72, who specifically quotes Plato’s Philebus 16–18, 23c–30, 61–67; Statesman 283b–285a; Laws 716c; Sophist 265e. For Plato’s application of the notion of limit to the creation of the world see Plato Timaeus 31a-b, 32c-33a, 55c-d. For the Stoics, see Plutarch, De communibus notitiis 30, 1074b7-c3 (SVF II 525, p. 167.28 – 168.1), which links infinity to indeterminacy, incompletion and disorderliness; Sextus Empiricus, Against the Professors 9.148–149, which rehearses a Stoic argument for the limited nature of the divine; and Cleomedes 1.1, 7–17 (SVF II 534), which emphasises the limited nature of the created world. 66  Even Plutarch, while admitting a plurality of worlds (see n63 above), still stresses the finitude of nature (Plutarch, De defectu oraculorum 24, 423c7-11 and 25, 424a8-12) and god (ibid. 30, 426d8-10). 67  Clarke 1994, 75–79.

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infinite number of others.68 Therefore, Lucretius’ argument against divine intervention will convince only those who are already convinced that worlds do not come about due to divine intervention.

3.3.3  Chance and the Power of Infinity What the Epicureans had to do, therefore, was to show that the world could have come into being even without divine intervention, as a result of mere chance. Now, that such an orderly and complex structure as our world should arise by chance seems exceedingly unlikely. The odds are dramatically increased, however, if infinity is brought into play: according to the principle of plenitude, given infinite opportunity, everything that is possible must be realised. Accordingly, even without divine intervention, the infinity of the universe makes the coming-into-being of a world like ours not only possible but even inevitable.69 However, as James Warren notes, for this conclusion to obtain the Epicureans did not have to postulate the infinity of matter and space; the infinity of time alone, which the Epicureans commonly accepted, would suffice to guarantee that any possible configuration would be realized, and not once, but infinitely many times.70 What is more, in the two passages where Lucretius actually applies the principle of plenitude to the formation of the cosmos (1.1021–1028 and 5.419–431), he only refers to the infinity of time, not of matter and space. I quote the second passage, which is the clearest in this respect: For certainly it was no design of the first-beginnings that led them to place themselves each in its own order with keen intelligence, nor assuredly did they make any bargain what motions each should produce; but because many first-beginnings of things in many ways, struck with blows and carried along by their own weight from infinite time up to the present, have been accustomed to move and to meet in all manner of ways, and to try all combinations, whatsoever they could produce by coming together, for this reason it comes to pass that being spread abroad through a vast time, by attempting every sort of combination and motion, at length those come together which, being suddenly brought together, often become the beginnings of great things, of earth and sea and sky and the generation of living creatures.71

68  So also Asmis 1984, 66 n19: “a demiurge would provide a reason why the number of possibilities should be restricted to a single possibility.” 69  For a lucid and very attractive exposition of this theory, see Sedley 2007, 137–139 and 155–166. 70  Warren 2004, 364, citing David Hume’s Dialogues Concerning Natural Religion, part 8. For the Epicureans’ implicit endorsement of the infinity of time see Sedley 1999, 373. 71  Lucretius 5.419-431: “nam certe neque consilio primordia rerum / ordine se suo quaeque sagaci mente locarunt / nec quos quaeque darent motus pepigere profecto, / sed quia multa modis multis primordia rerum / ex infinito iam tempore percita plagis / ponderibusque suis consuerunt concita ferri  /  omnimodisque coire atque omnia pertemptare,  /  quaecumque inter se possent congressa creare,  /  propterea fit uti magnum volgata per aevom,  /  omne genus coetus et motus experiundo, / tandem conveniant ea quae convecta repente / magnarum rerum fiunt exordia saepe, / terrai maris et caeli generisque animantum.” Text and translation in Rouse and Smith 1992, 410–413 (my emphasis).

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The same observation applies to Epicurus as well, who, according to one ancient testimony, stated that “nothing unfamiliar comes about in the universe, due to the infinity of time that has already passed.”72 In short, although it is often stated that the infinity of the universe was a necessary part of the Epicureans’ anti-teleological argument, the argument actually works just as well on the assumption of infinite time, and was, in fact, applied in this way by Lucretius and Epicurus themselves.

3.3.4  Infinity and the Truth of Multiple Explanations The Epicurean theory of infinite worlds also carries important epistemological consequences. In astronomical and meteorological matters the Epicureans famously prescribed the use of multiple explanations to account for each phenomenon, instead of just one.73 This might just be considered a kind of epistemic modesty: since in such matters the evidence does not allow us to discriminate between various explanations, all explanations that agree with the observations and do not violate the general principles of Epicurean physics must be retained. However, there is ample evidence that the Epicureans went beyond a mere sceptical affirmation of doubt. They did not doubt which of the accepted explanations was true: they were adamant that all accepted explanations – even mutually incompatible ones – were true.74 But how could the Epicureans assert the simultaneous truth of multiple explanations? Lucretius offers the following argument (DRN 5.526-533): For which of these causes holds in our world it is difficult to say for certain; but what may be done and is done through the whole universe in the various worlds made in various ways, that is what I teach, proceeding to set forth several causes which may account for the movements of the stars throughout the whole universe; one of which, however, must be that which gives force to the movement of the signs in our world also; but which may be the true one, is not his to lay down who proceeds step by step.75

There may be doubt as to which cause is operative in our world, but this does not mean that other explanations are not true: in the infinity of the universe every possible explanation must be actualized somewhere, and in this sense every possible

 Epicurus fr. 266 (in Usener 1887, 191) = ps.-Plutarch, Stromateis 8: οὐδὲν ξένον ἐν τῷ παντὶ Ἀποτελεῖται παρὰ τὸν ἤδη γεγενημένον χρόνον ἄπειρον (translation mine). 73  For an overview see e.g. Taub 2009, 110–112, 115, 120–123. 74  On the truth of multiple explanations see Striker 1974; Sedley 1982, 263–272; Asmis 1984, 178–180, 193–196, 211, 321–336; Long and Sedley 1987a, 90–97; Asmis 1999, 285–294; Allen 2001, 194–205 and 239–241; Bénatouïl 2003, 42–44; Verde 2013, 134–135; Bakker 2016, 13–31. 75  Lucretius 5.526–533: “Nam quid in hoc mundo sit eorum ponere certum / difficile est; sed quid possit fiatque per omne / in variis mundis varia ratione creatis, / id doceo, plurisque sequor disponere causas, / motibus astrorum quae possint esse per omne; / e quibus una tamen siet hic quoque causa necessest / quae vegeat motum signis; sed quae sit earum / praecipere haudquaquamst pedetemptim progredientis.” Text and translation from Rouse and Smith 1992, 418–419. 72

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explanation is also true. This is yet another application of the principle of plenitude. This method of multiple explanations was the Epicureans’ response to the dogmatic certainty with which other philosophers propounded single explanations. A sceptic detachment would not do, because this would leave open the possibility that the other philosophers were right after all. The Epicureans therefore countered the dogmatic assertion of single explanations with an equally dogmatic assertion of a multiple account.76 But why would the Epicureans want to oppose single explanations in the first place? As Epicurus himself repeatedly states, the principal reason for engaging in physical inquiry is to exclude the divine from the workings of nature, see e.g. Epicurus’ Letter to Herodotus 76–77: Furthermore, the motions of the heavenly bodies and their turnings and eclipses and risings and settings, and kindred phenomena to these, must not be thought to be due to any being who controls and ordains or has ordained them and at the same time enjoys perfect bliss together with immortality (for trouble and care and anger and kindness are not consistent with a life of blessedness, but these things come to pass where there is weakness and fear and dependence on neighbours).77

Elsewhere, too, Epicurus enjoins his reader not to resort to myth.78 However, if physical inquiry is all about excluding myth and divine intervention, why is one naturalistic explanation not enough?79 The answer to this question may be found in a number of passages in Epicurus’ Letter to Pythocles. In §87, for instance, Epicurus writes: But whenever one accepts one explanation while rejecting another that harmonizes just as well with the phenomenon, it is clear that one falls from scientific inquiry altogether and is plunged into myth.80

According to Epicurus, providing a single explanation when other explanations are equally plausible is in itself a kind of myth. But why should a single explanation amount to myth? Another relevant passage that may provide some further clues is §113:  See Warren 2004, 361: “With the addition of the conception of infinite kosmoi the Epicureans can claim not only that one of the possible explanations is the true one but that in fact all of them are true. In this way they can hope to bridge the gap between offering multiple merely possible explanations and the provision of sure, tranquillity-producing, conviction.” 77  Epicurus, Letter to Herodotus 76–77: Καὶ μὴν ἐν τοῖς μετεώροις φορὰν καὶ τροπὴν καὶ ἔκλειψιν καὶ Ἀνατολὴν καὶ δύσιν καὶ τὰ σύστοιχα τούτοις μήτε λειτουργοῦντός τινος νομίζειν δεῖ γίνεσθαι καὶ διατάττοντος ἢ διατάξαντος καὶ ἅμα τὴν πᾶσαν μακαριότητα ἔχοντος μετὰ Ἀφθαρσίας· οὐ γὰρ συμφωνοῦσι πραγματεῖαι καὶ φροντίδες καὶ ὀργαὶ καὶ χάριτες μακαριότητι, Ἀλλ’ ἐν Ἀσθενείᾳ καὶ φόβῳ καὶ προσδεήσει τῶν πλησίον ταῦτα γίνεται. Translation in Bailey 1926, 49. 78  Epicurus, Letter to Pythocles 104.3: μόνον ὁ μῦθος Ἀπέστω. Cf. ibid. 115.8. 79  Similarly Verde 2013, 130. 80  Epicurus, Letter to Pythocles 87: ὅταν δέ τις τὸ μὲν Ἀπολίπῃ τὸ δὲ ἐκβάλῃ ὁμοίως σύμφωνον ὂν τῷ φαινομένῳ, δῆλον ὅτι καὶ ἐκ παντὸς ἐκπίπτει φυσιολογήματος, ἐπὶ δὲ τὸν μῦθον καταρρεῖ. Translation mine. 76

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But to assign a single cause for these phenomena, when the phenomena call for a plural account, is madness, and is unfittingly practised by those who are devoted to idle astronomy and vainly assign causes for certain phenomena, since (ὅταν) they do not free divine nature in any way from the burden of responsibilities.81

Providing single explanations for celestial phenomena is typically practised by devotees of astronomy – not just professional astronomers, but also those who accepted and incorporated the astronomers’ findings into their own cosmologies, like Plato, Aristotle and the Stoics.82 However, Epicurus’ criticism is not limited to these devotees of astronomy, but also applies to others who provide single explanations when the phenomena call for several, whether one is dealing with astronomical or atmospheric occurrences. Nor should the explanations provided by these devotees of astronomy and other proponents of single causes be spurned as such: this is made clear by the inclusion of many such views in Epicurus’ and Lucretius’ lists of multiple explanations.83 Apparently these views are only objectionable in so far as they are claimed to be uniquely true. But why would this be objectionable? The answer to this question is given in the concluding, subordinate clause of the cited passage. Unfortunately, the Greek here presents an ambiguity. According to Liddell and Scott’s Greek-English Lexicon, ὅταν, the conjunction which starts the clause, normally means “whenever, with a conditional force.”84 Yet if the conjunction is taken in this sense, one might conclude that assigning single causes is okay after all, as long as the gods are not involved. This would be a very weak conclusion after Epicurus’ insistence on the need for multiple explanations both in the present passage and throughout the Letter to Pythocles, and would also be at odds with the previously quoted passage (from §87), where rashly opting for a single explanation (apparently regardless of its content) was equated to myth. However, Liddell and Scott also report a second meaning. Occasionally, ὅταν is also used in a causal sense (attested from Aristotle onwards), which may be rendered as ‘since.’85 If we take the conjunction in this sense, the final clause turns out to provide the very answer we were looking for: assigning single causes, when the phenomena call for several, is wrong, because this would imply divine involvement in the world. This conclusion seems to be confirmed by §97: And divine nature must not be applied to these things in any way, but must be preserved unburdened by responsibilities and in complete blessedness. For if this practice is not observed the entire inquiry into the causes of celestial phenomena will be idle, as it has already been for certain people who have not clung to the possible method, but have fallen back into idle talk by believing that things only happen in one way, and rejecting all other 81  Epicurus, Letter to Pythocles 113: τὸ δὲ μίαν αἰτίαν τούτων Ἀποδιδόναι, πλεοναχῶς τῶν φαινομένων ἐκκαλουμένων, μανικὸν καὶ οὐ καθηκόντως πραττόμενον ὑπὸ τῶν τὴν ματαίαν Ἀστρολογίαν ἐζηλωκότων καὶ εἰς τὸ κενὸν αἰτίας τινῶν Ἀποδιδόντων, ὅταν τὴν θείαν φύσιν μηθαμῇ λειτουργιῶν Ἀπολύωσι. Translation (and emphasis) mine. 82  See Bakker 2016, 57. 83  For the incorporation of the astronomers’ views in Epicurus’ and Lucretius’ lists of alternative explanations, see Bakker 2016, 42–58. 84  Liddell and Scott 1940, 1264, lemma ὅταν. 85  Admittedly, the use of ὅταν in this sense is otherwise unattested in Epicurus’ works.

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Although the statement is quite convoluted, it seems to imply that those “people who […] have fallen back into […] believing that things only happen in one way” have thereby failed to observe the practice of preserving divine nature “unburdened by responsibilities and in complete blessedness.” In short, according to Epicurus, assigning single explanations to celestial phenomena in itself (i.e. regardless of the content of each explanation) already amounts to involving the gods in the workings of nature. Why this should be so is not stated clearly anywhere by Epicurus. However, his explicit reference to the devotees of astronomy in §113 suggests that his quarrel is not so much with those who provide single causes on one or two occasions, but with those who do so systematically, like professional astronomers and their followers. Elsewhere I have argued, on the basis of the above and other passages, that Epicurus was opposed to the astronomers and their followers because of their groundless reliance on a preconceived theoretical model in which phenomena were accounted for with single explanations according to a unified explanatory principle.87 It was the belief in these general explanatory theories, often illustrated by means of tangible mechanical models,88 that Epicurus especially opposed, considering them to be nothing more than “empty assumptions and arbitrary principles,”89 without a firm basis in the phenomena. Moreover, by embracing these models the devotees of astronomy grant the world an amount of coherence and regularity that seems to point to an overall design.90 In fact, both Plato and the Stoics explicitly link the orderly nature of the world, and especially the heavenly sphere, to its being designed by a god. In Timaeus 34b-40d, Plato describes how the Demiurge successively created the heavens, the celestial orbits, and finally the heavenly bodies themselves as living gods, according to a single coherent and intelligent plan, the details of which can only be understood by the use of visible models; and in Laws 820e-822c he prescribes the study of astronomy in order to eradicate the erroneous and blasphemous view that the planets, being gods, should wander about aimlessly. The Stoics even made the order and

86  Epicurus, Letter to Pythocles 97: καὶ ἡ θεία φύσις πρὸς ταῦτα μηδαμῇ προσαγέσθω, Ἀλλ’ Ἀλειτούργητος διατηρείσθω καὶ ἐν τῇ πάσῃ μακαριότητι. ὡς εἰ τοῦτο μὴ πραχθήσεται ἅπασα ἡ τῶν μετεώρων αἰτιολογία ματαία ἔσται, καθάπερ τισὶν ἤδη ἐγένετο οὐ δυνατοῦ τρόπου ἐφαψαμένοις, εἰς δὲ τὸ μάταιον ἐκπεσοῦσι τῷ καθ’ ἕνα τρόπον μόνον οἴεσθαι γίνεσθαι, τοὺς δ’ ἄλλους πάντας τοὺς κατὰ τὸ ἐνδεχόμενον ἐκβάλλειν, εἴς τε τὸ Ἀδιανόητον φερομένους καὶ τὰ φαινόμενα ἃ δεῖ σημεῖα Ἀποδέχεσθαι μὴ δυναμένους συνθεωρεῖν. Translation mine. 87  Bakker 2016, 32–33, 263, 266–267; see also 57–58. 88  On the use of mechanical models in astronomy see Cornford 1935, 74–76; and Evans 1998, 78–84. On Epicurus’ opposition to this practice see Sedley 1976, 32, 37–39. 89  Epicurus, Letter to Pythocles 86: Οὐ γὰρ κατὰ Ἀξιώματα κενὰ καὶ νομοθεσίας φυσιολογητέον, Ἀλλ’ ὡς τὰ φαινόμενα ἐκκαλεῖται. Translation in Bailey 1926, 59. 90  Similarly Verde 2013, 131, 135.

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regularity of the celestial motions a prime exhibit in their argument from design, likening the heavenly sphere to a man-made orrery.91 In this way the systematic application of single explanations could be taken to imply a belief in divine creation, to which the systematic and dogmatic assertion of multiple explanations would provide an effective antidote. However, in order to perform this function, each of these multiple explanations has to be not merely possible, but actually true. And this is where, as we have seen, the infinity of worlds comes in: the principle of plenitude stipulates that in the infinity of the universe every possible explanation must be true somewhere. However, to this line of reasoning several objections can be made. Firstly, one might call into question whether single explanations really do imply divine governance. Epicurus may have believed so, but Lucretius, in those passages where he either expounds or applies the method of multiple explanations, never claims that multiple explanations as such are necessary to eliminate divine intervention. In fact, on several occasions where one might have expected a multiple account, Lucretius is content to give a single explanation, apparently without fearing thereby to make the gods responsible. A later Epicurean, Diogenes of Oenoanda, even gives up on the simultaneous truth of multiple explanations altogether, claiming instead that, “while all explanations are possible, this one is more plausible than that,” without worrying about theological consequences.92 Secondly, even if one accepts that the dogmatic assertion of multiple explanations is necessary to rule out divine involvement, one might still doubt whether a plurality of worlds is required to guarantee the truth of each individual explanation. In a recent article Francesco Verde has suggested that Lucretius may not have rendered Epicurus’ thought adequately in this respect.93 While emphasizing  – even more clearly than Epicurus himself  – the truth of every given explanation in the universe at large, Lucretius at the same time seems to slip right back into the scepticism that Epicurus wanted to avoid, by stressing that in this world only one ­explanation applies, although we do not know which one. Since in similar contexts Epicurus himself never refers to other worlds, the various individual explanations should be thought of as true even within this world: compatible explanations could be true at the same time, while incompatible ones may still be true sequentially. If Verde is right, then however important the method of multiple explanations may have been to demythologize the world, the infinity of the universe may not have played any part in it.

 Cicero, De natura deorum II 88.  Diogenes of Oenoanda fr.13 iii 10–12 (in Smith 1993, 171). For the epistemological import of this passage see Verde 2013, 136–137; Bakker 2016, 37–42, 242; Leone 2017, 97–100; and especially Corsi 2017, 277–282. 93  Verde 2013, 139–141. See also Corsi 2017, 262–263. 91 92

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3.3.5  Summary Although the infinity of atoms, and consequently of worlds, appears as a premise in several actual or presumed Epicurean arguments against divine intervention, it turns out to be neither sufficient nor necessary to arrive at the desired conclusion. True, the infinity of worlds rules out divine intervention (at least as conceived by Plato and the Stoics), but this can only be established after divine intervention has been ruled out already. True, the joint infinity of atoms and void guarantees that any configuration of atoms, including our cosmos, will be realized even without divine intervention, but so does the infinity of time, and, in fact, the Epicureans only invoked the latter. True, the infinity of worlds would ensure that every objectively possible explanation is also true, as Lucretius claims; but it is debatable, firstly, to what extent Epicurus himself used or needed the infinity of worlds to account for the truth of multiple explanations; secondly, to what extent later Epicureans still endorsed the truth of multiple explanations, as opposed to their mere possibility or probability; and thirdly, to what extent later Epicureans were still committed to the thesis that divine intervention can only be eliminated by multiple, as opposed to single, naturalistic explanations. In sum, there is no reason to assume that the Epicureans had strong theological motives for positing and upholding the joint infinity of atoms and void.

3.4  Conclusion In this chapter I have tried to establish why the Epicureans, in contrast to every other ancient school of philosophy, posited an infinite amount of matter. I have approached this question from two different angles. In the first half of the chapter the physical arguments for the infinity of matter were discussed. In both Epicurus’ Letter to Herodotus and Lucretius’ De rerum natura the infinite number of atoms is inferred from the infinity of space, on the assumption that a finite number of atoms would be scattered abroad and not be able to meet and produce anything. For Epicurus this was the end of the matter, but later Epicureans had to deal with a rival theory that threatened to undermine the Epicurean argument: by assuming a theory of centripetal gravity the Stoics were able to account for the infinity of space without the need for a corresponding infinity of matter. Lucretius offers a refutation of the Stoic view, but his counter-arguments appear to be either unfounded or unconvincing, and are further undermined by Lucretius’ implicit endorsement, later on in his work, of centripetal gravity. In the second half of the chapter I have looked at the question from another point of view. If the physical arguments are not strong enough to prove the infinity of atoms, the Epicureans may have had other – theological and ethical – motives to uphold this thesis. In the writings of Epicurus and Lucretius several arguments are found or are thought to be implied in which the infinity of matter rules out divine

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intervention in the world. However, as we have just seen, none of these arguments holds up to scrutiny. The somewhat disappointing conclusion is that the Epicurean endorsement of the infinity of matter, and hence of worlds, was warranted neither by physical nor by ethical considerations. Epicurus himself, blissfully ignorant of the challenge that would be posed by the Stoics, may still have believed that his proof of the infinity of atoms was conclusive, and hence could be used, perhaps not as sufficient, but at least as supporting evidence against divine intervention. Later Epicureans, however, felt obliged to defend a thesis that was neither consequent upon the principles of Epicurean physics, nor antecedent to the main doctrines of Epicurean ethics, but one that nevertheless had become a defining tenet of their sect.94

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———. 1998. Lucretius and the Transformation of Greek Wisdom. Cambridge: Cambridge University Press. ———. 1999. Hellenistic Physics and Metaphysics. In The Cambridge History of Hellenistic Philosophy, ed. Keimpe Algra, Jonathan Barnes, Jaap Mansfeld, and Malcolm Schofield, 355– 411. Cambridge: Cambridge University Press. ———. 2007. Creationism and its Critics in Antiquity. Berkeley: University of California Press. ———. 2013. Lucretius. In The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), ed. Edward N. Zalta. https://plato.stanford.edu/archives/fall2013/entries/lucretius/. Smith, Martin F. 1993. Diogenes of Oinoanda: The Epicurean Inscription. Naples: Bibliopolis. Spoerri, Walter. 1959. Späthellenistische Berichte über Welt, Kultur und Götter: Untersuchungen zu Diodor von Sizilien. Basel: Friedrich Reinhardt. Striker, Gisela. 1974. Κριτήριον τῆς Ἀληθείας. Nachrichten der Akademie der Wissenschaften zu Göttingen I. Philologisch-Historische Klasse 2: 48–110. Taub, Liba. 2009. Cosmology and Meteorology. In The Cambridge Companion to Epicureanism, ed. James Warren, 124. Cambridge: Cambridge University Press. Traphagan, John. 2015. Extraterrestrial Intelligence and Human Imagination: SETI at the Intersection of Science, Religion and Culture. Cham: Springer. Usener, Hermann. 1887. Epicurea. Leipzig: Teubner. Verde, Francesco. 2013. Cause epicuree. Antiquorum Philosophia 7: 127–142. Warren, James. 2004. Ancient Atomists on the Plurality of Worlds. The Classical Quarterly 54 (2): 354–365. Wolff, Michael. 1988. Hipparchus and the Stoic Theory of Motion. In Matter and Metaphysics: Fourth Symposium Hellenisticum (Elenchos 14), ed. Jonathan Barnes and Mario Mignucci, 346–419. Naples: Bibliopolis.

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Chapter 4

Space and Movement in Medieval Thought: The Angelological Shift Tiziana Suarez-Nani

Oportet hic considerare de loco eorum [sc. substantiarum spiritualium], quod non habet aliquid difficilius se in tota speculatione sapientiae. Here it is necessary to take into account their place [sc. of spiritual substances]: nothing is more difficult in the whole speculation of wisdom. Roger Bacon, Opus tertium, c. XLVII in Roger Bacon 1859, Chap. 6, 172.

Abstract  This paper explores the contribution of medieval metaphysics to the development of the theories of space and movement through an investigation of some metaphysical conceptions of the late thirteenth and early fourteenth centuries. If treatises on the philosophy of nature – especially the commentaries on Aristotle’s Physics and De caelo  – generally provided the theoretical context for notions of place, location and space in medieval thought, medieval thinkers also examined these notions in a metaphysical context in order to explain the relationship between immaterial substances (souls, angels and God) on one hand, and the space of the physical World on the other. This paper outlines three different medieval modalities of location: the circumscription of bodies, divine ubiquity, and the delimitation of souls and angels. On the basis of these modalities, medieval thinkers developed two types of explanation for the location of created immaterial substances: firstly, location through operations, and secondly, location through the being. According to these models, space is an external (first model) or internal property of the being itself (second model). These conceptions bear important consequences on the theo-

I would like to thank the editors for their careful reading of this article, their remarks on the same, and suggestions for improvement. All translations are the author’s except where otherwise noted. T. Suarez-Nani (*) University of Fribourg, Fribourg, Switzerland e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_4

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ries of movement, especially those focusing on the movement of indivisibles (that is, non-extended substances like spirits) in the physical extended space. In this ­context medieval thinkers intensely discussed the possibility of instantaneous movement and elaborated a complex notion of resistance as crucial to each movement in the world.

4.1  Introduction The importance of medieval conceptions of space and place in the genesis of early modern physics is, by now, a well-documented fact. Over the last two decades numerous works have enabled us to better know and appreciate the doctrines of several thinkers, as well as the ramifications of their theories and their contributions to what we might call an ‘occidental philosophy of space.’1 This paper approaches the importance of medieval theories of space and place from a specific vantage point: it will highlight the role of the doctrines concerning spiritual creatures in this context by investigating the conditions of the localization and motion of immaterial substances in physical and material space. From the thirteenth century onwards medieval natural philosophy developed within the framework of commentaries on the Aristotelian corpus, in particular those on the Physics and On the Heavens, as well as in the context of metaphysical and theological texts such as the Commentaries on the Sentences or the Disputationes de quolibet (open disputations).2 These texts discuss important questions on matter, body and spirit, as well as movement, place, and the localization of God and spiritual creatures. These are not basic commentaries, but rather essentially doctrinal treatises that construct novel conceptions; advance natural philosophy through the acquisition of new instruments of thought (such as the important linguistic and terminological analyses of the fourteenth century); and encourage the formulation of 1  Among these studies, note particularly – in addition to the classic studies of Pierre Duhem 1913 and Anneliese Maier 1955 and 1966 – the following publications of a more general and/or interdisciplinary character: Sorabji 1983; Aertsen and Speer 1998; Moraw 2002; Uomo e spazio 2003; Suarez-Nani and Rohde 2011. Additionally there are studies specific to medieval theories of space and place, for example, Grant 1981; Cross 1998; Trifogli 2000; Grellard and Robert 2009; Biard and Rommevaux 2012; Weill-Parot 2013. 2  Written around the middle of the twelfth century, Peter Lombard’s Sentences is a collection, in four books, of statements (‘sentences’) from patristic writings (especially Augustine, but also Ambrose, Hilary, and Jerome): the first book deals with God, the second with angels and human beings, the third with Christ, and the fourth with the sacraments. At the beginning of the thirteenth century, this work was adopted as a university textbook in medieval universities: the training curriculum for the masters of theology required them to comment on the ‘Sentences,’ that is to say, to explain their content and to discuss the topics that were raised within them. Therefore, in commenting on book II, masters of theology discussed numerous questions pertaining to spiritual creatures, including their relations to places in the material world. Since commenting on the ‘Sentences’ was compulsory, numerous commentaries survive, and they constitute a specific literary genre through which medieval thought was conveyed. Cf. Evans 2002; Roseman 2004.

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new problems.3 These developments had considerable repercussions in medieval physics and metaphysics and beyond, and their contributions to the development of the concepts of space, place and localization were recognized by scholars from the mid-twentieth century onwards – in particular those of the medieval thinkers who went beyond the Aristotelian conception, and thus paved the way for its demise as brought about by Galileo and Newton.4 The questions that define the evolution of medieval theories of space and place include questions regarding the localization of God and spiritual creatures. Since Aristotelian physics of bodies does not offer valid conceptual tools for solving this problem, many thinkers looked for new solutions, and proposed new theoretical frameworks that would allow them to think about the relationships of spirits to physical places, and to clarify the conditions for including spirits within the space of the world.5 As early as 1964 Paul Vignaux emphasized the necessity of research into medieval philosophy for deepening the study of metaphysical doctrines on the relationships of spirits to places: We stand before a doctrine of space for which the point of departure is the relation of spirits to places. The detailed understanding of such reasoning […] [in this matter] requires a study of fourteenth-century speculation on the place of angels [de loco angelorum].6

Paul Vignaux was inclined to find the question of God’s relationship to the material world essential for a clarification of the concepts of space and place (especially through introducing the notion of spatial infinity) in the intellectual process leading “from the closed world to the infinite universe” (as illustrated in Alexandre Koyré’s famous work From the Closed World to the Infinite Universe).7 Vignaux thus noted that John of Ripa’s (fourteenth century) reflection on the coexistence of creatures with the “infinite imaginary void” focuses on the relationships between spirits (angels and souls) and places, which then become paradigmatic in his elaboration of his theory of space; Vignaux concluded that John of Ripa’s text is “invaluable for the history of the relationships between religious and scientific thought because of the radical distinction it presents between God’s immensity and spatial infinity, a  See Biard 2005, 289–300 (esp. 290).  See Clavelin 1968. Maurice Clavelin recognizes the importance of medieval antecedents for the development of Galilean mechanics, but proposes that the compartmentalization of disciplines prevented medieval thinkers from seeing in their ‘new solutions’ the roots of mechanical science, which would not see the light of day until Galileo’s time (cf. 121, 291); see also Koyré 1939; Wallace 1981. For Newton see also: Jammer 1954. See Funkenstein 1986; Sorabji 1988; Sylla 1997, 65–110; Leijenhorst, Lüthy and Thijssen 2002; esp. Sylla 2002, which discusses the evolution within the Aristotelian tradition; Giovannozzi and Veneziani 2014; Suarez-Nani, Ribordy and Petagine 2017; Suarez-Nani 2017a, 93–107. 5  These discussions would continue into the seventeenth century, in particular with Descartes, Henry More, Hobbes and Gassendi. Of the many studies dedicated to this subject the following shall be noted: Sylla 2002; Paganini 2005, esp. 258–339; Grant 2007, 127–155; Normore 2007, 271–287; Agostini 2011, 49–69; Pasnau 2007, 283–310; Anfray 2014, 23–46; Jaffro 2014, 3–22; Suarez-Nani forthcoming. 6  See Vignaux 1967, 194. 7  Koyré 1957. 3 4

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distinction that began to haunt natural philosophy.”8 Vignaux’s statement has a general import and can be applied to numerous medieval doctrines on the relationships of spirits (God, angels, and human souls) to places; such doctrines propose new notions and hypotheses that are not found in treatises on physics (which largely remain indebted to Aristotle’s conception). These doctrines, indeed, represent a major milestone on the path leading towards the demise of the Aristotelian paradigm. It is, therefore, both important and interesting to explore angelological doctrines related to questions on the relationships between spirits and space. This paper will present some prominent aspects of the doctrine of space and place developed by medieval thinkers in an angelological doctrinal context before approaching a hitherto unexplored problem: the role ascribed to resistance in medieval theories of the movement of immaterial substances. In the second part of this article, once the specific mode of localization of spiritual substances in physical space has been explained, I will evaluate to what extent the analysis elaborated in the angelological context modifies the conception of local motion: what is at stake here becomes especially obvious in my analysis of the role of resistance – a condition that necessarily determines the movement of bodies – in the transport of immaterial substances.

4.2  Place, Space and Movement of Spiritual Creatures 4.2.1  Relationships to Place/Space In the medieval period the relationship of spiritual creatures to space was addressed via two very different questions: “Where are the angels?” (ubi sunt angeli), and “Are angels in a place?” (utrum angeli sint in loco). The reply to the first question – which assumed that angels can be located in a place – was theological in nature, stating that the angels and the blessed are in the Empyreum: not an astronomical, but a ‘theological’ or spiritual heaven, created by God in order to host the blessed spirits (the angels and those human souls that deserved beatitude).9  Vignaux 1967, 209.  Deriving from a long tradition dating back to Antiquity (especially the school of Gnosticism, the Chaldean Oracles, and some Neo-Platonic thought) the Empyreum was introduced into medieval Christian theology by Valafridus Strabo, a monk of the first half of the ninth century and disciple of Raban Maur. Its reality was widely accepted thanks to its association with the theological tradition, which lent it authority. The Empyreum was conceived as a spiritual or intellectual sphere (sometimes ‘sphere of fire’ or ‘sphere of light’) surrounding the material world. It was, thus, considered the tenth celestial sphere, which was immobile and located beyond the Primum Mobile, i.e. outside the ninth sphere according to the Aristotelian-Ptolemaic cosmology. The Empyreum’s influence upon the inferior world was, however, not unanimously accepted: Bonaventure, Richard of Middleton and Giles of Rome acknowledged it, while Thomas Aquinas and the Aristotelians rejected it. On the medieval doctrine of the Empyreum see Nardi 1967, 167–214. Regarding the angels’ cosmological function as movers of the celestial spheres, there was no unanimous agree8 9

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But even if this reply allowed for the angels to be somewhere within the created universe it in no way accounted for their presence in the material world, nor did it explain which type of relationship to physical space angels might have. By contrast, the second question (the question on which this paper will focus in particular) addressed precisely this subject, and was more specifically philosophical in nature, as it questioned the conditions for the localization of spirits in the material world. It is worth emphasizing here that, for medieval thinkers, there was no doubt that immaterial substances were related to and located in physical space. On the one hand, biblical passages  – incontestable authorities  – told of many angelic movements from the sky to the earth.10 On the other hand, the intrinsic limits of the created world required the inclusion of all creatures (even spiritual creatures) in a spatio-temporal framework. The specific way in which purely immaterial substances were localized, then, had to be examined and determined, since in this case the Aristotelian conception of place as the limit of a surrounding body did not apply.11 Thus, from the middle of the twelfth century onwards, Peter Lombard gathered specific elements from the earlier tradition and formulated three possible modalities of localization: through the circumscription of bodies (circumscriptio); by divine ubiquity (ubiquitas); and finally, through definition or delimitation (definitio). The first of these methods defines the relationship of bodies to their respective places: each body is, literally, circumscribed, i.e. it is contained in a place dependent on its dimensions. The second method characterizes divine reality only: ubiquity means that God is present everywhere, without being contained in a determined place. And the third method corresponds exactly to the manner of localization proper to created spirits, since spirits are neither circumscribed in physical space, nor, like God, present everywhere, but rather necessarily delimited in relation to a place, that is to say “situated somewhere, such that they cannot be everywhere simultaneously.”12 The notion of a ‘definition’ or ‘delimitation’ in a place, which was generally accepted by medieval thinkers, nevertheless gave rise to many interpretations, notably when it came to clarifying the how and why of delimitation in space. On this basis two principal explanations of local ‘definition’ or ‘delimitation’ with regard to place emerged: one anchored the localization of spirits in their operations, the other in their being. Adopted, notably, by Thomas Aquinas in the wake of Albert the Great, the thesis of localization by activity led to the attribution of an extrinsic ment, either: while Bonaventure conceived this function in strictly theological terms, Aquinas transformed it into a philosophical thesis, creating the possibility of accounting for universal dynamism; see Suarez-Nani and Faes de Mottoni 2002, 717–751; Suarez-Nani 2002, 91–164. 10  See, among others, Tobit 3:25; Luke 1:26 and 8:35–36; Acts 2:31. 11  Physics in Aristotle 1937, IV, 4, 212a20: “place is the immobile limit of the containing body.” 12  Sententiae in Peter Lombard 1981, l. I, d. XXXVII, chap. 6, 270: “spiritus vero creatus quodam modo localis est, et quodam modo non est localis. Localis quidem dicitur, quia definitione loci terminatur, quoniam cum alicubi praesens sit totus, alibi non invenitur; non autem ita localis est, ut dimensionem capiens, distantiam in  loco faciat.” The distinction between circumscription and delimitation goes back to De fide orthodoxa in John of Damascus 2010–2011, I, chap. 13; it is taken up by, among others, Hugh of St. Victor in De sacramentis, see Hugh of St. Victor 2008, I, pars 3, chap. 18.

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r­elation between angels and physical space, because such activity referred exclusively to operations they could carry out on bodies.13 In this theory, an angel who does not act is not localized in the space of the material world. An inactive angel is, essentially, nowhere, while yet in the Empyreum, which is not a material place. For thinkers following this school of thought angels were not involved in spatial dimensionality, since they are totally foreign to the material world’s conditions. They were, nevertheless, endowed with a ‘quantity of power’” (quantitas virtutis), with which they could act on bodies and their places, such that angels were situated without being circumscribed.14 This sort of localization resulted from a causality between the angel entering into contact (contactum virtutis) with the place of the body upon which it acted, and therefore being delimited or localized in that place ‘from outside.’15 This explanation, then, allowed for the possibility of an extrinsic relation to space: a relation that is qualitatively different from the spatial relationships of bodies because it is freed of all mass and all material conditions. The second explanation of definitio, in contrast to the first, somewhat interiorized of the relationship of angels to space by defining localization as based in the being of created spirits themselves. This position had already been defended by Bonaventure,16 and became predominant after the condemnation of 1277, which censured the thesis that an angel is located nowhere,17 as well as the thesis that an angel is localized by its operations.18 The theory was supported by Peter John Olivi, Mattew of Aquasparta, Henry of Ghent, Richard of Middleton, John Duns Scotus and others, and conceived the relationship to physical place as a necessary and  Sententiae in Albert the Great 1893, d. XXXVII, a. XVIII, 254–255: “Dicendum quod non est idem in loco esse, et locale esse […]. Locatum enim proprie non est nisi corpus: cum tamen spiritus creatus diffinitive sit in  loco, et non locatus, nec localis, nisi secundum quid, ut dicit in littera.” 14  Summa theologiae in Thomas Aquinas 1889, I, q. 52, a. 1, vol. V, 20: “angelo convenit esse in loco: aequivoce tamen dicitur angelus esse in loco et corpus. Corpus enim est in loco per […] contactum dimensivae quantitatis. Quae quidem in angelis non est; sed est in eis quantitas virtualis. Per applicationem igitur virtutis angelicae ad aliquem locum qualitercumque dicitur angelus esse in loco corporeo.” The same thesis is formulated in: Scriptum in I Sent., in Thomas Aquinas 1929, d. 37, q. 4, a. 1 and in the Quodlibet in Thomas Aquinas 1956, I, q. 3, a1. For the Thomist conception, see Suarez-Nani 2002, 87–90, as well as Suarez-Nani 2011, esp. 126–127. 15  Summa theologiae in Thomas Aquinas 1889, I, q. 53, a. 1, 30: “Sed angelus non est in loco ut commensuratus et contentus, sed magis ut continens. Unde motus angeli in loco non oportet quod commensuretur loco, nec quod sit secundum exigentiam eius, ut habeat continuitatem ex loco, sed est motus non continuus. Quia enim angelus non est in loco nisi secundum contactum virtutis, ut dictum est, necesse est quod motus angeli in loco nihil aliud sit quam diversi contactus diversorum locorum successive et non simul, quia angelus non potest esse simul in pluribus locis.” 16  Sententiae in Bonaventure 1885, dist. II, pars II, a. II, q. III, vol. II, 81–82: “Et ideo est tertia positio, quod angelus, cum contineatur a loco corporali, quod est in loco partibili, tamquam in loco primo; et quoniam non potest extendi in eo, ideo necesse est, quod sit in toto, ita quod totus in toto, et totus in qualibet parte.” 17  This thesis was, notably, defended by Roger Bacon: cf. Panti 2017, 57–77. 18  See Denifle and Chatelain 1889, vol. I, art. 204, 218 and 219, 554–555; Hissette 1977, art. 53–55, 104–110; see also Piché 1999, 140, 144 and 146. On the echoes of this condemnation, see Mahoney 2001, 902–930. 13

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intrinsic condition of all creatures, both material and immaterial.19 From this perspective, the question de loco angelorum was to make the relationship to space uniform for all created beings, based on their finitude. This motif was present in most of the arguments looking to prove the intrinsic character of the relationship of all beings to physical place, beyond and independently of the quantitative dimensionality and proper conditions determining the circumscription of the bodies.20 Despite their shared appeal to the motif of finitude, the argumentative strategies often differed from one another significantly, sometimes giving place to novel explanations of the nature of the relationship between spirits and physical space. To take only two examples, we will now look briefly at the doctrines of Henry of Ghent and of John Duns Scotus. 4.2.1.1  Henry of Ghent According to Henry of Ghent, it “is necessary for the angel to be located somewhere in the corporeal universe: not nowhere, nor everywhere, but somewhere, even if the angel is not in a determined manner only here or only there.”21 Freed from the conditions for the localization of the body, this way of being in space does not imply any relationship of co-naturality, dependence or commensurability between the angel and the place it occupies. This thesis results from a twofold distinction: that between place (locus) and position (situs) on the one hand, and that between ‘natural position’ (situs naturalis) and ‘mathematical position’ (situs mathematicus) on the other. The ‘natural position’ implies a (natural) dependence of the localized object on the body that contains it, while the situs mathematicus is not dependent upon or attached to one position rather than another.22 Henry clarifies that only the category of position (situs) befits an angel, which is, thus, only localized in the sense that it is necessarily  I have analysed these authors’ doctrines in: Suarez-Nani 2003, 233–316 (esp. 262–274); SuarezNani 2008, 89–111; Suarez-Nani 2017b, 123–133. 20  Francis of Marchia’s position is significant in this regard; see Suarez-Nani 2015a, 237–274. 21  Quodlibet in Henry of Ghent 1983, q. 9, 68. 22  Ibid., 60: “Appellatur autem ‘situs naturalis’ rei, ad quem se habet per naturalem dependentiam, ut naturale sit ei esse in illo, et violentum et extra naturam esse alibi et extra illum […]. Appellatur autem ‘situs mathematicus’ applicatio rei ad ‘ubi’ aliquod determinatum, sive supra sive infra, sive in oriente sive in occidente, sine aliqua naturali dependentia et determinatione plus ad unum quam ad alterum, ita tamen quod necesse est rei ex sua natura esse in aliquo illorum.” The distinction between ‘natural place’ and ‘mathematical place’ had already been introduced in question 5 of the same Quodlibet, to explain the means by which Christ’s body is present in the Eucharistic sacrament: “Et hoc modo, sicut substantia panis per sua accidentia habuit esse in loco non naturali sed mathematico in altari, et substantia corporis Christi non habet ibi esse nisi quatenus transsubstantiata est substantia panis sub illis speciebus ibi existens in corpus Christi” (29–30). 19

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‘situated’ somewhere, according to the mode of situs mathematicus; that is to say, it is ‘situated’ without any natural link with or dependence on the place where it finds itself.23 It seems clear that this argument implies an important modification of the Aristotelian doctrine: given that the relationship of an angel to a place is devoid of all natural character, Henry was able to formulate the innovative idea of a place or mathematical position separate from a body, and therefore also independent of bodily qualities. 4.2.1.2  John Duns Scotus Similarly to Henry of Ghent, John Duns Scotus, while appealing to Aristotle, proposes a novel conception of the place of bodies.24 He conceives of place as a mathematical quantity or dimension rather than a physical property. Place is presented as a homogenous entity, a “form without content,” that is, “an absolute mathematical property of all corporeal or incorporeal being.”25 Thus, Scotus does not base localization on the physical or natural properties of things, but on a ‘passive potency,’ in virtue of which each thing relates to a place; as a consequence, this relationship is not one of necessity but becomes, strictly speaking (de iure), nothing more than a simple possibility.26 In this way, Scotus removes localization from the network of physical qualities and the relationships between bodies. This conception has wide-ranging implications when applied to separate substances for which, just as for natural bodies, Duns Scotus rejects the necessity of a relationship between separate substances and physical places. For him, such a relationship is nothing but a possibility due to the ‘passive potency’ by which an angel can be in a place.27 This means that, for Scotus, angels do not necessarily have to be  Ibid., 59: “loquendo proprie de esse in tali loco sub ratione tali, quia angelus simplex est, omni ratione quantitatis dimensivae carens, nullo modo angelus intelligitur esse in loco secundum suam substantiam […]. Nec de hoc modo essendi in loco est quaestio. Sed solum est quaestio extendendo ‘locum’ ad omnem rationem situs, ut dicatur esse in loco, quod situm sibi aliquod determinat per suam praesentiam alicubi.” 24  For Scotus see also Duba’s Chapter 5 in this volume. 25  See Boulnois 1998, esp. 325, 327 and 330. 26  Ordinatio in Duns Scotus 1973, II, d. 2, p. 2, q. 1–2, 259: “Per nihil igitur absolutum in alio, requirit necessario esse in loco, sed tantum habet necessario potentiam passivam qua posset esse in loco”; see also Quodlibet in idem 1895, q. XI, a. 2, 444–446. This doctrine, which does not de facto preclude creatures from being located in cosmic space, relies on the principle of divine omnipotence and on the hypothesis that “God could create a stone in the absence of any other containing body or create it outside the universe,” see Ordinatio in Duns Scotus 1973, d. 2, p. 2, q. 1–2, 259. 27  Ordinatio in Duns Scotus 1973, II, d. 2, p. 2, q. 1–2, 261: “Ad propositum igitur ista applicando de angelo, dico quod angelus non necessario est in loco, quia multo magis posset fieri sine creatione creaturae corporalis, vel facta creatura corporali posset fieri et esse extra omnem creaturam corporalem. Et tamen in angelo est potentia passiva, qua potest esse in loco”; if the angel is not localized de iure, according to Scotus, it is nevertheless localized de facto; see Suarez-Nani 2008. 23

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in the cosmos. Moreover, he considers this passive potency ‘neutral’ for angels, that is, neither natural nor violent.28 Strictly speaking, the angel is ‘indifferent’ to all spatial configurations, and can therefore occupy any place.29 This thesis marks a noteworthy theoretical step within medieval theory: the notions of limit and capacity, as well as the natural proximity of a place to a located substance – all of which constitute fundamental elements of Aristotle’s natural philosophy – are overtaken by an idea of place as a mathematical dimension (homogenous and neutral), and by a conception of localization as the pure possibility of relating to space. Whether speaking of a body or a spirit, Duns Scotus (even more radically than Henry of Ghent) moves towards a separation of place and the localized substance.

4.2.2  Movement of Spiritual Creatures Medieval doctrines on the movement of angels attest to a similar dynamic of thought. Peter Lombard identified two different schools within them: one held that spiritual creatures did not move in space but only in time; the other, that spiritual creatures were subject to local motion.30 From the mid-thirteenth century onwards views on the angels’ ability to move converged, but opinions were divided regarding the manner of their local movement. Albert the Great and Thomas Aquinas, among others, considered the local movement of angels not natural but voluntary, and concluded that angels did not successively cross the intermediate space between the points of departure and arrival. Here, the movement of an indivisible (such as an angel) is necessarily discontinuous and indivisible, because it is constituted by a succession of instantaneous and indivisible movements.31 In other words, Albert and Thomas thought it impossible that an indivisible might move continuously in a continuous and divisible space. 28  Ordinatio in Duns  Scotus  1973, II, d. 2, p.  2, 1. 1–2, 267: “ista potentia passiva (quae est in angelo ad essendum in loco) non est naturalis nec violenta, sed neutra.” 29  Nevertheless, Scotus leaves a lingering doubt about the compatibility between the virtual quantity of the angel and the quantity of the place it occupies: cf. Ordinatio in Duns Scotus 1973, d. 2, p. 2, q. 1–2, 264–265. 30  Sententiae in Peter Lombard 1981, I, chap. 8, 272–273. The first position appealed to Augustine, De Genesi ad litteram, VIII, chap. 26; the second to biblical passages such as Luke 1:19, and Isaiah 6:6. 31  In I Sententiarum in Albert the Great 1893, d. XXXVII, a. XVIII, 259–261: “Dicetur quod angeli moventur localiter […]. Sine praeiudicio loquendo, dico quod [angelus] transit medium […] et ideo dico quod transit spatium indivisibiliter: et sibi efficitur totum spatium sicut unum indivisibile”; Summa theologiae in Thomas Aquinas 1889, I, q. 53, a. 1, 30: “Sed angelus non est in loco ut commensuratus et contentus, sed magis ut continens. Unde motus angeli in loco non oportet quod commensuretur loco, nec quod sit secundum exigentiam eius, ut habeat continuitatem ex loco, sed est motus non continuus. Quia enim angelus non est in loco nisi secundum contactum virtutis, ut dictum est, necesse est quod motus angeli in loco nihil aliud sit quam diversi contactus diversorum locorum successive et non simul, quia angelus non potest esse simul in pluribus loci.”

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The opposite approach to this attributes to angels a local movement that is continuous and successive across the intermediate space between the points of departure and arrival, and continuous in time.32 This position would dominate the works of numerous authors after 1277, among them Matthew of Aquasparta, Richard of Middleton and Peter John Olivi.33 In their wake Duns Scotus, too, rejects instantaneous angelic movement and defends the thesis of continuity, his argument resting as much on the continuum of space traversed as on the continuum of time that measures each movement. He thus explicitly maintains the – non-Aristotelian – thesis of the successive and continuous movement of an indivisible through continuous and divisible space.34

4.3  T  he Problem of Resistance in the Movement of Immaterial Substances The question of the movement of spirits also involved the question of resistance as one of the factors determining the local movement of bodies. According to Aristotle’s doctrine, the medium in which movement takes place is crucial.35 For projectile movement, the surrounding air was considered responsible for prolonging the See Suarez-Nani 2015b, 427–443. This angelological position is closely related to the physical doctrine developed by certain ‘finitists’ of the fourteenth century, including Walter Chatton. In the context of the Pythagorean and Platonic tradition, they considered place the finite sum of ‘punctual places’ occupied by the points that compose bodies. Some of these thinkers, like Marco Trevisano, went so far as to defend the movement of an indivisible as a change of position through indivisible instants; see Robert 2017, 182–206. 32  In II librum Sententiarum in Bonaventure 1885, dist. II, pars II, a. II, q. III, 81–82 (see above, note 16); ibid., in Bonaventure 1885, dist. XXXVII, pars II, a. II, q. III vol. I, 657–663: “Dicendum quod angelus, sicut dicit Scriptura, habet moveri. […] Rationabiliter dicitur, quod angelus per medium movetur. […] Sed quoniam difficile videtur intelligere, quod pertranseat medium, quin sit in pluribus partibus medii; et ponere, quod subito moveatur et sit in pluribus partibus medii, est ponere in illo motu, quod sit in pluribus locis simul; et hoc omnino est absurdum dicere de angelo […], ideo dicendum est, quod angelus non movetur per medium motu subito, sed successivo. […] Concedendum est igitur quod motus angeli per medium non est perfecta successione successivus, quia deficit ibi resistentia spatii et partibilitas mobilis; est tamen successivus ratione distantiae spatii, in qua non potest esse simul per totam, et finitatis virtutis moventis, quae non excedit medium improportionabiliter.” 33  See Cappelletti 2009, 433–451, as well as idem 2011; In I librum Sententiarum in Richard of Middleton 1591, d. XXXVII, a. III, q. 3, vol. I, 333; Quaestiones in II Sententiarum in Olivi 1922, q. XXXII, vol. I, 571–591; Demange forthcoming; Suarez-Nani 2003, 262–278. 34  Ordinatio in Duns Scotus 1973, II, d. 2, p. 2, q. 5, 288–289; q. 7, 382 and q. 8, 385–387. On this, see Suarez-Nani 2017a, and Suarez-Nani 2015b, 441–442. Indeed, Duns Scotus was not alone in defending the possibility of local movement of the indivisible. He would be followed by Francis of Marchia, among others, and also Walter Chatton, whose doctrine was studied by Robert 2012, 78–79. 35  Nevertheless, according to Aristotle, other factors contribute to the movement; see Esmaeili 2011, 13–34.

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movement once the object’s contact with the motor had ceased. Also, according to a greater or lesser density (of air or water) the medium exerts resistance and determines the speed of the mobile’s displacement.36 In an angelological context, these elements of Aristotelian doctrine were taken into consideration in the question of whether spirits moved instantaneously: (utrum angelus possit moveri in instanti). Given that an instant does not have a temporal span and designates nothing other than a limit of time, the reply to this question necessarily determined whether the movement of spirits was temporal – and, consequently, measured by cosmic (or continuous) time – or instantaneous and indivisible. Instantaneousness could be taken to mean either that the angel instantaneously traversed the medium located between two termini of displacement; or that the angel instantaneously jumped from one point to another without crossing the intermediate distance.37

4.3.1  Three Possible Solutions Given the above, three possible answers to the question “utrum angelus possit moveri in instanti” emerge: (a) an angel cannot move instantaneously; (b) an angel can move instantaneously by crossing the intermediate space between the points of departure and arrival; (c) an angel can move instantaneously without crossing the intermediate space between the points of departure and arrival. The two underlying concerns regarding the local movement of spirits (its spatial continuity and its temporality) arise because, according to the doctrine formulated by Aristotle in books four and five of the Physics, distance and duration are the inherent conditions for local motion. That a local movement, caused by whatever object or subject, implied a distance to cross was, indeed, considered indisputable. Consequently, in the case of moving spirits, not just spatial continuity, but also duration or temporal continuity of movement posed a problem. If, following Aristotle, continuity or temporal succession in  See Physics in Aristotle 1937, IV 8, 215a1–215b15; VII 10, 266b27–267a12; here one of the reasons emerges for Aristotle’s rejection of the vacuum, which for him made movement and time (which measured movement) impossible: there cannot be movement in a medium without resistance, because then the speed of the mobile would be infinite. On specific aspects of the medieval reception of Aristotle’s doctrine of movement see Biard 1991, 1–32, which discusses John Buridan’s critique of the thesis that projectile movement is caused by the medium. For another example of the reworking of the Aristotelian notion of ‘medium’ and its function in movement see Weill-Parot 2014, 59–71, which examines the question of the ‘medium’ in relation to magnetic attraction. 37  These two aspects are clearly articulated in the Lectura in Gregory of Rimini 1979, d. 6, q. 3, vol. V, 47. 36

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movement was due to the resistance applied by the medium, continuity and ­temporality in movement had to be rejected should this medium not give any resistance to immaterial entities. Appealing to Averroes – who had clarified and further developed Aristotle’s doctrine on this matter – medieval thinkers conceived resistance to the movement in three ways: first, as the resistance of a moving body to its motor (the latter always distinct from the former, according to the Aristotelian principle that “what is moved is moved by something”)38; secondly, as the resistance of the medium to the moving body; and thirdly, as the simultaneous resistance of the moving body and the medium.39 Any examination of the movement of spiritual creatures, therefore, required a verification of the presence of one or another kind of resistance, or their absence, in order to establish if the movement of the immaterial substances was temporal and successive or, on the contrary, discontinuous and instantaneous. It is not surprising to see that in the attempts to find a solution for this question, the divisions of opinion that we have considered above appear to repeat themselves. 4.3.1.1  Thomas Aquinas’ and Giles of Rome’s Solution As partisans of instantaneous spiritual movement (not subject to the necessity of crossing the intermediate space between two points, see solution c) above), Thomas Aquinas and Giles of Rome thought the movement of angels to result only from the succession of the angels’ operations on physical bodies and places. As mentioned above, this succession followed the will of the acting subject, meaning that the angel was not in itself dependent on the spatial continuum it traversed. Each angelic operation corresponds to an indivisible instant, such that the resulting movement is discontinuous (immediate displacement from one point to another), just like the time that measures theirs operations, which is composed of instants.40 According to this  Physics in Aristotle 1937, III 1, 202a9–11. Joël Biard has noted the modification used by medieval thinkers regarding this principle: “moved by something” becomes for medieval thinkers “moved by another” (Biard 1991, 3). 39  In Aristotelis Physicam in Averroes 1562, vol. IV, ff. 161M-162B: “Nos autem dicamus quod necesse est quod inter motorem et rem motam sit resistentia. Motor enim movet rem motam secundum quod est contrarium et res mota movetur ab illo, secundum quod est similis [...] et ista resistentia aut erit ex ipso moto [...], aut erit ex ipso medio [...], aut resistentia erit ex utroque, scilicet ex re mota et ex medio.” This passage from Averroes is often cited and employed by medieval thinkers: we can note as examples In I Sententiarum in Giles of Rome 1521, d. XXXVII, pars II, princ. II, q. III, f. 198r; Ordinatio in Duns Scotus  1973, II, d. 2, pars II, q. 5, 286; Lectura in Gregory of Rimini 1979, d. 6, q. 3, 47. Galileo, referring to the medieval doctrine of the resistance of medium and mobile, would say that it amounts to one and the same sort of resistance: see De motu in Galilei 1890–1909, vol. I, 410. 40  Summa theologiae in Thomas Aquinas 1889, I, q. 53, a. 1–3; and Scriptum in I librum Sententiarum in Thomas Aquinas 1929, d. XXXVII, q. IV, a. III, vol. I, 889–890: “Unde cum motus angeli non sit continuus, quia non est secundum necessitatem conditiones habens magnitudinis per quam transit, […] sed per successionem operationum in quibus nulla est ratio continuitatis; 38

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theory, it was therefore inconceivable that an indivisible subject should traverse a divisible space successively and continuously, given that such a space exerts no resistance on it. Giles of Rome, nevertheless, admits a form of resistance in the local movement of spirits, attributing it to the distinction between motor and mobile: there is, in effect, a resistance between the force applied (through which the angel-motor acts) and spatial points on which the angelic power is applied. This form of resistance is, however, restrained, and serves only to justify the sui generis temporality of spiritual movement – a temporality which for Thomas Aquinas is completely different from the continuity of cosmic time. The angel thus moves in a discontinuous and instantaneous manner, that is, in the time (composed of instants) proper to immaterial substances.41 4.3.1.2  Duns Scotus’ and Francis of Marchia’s Solution The position taken by Thomas Aquinas and Giles of Rome was rejected by a number of authors, including those from the abovementioned Franciscan tradition, who vigorously rejected the idea that an angel could move instantaneously. In their wake, Duns Scotus insisted on the continuity and the successive character of the local movement of angels, both because of the divisibility of the spatial continuum and because of the resistance of the mobile with respect to the motor.42 Scotus’ doctrine attracted many followers, among them the early Scotist Francis of Marchia, who commented on the Sentences in Paris in the years 1319/1320.43 ideo tempus illud non est continuus, sed est compositum ex ‘nunc’ succedentibus sibi […]. Quamvis linea sit continua per quam angelus transit, non tamen est continuitas secundum quod refertur ad motum angeli, qui diversa ‘ubi’ non continuatim pertransit.” Cf. Suarez-Nani 2015c, 71–96. 41  In I librum Sententiarum in Giles of Rome 1521, d. XXXVII, pars II, princ. II, q. III, f. 198r: “Ad cuius evidentiam notandum quod angelus dupliciter movetur. Primo in corpore assumpto. Secundo per applicationem virtutis ad diversa spatia [...]. Cum autem movetur per applicationem virtutis ad diversa locorum spatia, tunc requiritur ibi tempus propter distinctionem angeli applicantis virtutem suam ad corpus ad quod eam applicat. Istud tamen tempus quod requiritur ad talem applicationem non est eiusdem rationis cum tempore quod est passio primi motus, quia talis applicatio non reducitur in motum caeli. Patet ergo etiam ratione resistentiae motus angeli fieri in tempore accipiendo resistentiam non solum pro impedimento medii, sed large ut dicamus talem resistentiam esse cum est distinctio motoris ad mobile vel applicantis virtutem ad id cui applicat.” 42  Ordinatio in Duns Scotus 1973, II, d. 2, p. 2, q. 5, 344–346: “sed talis resistentia [consistit in hoc], quod mobile semper stat sub aliquo cui non potest immediate succedere terminus intentus a movente. Et ista resistentia mobilis ad motorem est propter defectum virtutis moventis […]; si enim esset virtus infinita, posset ponere mobile statim in termino ad quem. […] Necessitas tamen successionis […] est […] praecise comparando illam [resistentiam] ad agens, cui mobile resistit propter istam resistentiam medii ad ipsum, − ita quod, sicut erat possibilitas ex sola resistentia medii ad mobile, ita virtus illa limitata non possit tollere istam resistentiam; et ideo resistit ista resistentia agenti, ne statim inducat terminum.” 43  One example is Nicolaus Bonetus, who was already noted by Duhem; concerning resistance, which arises as much in the question of angelic movement as in movement in a vacuum, Duhem

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Francis shared Duns Scotus’ thesis of continuous movement of indivisibles in a divisible space. His argument, however, introduced a novel reference to the notion of ‘divisibility:’ according to Francis, it is necessary to distinguish between a ‘formal’ divisibility (applicable to whatever is intrinsically divisible) and a ‘virtual’ or ‘causal’ divisibility that only bears relevance to the effect produced, such as movement in physical space. Attributing this form of divisibility to non-dimensional (that is, formally indivisible) entities, Francis concluded that the movement produced and effected by an angel is divisible, because a spirit cannot entirely be present in two parts of space at the same time, that is, it cannot produce two distinct effects at the same time.44 In his examination of the question whether angelic movement is instantaneous, Francis proceeded in an analogous way, submitting the notion of resistance to a revision which guaranteed its pertinence while permitting him to apply this notion to the movement of spiritual entities. After considering the points in favor of instantaneousness, Francis argued for an angelic movement that is temporal, continuous and successive, in order to avoid the possibility – which he finds unacceptable – that an angel could be simultaneously at the departure point and end point of its movement, and that it could thus occupy two places at the same time.45 To justify this position, Francis criticised Duns Scotus, who saw in the continuity and divisibility of space a sufficient – while non-exclusive – reason for the continuity and succession of angelic movement.46 In agreement with Averroes, Francis underlines that some form of ‘resistance’ determines each local movement, includinsists on the elements of Bonetus’ doctrine that would lead to “the Dynamics of Galileo, of Descartes and of Beeckman” (Duhem 1913, 78–81). 44  More precisely, according to Francis the moving angel is partly in the first term and partly in the final term of its movement, while being in each of them entirely (because he is not quantitatively divisible), but not totally (because he cannot occupy two places at the same time): in other words, an angel can travel from one place to the other while entirely occupying the place where he is, but without occupying the totality of space he has to go through. Cf. Quaestiones in II Sententiarum in Francis of Marchia 2010, q. 16, vol. II, 75–106, 98: “Angelus autem, quia est divisibilis non formaliter, sed tantum causaliter in ordine ad effectum, ideo est partim in termino a quo et partim in termino ad quem non prout ‘partim et partim’ opponuntur ‘toto,’ sed prout opponuntur ‘totaliter’.” See Suarez-Nani 2017b. 45  Quaestiones in II Sententiarum in Francis of Marchia 2010, q. 16, 100: “Tunc per hoc potest argui sic ad propositum [...]; sed medii per quod angelus movetur ad medium per quod corpus movetur nulla est proportio quantum ad resistentiam, cum medium per quod angelus movetur nullo modo resistat angelo; ergo nec motus angeli ad motum corporis erit aliqua proportio in velocitate. Ergo est in instanti.” Francis adds other arguments, notably referring to the Aristotelian thesis that, if there were movement in a vacuum, it would be instantaneous due to the absence of resistance. Ibid., 102: “Dico tamen quantum ad hoc quod angelus non potest naturaliter virtute sua moveri localiter in instanti. Hoc probo sic: illud quod in eodem instanti movetur de loco ad locum per medium in eodem instanti est in termino a quo et in termino ad quem; sed angelus non potest simul esse in pluribus locis sibi aequalibus; ergo non potest de loco sibi aequali et proportionato moveri in instanti ad alium ab illo loco priori distantem.” 46  Ordinatio in Duns Scotus 1973, II, d. II, p. 2 q. 5, 341: “in motu locali est successio ex duplici causa, videlicet ex divisibilitate mobilis et ex divisibilitate spatii – quarum utraque causa, si esset per se et praecisa, esset sufficiens ratio successionis.”

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ing that of spirits: this movement is certainly free of any resistance exerted by the medium, but nevertheless subject to the resistance of the mobile with respect to the motor.47 It is precisely on this point that Francis makes an original contribution to the debate, with his distinction between two types of resistance. A first form of resistance may be due to the natural inclination of the mobile towards a place opposite to the place to which it is moved by its motor. This is the resistance at work in the movement of bodies, for example the resistance acting on a stone thrown upwards, when its natural inclination pushes it downwards. But another form of resistance comes into play when the mobile does not perfectly ‘obey’ a motor of limited power: in this case the mobile cannot be perfectly moved from one place to another, and thus it resists the movement; this applies, for example, to an angel who cannot instantaneously transport himself from one place to the other because of his lack of a moving force.48 This second type of resistance, resulting from the limits of a mover’s force, is called ‘privative resistance,’ to distinguish it from ‘positive resistance,’ which corresponds to the physical resistance exerted by the medium on the material mobile. It is this privative resistance that applies to the local movement of angels, and determines its temporal succession: angelic movement cannot be instantaneous due to the privative resistance of the mobile with respect to the motor.49 Yet this resistance is completely different from the resistance affecting bodies: indeed, it is conceivable that it might be annulled, to the extent that the angel as moving entity would be capable of achieving a state of pure obedience with itself as motor – something that is simply impossible for bodies because of their materiality.50 The originality of Francis’ position lies in his invention of the concept of ‘privative’ resistance

47  Duns Scotus had also taken this type of resistance into account; see Ordinatio in Duns Scotus 1973, 345. 48  Quaestiones in II Sententiarum in Francis of Marchia 2010, q. 16, 103: “Ubi tamen advertendum quod mobile resistere motori potest esse duplici de causa: uno modo aliquod mobile resistit motori ex hoc quod habet inclinationem naturalem ad aliquod ubi oppositum illi ubi ad quod movetur. [...] Alio modo aliquod mobile potest resistere suo motori [...] solum quia non habet perfectam oboedientiam ad ipsum; quia enim istud mobile, quodcumque sit, non potest simul esse naturaliter in pluribus locis, ideo quando est in uno loco, non potest esse in alio. Nec est in perfecta oboedientia respectu alicuius agentis finiti quod possit moveri ab isto [loco] et poni in alio in quacumque mensura.” By introducing the second type of resistance, Francis aims to avoid the possibility that an angel could perform an instantaneous motion. 49  Ibid., 104: “Dico ergo quod […] causa successionis motus [est] etiam resistentia privativa, qualis est in quocumque motu locali cuiuscumque rei finitae, sive corporalis sive spiritualis, facto a virtute finita. Ex quo concludo quod angelus potest movere se ipsum et  alia successive et non in instanti propter rationem iam dictam, quia, scilicet in eius motu quo movet se localiter non sit resistentia mobilis ad motorem positiva contraria, est tamen ibi, ut dictum est, resistentia privativa.” 50  Ibid., 105: “Angelus etiam resistit sibi, sed ista resistentia qua angelus ut mobile resistit suae virtuti motivae alterius rationis est ab illa resistentia qua corpus resistit sibi vel cuicumque alteri, et minor illa. [...] Nec corpus posset esse in illa perfecta oboedientia ad motum localem respectu angeli, nec etiam respectu alicuius alterius, sicut est ipse angelus.” See Schabel 2001, 175–89 (esp. 187–188).

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as a metaphysical counterpart to the concept of ‘positive’ or physical resistance which plays an important role in the explanation of the local motion of bodies. Francis of Marchia’s contemporary Walter Chatton defends a similar position (although without the outlined distinction between different types of resistance). For Chatton, the resistance of a mobile to a motor plays a role in the local movement of angels, due to the limited power of an angel as a motor, and also the fact that an angel cannot coexist simultaneously at all points of the spatial distance that is traversed.51 4.3.1.3  Gregory of Rimini’s Solution Twenty-five years after Francis of Marchia and Walter Chatton, Gregory of Rimini examined the same question in its different aspects, and came to two conclusions: firstly, that an angel can move instantaneously from one place to another by crossing the intermediate space (solution b) above); and secondly, that God’s agency can cause an angel to move instantaneously from one place to another without crossing the intermediate space.52 The first thesis presents an intermediate solution between the two mentioned before (solutions a) and c)): it admits the natural possibility of instantaneous angelic movement, exempt from resistance, but with the necessity of crossing intermediate space. This position is defended by different arguments, the most important of which is based on an analogy between angelic movement and the movement of a body in a vacuum: appealing to an existing hypothesis, albeit not one accepted by Aristotle, Gregory observed that if a body were to move in a vacuum it would meet no resistance, so that its movement would be instantaneous. The same applies to angelic movement, which experiences no resistance from the medium.53 Gregory’s second thesis, by contrast, admits the possibility of surpassing all the natural conditions for local movement (spatial distance, temporality and resistance), but only by virtue of divine power. He considers this in analogy with the Eucharistic transubstantiation, in which the matter of the bread is instantaneously transformed into the body of Christ, that is, without intermediate steps. According to Gregory, God might operate in a similar fashion with angels, moving them from one place to another, without the necessity to pass through intermediate places.54

 Reportatio super Sententias in Chatton 2004, l. II, 173–174; and analysis in Robert 2012, 78–79.  Lectura in Gregory of Rimini 1979, d. 6, q. 3, 47: “Hiis praemissis pono duas conclusiones: Prima est quod angelus potest a seipso mutari de loco ad locum in instanti, transeundo per totum medium. Secunda, quod potest a deo mutari de loco ad  locum in instanti, non transeundo per medium.” Gregory discusses the problem of angelic location in ibid., d. 2, q. 2, vol. IV, 331–343. 53  Ibid., 47 and 49–50. In this way Gregory of Rimini criticizes Giles of Rome’s theses. For the latter, whenever there is a distinction between motor and mobile, there is necessarily resistance that makes the movement temporal. 54  Ibid., 50. 51 52

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Gregory’s position provides a nuanced approach, which requires him to differentiate between two orders of argument: the first concerns the natural capacities of created spirits; the other privileges supernatural intervention. The interesting aspect and importance of his approach lies in the analogy he develops between the movement of angels and that of bodies in a vacuum – an approach that allows him to view resistance no longer necessary, nor an intrinsic condition for all local movement.

4.4  Concluding Remarks I will conclude this short investigation with three points. First, far from constituting a uniform doctrinal corpus, medieval theories of space, place and movement show a great diversity of approaches that coexist and compete with one another, certainly in a shared cultural space, but with differentiated, and even diametrically opposed, sensibilities and philosophical aims. Secondly, while all positions of the medieval thinkers discussed in this study draw from the natural philosophy of Aristotle, they dispose of his doctrinal authority in some fundamental points, and thereby evolve further in new and interesting ways. Indeed, it is through appealing to the doctrinal canon of the Physics while, at the same time, distancing themselves from it that medieval thinkers can formulate concepts including a ‘mathematical position,’ ‘passive power,’ ‘causal divisibility,’ and ‘privative resistance,’ and theses on continuous or instantaneous movement of indivisibles, or even on local movement that knows no resistance whatsoever. Thirdly  – and it is here that we find the hypothesis that has directed my own research for several years – it appears that the development of medieval theories of place, space and movement were strongly dependent on metaphysical reflections applied to questions of natural philosophy. As we have seen, thinkers of the Middle Ages submit certain fundamental notions in physics to an interrogation that is, in fact, metaphysical: what happens with place and movement when it comes to immaterial, purely spiritual, entities such as angels? For medieval thinkers, there was nothing strange about this approach, which gained far-reaching importance in the history of ideas.55 Indeed, the metaphysical construct of angelology constituted a  Indeed, the importance of angelological considerations in the development of conceptions of place and movement should not conceal other factors that, in the framework of natural philosophy, contributed to developing medieval doctrines and to the progressive shift away from Aristotle. We should consider, for example, the position of Gerardus Odon, studied by Bakker and De Boer 2009, 149–184. Not knowing specific critiques (those of Philoponus, for example) already mounted against the Aristotelian conceptions of place and movement – except for Avempace’s, reported by Averroes in the latter’s In Libros Physicorum Aristotelis, l. IV, fol. 160C – these questions and developments were internal to medieval thought, as were the new requirements to which thinkers had to respond, requirements that favored a certain surpassing of the Aristotelian paradigm. Medieval thinkers from the thirteenth century onward were, however, very attached to this paradigm, as Richard Sorabji has observed (see Sorabji 1987, 15: “What is surprising is that the medieval Latin West was less robust in rejecting Aristotle’s account of place, and was prepared to go through many contortions to preserve it”). The relationship of medieval thinkers to the paradigm

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genuine laboratory of thought experiments that allowed medieval thinkers to handle innovative concepts and to open new perspectives – perspectives that announced in nuce the coming of a new way to see and understand the physical world.

References Aertsen, Jan, and Andreas Speer, eds. 1998. Raum und Raumvorstellungen im Mittelalter. Berlin: De Gruyter. Agostini, Igor. 2011. Henry More e le fonti della dottrina dell’estensione spirituale. In Eredità cartesiane nella cultura britannica, ed. Paola Dessi and Brunello Lotti, 49–69. Florence: Le Lettere. Albert the Great. 1893. In I librum Sententiarum, ed. Auguste Borgnet. In Opera Omnia, vol. XXVI. Paris: Vivès. Anfray, Jean-Pascal. 2014. Étendue spatiale et temporelle des esprits: Descartes et le holenmérisme. Revue philosophique de la France et de l’Étranger 139: 23–46. Aristotle. 1937. Physics, ed. Immanuel Bekker. Oxford: Clarendon Press. Averroes. 1562. In Aristotelis Physicam. In Aristotelis Opera cum Averrois Commentariis. Venice: Apud Junctas. Bakker, Paul, and Sander de Boer. 2009. Locus est spatium: On Gerald Odonis’ Quaestio de loco. Vivarium 47: 295–330. Biard, Joël. 1991. Le mouvement comme problème logique et métaphysique chez Jean Buridan. Les papiers du Collège international de philosophie 7: 1–32. ———. 2005. Tradition et innovation dans les commentaires de la Physique: L’exemple de Jacques Zabarella. In La transmission des savoirs au Moyen Age et à la Renaissance, ed. Frank La Brasca and Alfredo Perifano, 289–300. Besançon: Presses universitaires de Franche-Comté. Biard, Joël, and Sabine Rommevaux, eds. 2012. La nature et le vide dans la physique médiévale: Études dédiées à E. Grant. Turnhout: Brepols. Bonaventure. 1885. In libros Sententiarum, ed. Collegii S. Bonaventurae. Quaracchi: Ad Claras Aquas. Boulnois, Olivier. 1998. Du lieu cosmique à l’espace continu? La représentation de l’espace selon Duns Scot et les condamnations de 1277. Miscellanea mediaevalia 25: 314–331. Cappelletti, Leonardo. 2009. Le condanne parigine sul moto locale delle sostanze separate nelle Quaestiones de anima separata di Matteo d’Acquasparta. La Cultura 47: 433–451. ———. 2011. Matteo d’Aquasparta vs Tommaso d’Aquino: Il dibattito teologico–filosofico nelle Quaestiones de anima. Rome: Aracne. Clavelin, Maurice. 1968. La philosophie naturelle de Galilée. Paris: Albin-Michel. Cross, Richard. 1998. The Physics of Duns Scotus: The Scientific Context of a Theological Vision. Oxford: Clarendon Press. Demange, Dominique. Forthcoming. Puissance, action, mouvement: Étude sur l’ontologie dynamique de Pierre de Jean Olivi. Fribourg/Paris: Academic Press/Éditions du Cerf. Denifle, Heinrich, and André Chatelain, eds. 1889. Chartularium Universitatis Parisiensis. Vol. I. Paris: Delalain. Duhem, Pierre. 1913. La physique parisienne au XIVe siècle. In Le système du monde: Histoire des doctrines cosmologiques de Platon à Copernic, vol. VIII. Paris: Hermann et fils.

of Aristotelian physics – one of faithfulness, innovation and ‘reinvention’ – is clearly shown by Nicolas Weill-Parot, in relation to the issue of magnetic attraction; cf. Weill-Parot 2014, 70–71. For the reception of medieval cosmological approaches by Galileo see Palmerino 2011, 103–125.

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Esmaeili, Mohammad J.  2011. Ibn Sîna on Dynamics: Historical Context and Conceptual Development in Greek, Arabic and Latin Sources. In Acts to the Kyoto Conference, 13–34. Kyoto. Evans, Gillian R., ed. 2002. Mediaeval Commentaries on the Sentences of Peter Lombard. Leiden: Brill. Francis of Marchia. 2010. Francisci de Marchia Quaestiones in II librum Sententiarum. In Opera philosophica et theologica, vol. II.3, ed. Tiziana Suarez-Nani, William Duba, Emmanuel Babey, and Girard Etzkorn. Leuven: Leuven University Press. Funkenstein, Amos. 1986. Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century. Princeton: Princeton University Press. Galilei, Galileo. 1890–1909. De motu. In Le opere di Galileo Galilei, ed. Antonio Favaro. Florence: Tipografia di G. Barbera. Giles of Rome. 1521. In libros Sententiarum. Venice. Giovannozzi, Delfina, and Marco Veneziani, eds. 2014. Locus-Spatium (Lessico intellettuale europeo). Florence: Olschki Editori. Grant, Edward. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. ———. 2007. The Transformation of Medieval Cosmology by Jesuits in the Sixteenth and Seventeenth Centuries. In Jesuit Science and the Republic of Letters, ed. Mordechai Feingold, 127–155. Cambridge, MA/London: MIT Press. Gregory of Rimini. 1979. Lectura super secundum Sententiarum. In Gregorii Ariminensis Lectura super primum et secundum Sententiarum, vol. V (Spätmittelalter und Reformation: Texte und Untersuchungen, ed. Heiko Obermann vol. X), ed. Damasus Trapp. Berlin/New York: De Gruyter. Grellard, Christophe, and Aurélien Robert, eds. 2009. Atomism in Late Medieval Philosophy and Theology. Leiden: Brill. Henry of Ghent. 1983. Quodlibet II. In Henrici de Gandavo Opera Omnia, vol. VI: Ancient and medieval philosophy series II, ed. Robert Wielocks. Leuven: Leuven University Press. Hissette, Roland. 1977. Enquête sur les 219 articles condamnés à Paris le 7 mars 1277. Paris/ Leuven: Louvain Publications Universitaires. Hugo of St. Victor. 2008. De sacramentis, ed. Rainer Berndt. Münster: Aschendorff. Jaffro, Laurent. 2014. Esprit où es-tu? Pérennité de la distinction entre présence locale et présence virtuelle. Revue philosophique de la France et de l’Étranger 139: 3–22. Jammer, Max. 1954. Concepts of Space: The History of Theories of Space in Physics. Cambridge, MA: Dover. John Duns Scotus. 1895. Quodlibet. Paris: Vivès. ———. 1973. Ordinatio. In Opera Omnia, ed. Vaticana, vol. VII. Rome: Civitas Vaticana. John of Damascus. 2010–2011. De fide orthodoxa, ed. Bonifatius Kotter, with French translation by Pierre Ledrux. In Sources chrétiennes, vols. 535 and 540. Paris: Éditions du Cerf. Koyré, Alexandre. 1939. Études galiléennes. Vol. I. Paris: Hermann. ———. 1957. From the Closed World to the Infinite Universe. Baltimore: The Johns Hopkins Press. Leijenhorst, Cees, Christoph Lüthy, and Johannes M.M.H.  Thijssen. 2002. The Dynamics of Aristotelian Natural Philosophy from Antiquity to the Seventeenth Century. Leiden/Boston/ Cologne: Brill. Mahoney, Edward. 2001. Reverberations of the condemnation of 1277. In Nach der Verurteilung von 1277: Philosophie und Theologie an der Universität von Paris im letzten Viertel des 13. Jahrhunderts, ed. Jan Aertsen, Kent Emery, and Andreas Speer, 902–930. Berlin/New York: De Gruyter. Maier, Anneliese. 1955. Metaphysische Hintergründe der Spätscholastischen Naturphilosophie. Rome: Edizioni di storia e letteratura. ———. 1966. Die Vorläufer Galileis im XIV Jahrhunderts: Studien zur Naturphilosophie der Spätscholastik. Rome: Edizioni di storia e letteratura.

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Moraw, Peter. 2002. Raumerfassung und Raumbewußtsein im späteren Mittelalter. Ostfildern: Thorbecke. Nardi, Bruno. 1967. La dottrina dell’Empireo nella sua genesi storica e nel pensiero dantesco. In Saggi di filosofia dantesca, 167–214. Florence: La Nuova Italia. Normore, Calvin. 2007. Descartes and the Metaphysics of Extension. In A Companion to Descartes, ed. Janet Broughton and John Peter Carriero, 271–287. Oxford: Blackwell. Paganini, Gianni. 2005. Hobbes, Gassendi und die Hypothese der Weltvernichtung. In Konstellationsforschung, ed. Martin Muslov and Marcelo Stamm, 258–339. Frankfurt a.M.: Suhrkamp. Palmerino, Carla Rita. 2011. Galileo’s Use of Medieval Thought Experiments. In Thought Experiments in Methodological and Historical Context, ed. Katerina Ierodiakonou and Sophie Roux, 103–125. Leiden/Boston: Brill. Panti, Cecilia. 2017. ‘Non abest nec distat.’ Space and Movement According to Robert Grosseteste, Adam Marsh and Roger Bacon. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe-XVIe siècles), ed. Tiziana Suarez-Nani, Olivier Ribordy, and Antonio Petagine, 57–77. Barcelona/Rome: FIDEM. Pasnau, Robert. 2007. Mind and Extension (Descartes, Hobbes, More). In Forming the Mind. Essays on the Internal Senses and the Mind/Body Problem from Avicenna to the Medical Enlightenment, ed. Henrik Lagerlund, 283–310. Dordrecht: Springer. Peter John Olivi. 1922–1924. Quaestiones in II Sententiarum, ed. Bernhard Jansen. Quaracchi: Ad Claras Aquas. Peter Lombard. 1981. Sententiae in IV libris distinctae, ed. Collegii S. Bonaventurae. Quaracchi: Ad Claras Aquas. Piché, David. 1999. La condamnation parisienne de 1277. Paris: J. Vrin. Richard of Middleton. 1591. Super primum librum Sententiarum Petri Lombardi questiones subtilissimae. Brescia: De consensu superiorum. Robert, Aurélien. 2012. Le vide, le lieu et l’espace chez quelques atomistes du XIVe siècle. In La nature et le vide dans la physique médievale: Études dédiées à E. Grant, ed. Joël Biard and Sabine Rommevaux, 67–98. Turnhout: Brepols. ———. 2017. Atomisme pythagoricien et espace géométrique au Moyen Age. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe–XVIe siècles), ed. Tiziana Suarez-­ Nani, Olivier Ribordy, and Antonio Petagine, 182–206. Barcelona/Rome: FIDEM. Roger Bacon. 1859. Opus tertium, ed. James S. Brewer. In Opera quaedam hactenus inedita, vol. I. London: Logman, Green, Longman and Roberts. Roseman, Philip W. 2004. Peter Lombard (Great Mediaeval Thinkers). Oxford: Oxford University Press. Schabel, Christopher. 2001. On the Threshold of Inertial Mass? Francis of Appignano on Resistance and Infinite Velocity. In Atti del I° Convegno internazionale su Francesco di Appignano, ed. Domenico Priori, 175–189. Appignano del Tronto: Centro Studi Francesco di Appignano. Sorabji, Richard. 1983. Time, Creation and the Continuum: Theories in Antiquity and the Early Middle Ages. London: Duckworth. ———. 1987. Philoponus and the Rejection of Aristotelian Science. London: Institute of Classical Studies. ———. 1988. Matter, Space and Motion. London: Duckworth. Suarez-Nani, Tiziana. 2002. Les anges et la philosophie: Subjectivité et fonction cosmologique des substances séparées au XIIIe siècle. Paris: J. Vrin. ———. 2003. Pierre de Jean Olivi et la subjectivité angélique. Archives d’histoire doctrinale et littéraire du Moyen Age 70: 233–316. ———. 2008. Angels, Space and Place: The Location of Separate Substances According to John Duns Scotus. In Angels in Mediaeval Philosophical Inquiry: Their Function and Significance, ed. Isabel Iribarren and Martin Lenz, 89–112. Aldershot: Ashgate Publishing. ———. 2011. Vers le dépassement du lieu: L’ange, l’espace et le point. In Représentations et conceptions de l’espace dans la culture médiévale, ed. Tiziana Suarez-Nani and Martin Rohde, 121–146. Berlin/Boston: De Gruyter.

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———. 2015a. La matière et l’esprit: Études sur François de la Marche. Fribourg/Paris: Academic Press/Éditions du Cerf. ———. 2015b. De la théologie à la physique: L’ange, le lieu et le mouvement. Micrologus (Angelos) 23: 427–443. ———. 2015c. Luogo, spazio e tempo nel pensiero medievale: Il contributo dell’angelologia. In ‘De tempore.’ L’enigma dell’ora, ed. Anselmo Aportone and Gianna Gigliotti, 71–96. Napoli: Bibliopolis. ———. 2017a. L’espace sans corps: Étapes Médiévales de l’hypothèse de l’annihilatio mundi. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe-XVIe siècles), ed. Tiziana Suarez-Nani, Olivier Ribordy, and Antonio Petagine, 93–108. Barcelona/Rome: FIDEM. ———. 2017b. Le mouvement de l’indivisible: Notes sur le déplacement des anges selon François de la Marche. In Miroir de l’amitié: Mélanges offerts à Joël Biard, ed. Christophe Grellard, 123–133. Paris: J. Vrin. ———. Forthcoming. Le lieu de l’esprit: Échos du Moyen Age dans la correspondance de Descartes avec Henry More. In Descartes en dialogue, ed. Olivier Ribordy and Isabelle Wienand. Basel: Schwabe. Suarez-Nani, Tiziana, and Barbara Faes de Mottoni. 2002. Hiérarchie, miracles et fonction cosmologique des anges au XIIIe siècle. In Les anges et la magie au Moyen Age, ed. Henry Bresc and Benoît Grévin, 717–751. Rome: Mélanges de l’École française. Suarez-Nani, Tiziana, and Martin Rohde, eds. 2011. Représentations et conceptions de l’espace dans la culture médiévale. Berlin/New York: De Gruyter. Suarez-Nani, Tiziana, Olivier Ribordy, and Antonio Petagine, eds. 2017. Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe-XVIe siècles). Barcelona/Rome: FIDEM. Sylla, Edith. 1997. The Transmission of the New Physics of the Fourteenth Century from England to the Continent. In La nouvelle physique du XIVe siècle, ed. Stefano Caroti and Pierre Souffrin, 65–109. Florence: Olschki. ———. 2002. Space and Spirit in the Transition from Aristotelian to Newtonian Science. In The Dynamics of the Aristotelian Natural Philosophy from Antiquity to the Seventeenth Century, ed. Cees Leijenhorst, Christoph Lüthy, and Johannes M.M.H.  Thijssen, 249–287. Leiden/ Boston/Cologne: Brill. Thomas Aquinas. 1889. Summa theologiae. (‘Editio Leonina,’ vol. V). Rome: Ex typographia polyglotta de propaganda fidei. ———. 1929. Scriptum super I librum Sententiarum, ed. Pierre Mandonnet. Paris: Lethielleux. ———. 1956. Quodlibeta, ed. Raimundus Spiazzi. Torino: Marietti. Trifogli, Cecilia. 2000. Oxford Physics in the Thirteenth Century (ca. 1250–1270): Motion, Infinity, Place and Time. Leiden/Boston/Cologne: Brill. Uomo e spazio nell’alto Medioevo. Spoleto: Centro italiano di studi sull’Alto Medioevo, 2003. Vignaux, Paul. 1967. Immensité divine et infinité spatiale. Traditio 23: 191–209. Wallace, William A. 1981. Prelude to Galileo: Essay on Medieval and Sixteenth-Century Sources of Galileo’s Thought. Dordrecht: D. Reidel. Walter Chatton. 2004. Reportatio super Sententias, ed. Joseph Wey and Girard Etzkorn. Turnhout: Brepols. Weill-Parot, Nicolas. 2013. Points aveugles de la nature: La rationalité scientifique médiévale face à l’occulte, l’attraction magnétique et l’horreur du vide (XIIIe-milieu du XVe siècle). Paris: Les Belles Lettres. ———. 2014. Innovations et science scolastique de la nature (v. 1260 – milieu du XIVe siècle). Cahiers de recherches médiévales et humanistes 27: 59–71.

Chapter 5

Mathematical and Metaphysical Space in the Early Fourteenth Century William O. Duba

Abstract  Medieval philosophers did not unequivocally support the Aristotelian doctrine of container-place, that is, that the place of a thing is the first immobile surface of what contains the thing. John Duns Scotus (d. 1308) famously developed a theory that tried to resolve the problems of container-place through an appeal to a notion of equivalence. Peter Auriol (d. 1322) took the radical step of reducing place to the category of position, understood with relation to the three-dimensional extension of the universe. Auriol called this “place according to metaphysical consideration” and contrasted it with “place according to physical consideration.” This division reflects one in another thinker, Nicholas Bonet (fl. 1333), who in his Philosophia naturalis distinguished between mathematical and natural senses of place. Rather than being influenced by Auriol, Bonet developed Scotus’ doctrine of equivalent place into a doctrine of mathematical place and time. To support his position, Bonet drew upon the Aristotelian notion of abstraction and selectively read Averroes as explicitly supporting his position.

5.1  Introduction Many thinkers found unsatisfactory Aristotle’s doctrine that place is the innermost surface of the containing body – a doctrine that, for the sake of simplicity, will be referred to here as ‘container-place.’1 Certainly, Aristotle’s doctrine solves the problem of giving place extramental existence; by making the place of a thing something other than the thing itself, Aristotle can hold that place is something real and show how something can change places without changing intrinsically. Yet, as Aristotle All translations are the author’s, except where otherwise noted.  For an account of the Aristotelian notions of place and space, see Algra’s Chapter 2 in this volume.

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W. O. Duba (*) Institut d’Études Médiévales, Université de Fribourg, Fribourg, Switzerland e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_5

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recognized, his solution gives rise to some absurd cases, most notably the cases where the container moves, with or without what it contains, the so-called problem of ‘mobile place.’ Scholastic thinkers had additional concerns. For example, purely spiritual beings, such as angels, can be said to be in place, but Aristotle’s discussion of place refers to material surfaces.2 Moreover, the celebrated Condemnation of 1277 required Parisian thinkers to hold several doctrines apparently at odds with Aristotle’s teaching, such as that God can move the heavens in a straight line, implying that the entire universe can change place3; but how can the universe change place without reference to a container? The Franciscan John Duns Scotus (d. 1308) suggested in passing a solution to the problems of mobile place by appealing to an otherwise-unspecified notion of equivalence, which some interpreters have claimed approaches “a conception of space as the three-dimensional container of bodies.”4 Scotus’ critic, the Franciscan Peter Auriol (d. 1322), came up with a more radical solution, reducing place to the category of position, situs, considered in reference to an arbitrary three-dimensional extension. Auriol distinguished this position-place from container-place by calling the latter ‘place according to physical consideration’ and apparently calling the former ‘place according to metaphysical consideration.’ Auriol’s radical view has attracted considerable attention for relegating Aristotelian container-place to a secondary role and promoting the primary sense of place as something approaching the notion of space.5 Whereas Scotus gives an embryonic account, Auriol is explicit. This difference has led to some confusion about the relative influence of the two doctrines on later thinkers who distinguish between multiple senses of place and who subscribe to a notion of place as three-dimensional extension. In particular, Chris Schabel has suggested a link between Auriol’s ‘metaphysical place’ and a similar notion defended by a later Franciscan, Nicholas Bonet. In the 1330s, Bonet famously distinguished between the ‘natural consideration of place’ and the ‘mathematical consideration of place,’ an abstracted notion of being-in-place with primarily mental existence. Schabel hypothesized that Bonet’s use of ‘mathematical’ “[m]ay be an error in the editions or in Bonet’s reading of an Auriol manuscript […] because the abbreviations for ‘mathematicus’ and ‘methaphisicus’ are often the same and frequently confused.”6 The inherent problems in Auriol’s passage and questions concerning its authenticity have led Schabel to attenuate his claim, now suggesting that Bonet’s doctrine

 See Tiziana Suarez-Nani’s Chapter 4 in this volume.  Piché-Lafleur 1999, 96 n49. As Algra’s Chapter 2 in this volume recalls, the first extant version of this thought experiment is found in the work of the Stoic philosopher Cleomedes. The same thought experiment plays a central role in the Leibniz-Clarke Correspondence; see Palmerino’s Chapter 12 in this volume. 4  Cross 1998, 211. 5  Schabel 2000, Maier 1968, Duhem 1956. 6  Schabel 2000, 140 n65. 2 3

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simply shares a common Aristotelian origin with that of Auriol.7 Nevertheless, this raises the question: what exactly is Bonet’s notion of mathematical place, and how does he develop it? In effect, Bonet’s doctrine is indebted to John Duns Scotus’ doctrine of container-place (Sect. 5.2). With regard to Peter Auriol’s doctrine of place as position and the specific doctrine of metaphysical place (Sect. 5.3), Bonet had an awareness of Auriol’s doctrine of place as situs, but he did not follow that route. Rather, Bonet’s notion of mathematical space traces its origins to a selective reading of a text, maybe even an abusive misreading, namely, of Averroes, which he uses in conjunction with the notion of equivalence to develop a doctrine of mathematical place and time (Sect. 5.4).

5.2  John Duns Scotus and Equivalent Place In his Ordinatio on book II of the Sentences, John Duns Scotus (d. 1308) defends a doctrine of container-place.8 This doctrine has a well-known problem, that of immobility: the containing body can change without the thing changing place; a river can dry up, and yet a boat anchored in the river will not change place. Scotus solves the problem of immobility with two propositions. First, he states that a container-place, qua container place, cannot move; if a thing that is a container-place moves, the place does not move with it. Since a place is an accident of its subject, when the subject changes (e.g., when container-air is replaced by container-water), a new accident of place takes over. As he puts it, “place has immobility that is entirely opposed to local motion”: The first statement is clear, because if it were in some way locally mobile, however much that mobility be in an accidental sense, it could be said to be in place and two different places could be assigned to it. For, although a likeness is moved almost accidentally through an accident (accidentaliter per accidens), namely as it is in the fourth or fifth degree (because first [there is] the body, and through the body the surface, and through the surface whiteness, and through whiteness the likeness), nevertheless, the surface or likeness truly exists in different places. Likewise, then something at rest could be moving locally, since what has different places successively is moved locally; but something fixed could have different containing places, if place were moved accidentally.9 7  Schabel 2011, 164: “But given that only one manuscript preserves what seems to be Auriol’s complete text, I now think it unlikely that Bonet had this text before his eyes, and that he was perhaps extrapolating from common statements on the mathematical vs. natural distinction going back to Aristotle himself.” 8  The standard reference for Scotus’ doctrines of place and space is Cross 1998, 193–213. 9  Ioannes Duns Scotus, Ordinatio II, d. 2, pars 2, q. 1–2 (1973, 256–257): “Dico igitur quod locus habet immobilitatem oppositam motui locali omnino, et incorruptibilitatem secundum aequivalentiam per comparationem ad motum localem. – Primum patet, quia si esset aliquo modo mobilis localiter, quantumcumque accipiatur per accidens, posset dici esse in loco et ei assignari posset alius et alius locus; sicut, licet similitudo moveatur quasi accidentaliter per accidens, scilicet quasi in quinto vel quarto gradu (quia primo corpus, et per hoc superficies, et per hoc albedo, et per hoc

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This immobility of place leads to the second proposition, that place has “incorruptibility according to equivalence by comparison to local motion.” That is, Scotus argues that the new and the old accidents of place are somehow the same place by equivalence: I prove the second statement, because, although place is corrupted when its subject moves locally, so that when the air moves locally, the same reason of place (ratio loci) as before does not remain in it (this is clear from what has already been proven), nor can the same reason of place remain in the water that follows, because numerically the same accident cannot remain in two subjects, nevertheless the reason of place that follows, which is different from the reason of place that precedes, in fact is the same as the preceding by equivalence, with respect to local motion. For it is just as incompossible for local motion to be from this place to that place as if it were entirely the same place in number. But no local motion can be from one where to another where, unless these two wheres correspond to two places that are different in species, since they (the places) have a different relation (respectus), not just in number, but also in species, to the whole universe. Thus, those relations that are only different in number seem to be one in number, because they are as indistinct with respect to local motion as if there were just one relation.10

According to this doctrine, a ship anchored in a river will have a place that is described by the inner surface of the surrounding water; as the river flows, that water constantly changes, and so the place of the ship constantly changes numerically. Nevertheless, those numerically distinct places are not different in species, for they maintain the same relation to the entire universe. Therefore, they are equivalently the same, and that equivalence suffices to guarantee the immobility of place. Scotus implies that we can speak of the same place in the way we can speak of two people owning the same handbag: they are two instantiations of the same species. The species of places, however, differ among themselves according to their respect to the whole universe. Subsequent Franciscans take Scotus’ doctrine in various directions. For his part, Nicholas Bonet is inspired by how Scotus abstracts place from distinct instantiations and equates those abstractions with each other. Peter Auriol, on the other hand, looks at Scotus’ claim for how places are different in species, namely by having a specifically different relation to the whole universe, and reduces place to the category of position. similitudo), tamen superficies vel similitudo vere est in alio et alio loco. – Similiter, tunc aliquid quiescens posset moveri localiter: nam quod habet alium et  alium locum successive, localiter movetur; fixum autem posset habere alium et alium locum continentem, si locus moveretur per accidens.” 10  Ioannes Duns Scotus, Ordinatio II, d. 2, pars 2, q. 1–2 (1973, 257–258): “Secundo probo, quia licet locus corrumpatur moto eius subiecto localiter, ita quod, moto aere localiter, non manet in eo eadem ratio loci quae prius (sicut patet ex iam probato), nec eadem ratio loci potest manere in aqua succedente, quia idem accidens numero non potest manere in duobus subiectis, − tamen illa ratio loci succedens (quae est alia a ratione praecedente) secundum veritatem est eadem praecedenti per aequivalentiam quantum ad motum localem, nam ita incompossibile est localem motum esse ab hoc loco in hunc locum sicut si esset omnino idem locus numero. Nullus autem motus localis potest esse ab uno ubi ad aliud ubi nisi quae duo ubi correspondent duobus locis differentibus specie, quia habentibus alium respectum – non tantum numero sed etiam specie – ad totum universum; ex hoc illi respectus qui sunt tantum alii numero videntur unus numero, quia ita sunt indistincti respectu motus localis sicut si tantum essent unus respectus.”

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5.3  Peter Auriol Peter Auriol lectured on the Sentences at Paris in the academic year 1317–1318.11 In the revised, written form of his lectures on book II, d. 2 of the Sentences, Peter Auriol raises the issue of the immobility of place. He states outright “that place in itself and primarily (per se et primo) is nothing other than position, for example, here or there.”12 Container-place, on the other hand, is only place in an accidental sense. By “position,” for which Auriol uses the terms positio or situs interchangeably, Auriol means the Aristotelian category, interpreted as the configuration of a body with respect to an imagined three-dimensional extension that contains the whole world.13 Auriol’s definition of the primary sense of place is at odds with the notion of container-place, and he sees container-place as accidental, namely as place “according to physical consideration.” A passage present only in one of the 12 extant manuscript witnesses, and therefore one whose authenticity has not been solidly established, distinguishes this from the primary sense: The description of place (ratio loci) is taken in one way according to metaphysical consideration, in another way according to physical consideration. For a physicist defines by matter, not indeed the matter that is the other part of a compound (because in that way a metaphysician defines by matter), but here “matter” should be taken for everything that is outside the description of a quiddity. According to this, therefore the consideration of a metaphysician differs from the consideration of a physician, because a metaphysician only treats what intrinsically pertains to a quiddity, while a physician treats material things and accidents and things extraneous to the quiddity. Whence, in his investigation the physician is concerned with the sensible qualities according to which the thing itself is subject to motion, action, and passion. Then, to the case at hand, I say that, of itself, the quiddity of place is nothing other than the description (ratio) of that where, and therefore place is quidditatively in the category of where. For this reason place according to metaphysical consideration is nothing other than that very where or position. And note that the immediate subject is a continuous quantity. Thus only something quantified is primarily and in itself capable of being situated, as could be evident elsewhere. This is the express intention of the Commentator, Metaphysics V, in the chapter on quantity, where he gives the reason why Aristotle does not count place among the species of category there [in the Metaphysics], as he does in the Categories. And the Commentator says “and perhaps he left aside place here, because according to him, place belongs to the passions of quantity.” Therefore, place is not quidditatively a quantity, but something that is accidental to quantity. But that is situation itself, that is, it is where, as was said.14  Duba and Schabel 2017.  Petrus Aureoli, In II Sententiarum, d. 2, pars 3, q. 1 (2000, 143–144): “Respondeo. Pono hic duas propositiones. Prima est quod locus per se et primo non est aliud quam positio, puta hic vel ibi. Secunda est quod per accidens locus est superficies corporis continentis.” 13  Schabel 2000. 14  Petrus Aureoli, In II Sententiarum, d. 2, pars 3, q. 1 (2000, 151–152): “Ratio loci aliter accipitur secundum considerationem metaphysicam, aliter secundum considerationem physicam. Physicus enim definit per materiam, non quidem per materiam quae est pars altera compositi, quia hoc modo metaphysicus definit per materiam, sed debet hic accipi “materia” pro omni eo quod est extra 11 12

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The text continues, and is joined by four other manuscript witnesses for the explanation of place in the physical sense: According to physical consideration, place beyond that where and situation means something material, say the extremity of the container, and thus place is not physically any one being in itself, but is one accidentally, aggregated from two categories. Or, if it is undesirable for it to be an accidental being such that it includes things of two genera in its direct and principal significate, one must at least say that it includes something in direct signification, say the quiddity of that place, and in oblique signification, in the manner of something connotated, it includes what is material to that place, namely the extremity of the container. And therefore, where Aristotle defined place physically, he said that it is the first immobile extremity of the container, not that it is formally and quidditatively the extremity of the container, because as such it would be quantity according to substance and would not be a passion of quantity, which the Commentator disproves above. Thus Physics IV, defining place, he means what is formal in place when he says “first immobile.” For place is only immobile because situation or place is immobile. He also means what is material when he says “extremity of the container.”15

In the passage available in one manuscript, the claim is raised that this place “according to metaphysical sense” is an accident that inheres in a continuous quantity. The position of this quantitative extension with respect to the quantitative extension of the universe makes place be place. By contrast, physical place, as discussed in five manuscripts, adds to place-as-position a material aspect, the container’s surface.

rationem quidditatis. Secundum hoc igitur differt consideratio metaphysici a consideratione physici, quia metaphysicus tantummodo accipit illud quod intrinsece pertinet ad quidditatem, sed physicus accipit materialia et accidentia ac extranea quidditati. Unde concernit in sua consideratione qualitates sensibiles secundum quas res ipsa est subiecta motui, actioni, et passioni. – Tunc ad propositum, dico quod de per se quidditate loci non est aliud quam ratio ipsius ubi, et ideo locus quidditative est in praedicamento ubi. Quapropter locus, secundum considerationem metaphysicam, non est aliud quam ipsum ubi sive positio. Et nota quod immediatum subiectum est quantitas continua. Unde nihil est situabile primo et per se nisi quantum, ut alibi apparere poterit. Haec est intentio Commentatoris expressa, V Metaphysicae, capitulo de quantitate, ubi reddit rationem quare Aristoteles ibi non numerat locum inter species quantitatis sicut in Praedicamentis. Et dicit ‘et forte dimisit hic locum quia apud ipsum locus est de passionibus quantitatis.’ Igitur quidditative locus non est quantitas, sed aliquid quod accidit quantitati. Illud autem est situs ipse, sive est ubi, ut dictum est.” 15  Petrus Aureoli, In II Sententiarum, d. 2, pars 3, q. 1 (2000, 152–153): “Sed secundum physicam considerationem, locus ultra ipsum ubi et situm dicit aliquid materiale, puta ultimum continentis, et sic locus physice non est aliquod unum ens per se, sed est unum per accidens ex duobus praedicamentis aggregatum. Aut si non placet quod sit ens per accidens, ita quod includat res duorum generum in recto et in principali significato, oportet saltem dicere quod aliquid includat in recto, puta quidditatem ipsius loci; et in obliquo per modum connotati includit illud quod est materiale ipsi loco, scilicet ultimum continentis. – Et idcirco, ubi Aristoteles definivit locum physice, dixit quod est ultimum continentis immobile primum, non quod formaliter sit ultimum continentis et quidditative, quia sic esset quantitas secundum substantiam et non esset passio quantitatis, quod improbat Commentator ubi supra. Unde 4° Physicorum, definiens locum, capit illud quod est formale in loco in hoc quod dicit ‘immobile primum.’ Non enim locus est immobilis nisi quia situs vel ubi est immobile. Capit etiam materiale cum dicit ‘ultimum continentis.’”

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The surface is materially in place, while place is formally built on the extension of the surface.16 Peter Auriol’s metaphysical consideration of place reduces it to the category of where, itself reduced to a type of position, namely position within the entire universe. For, Auriol opines, place is essentially such a position in the universe. According to physical consideration, however, place indicates something material: the container. Peter Auriol thus breaks place into two concepts: one physical, the other metaphysical.

5.4  Nicholas Bonet and the Philosophia naturalis Nicholas Bonet (or Bonetus) should need no introduction. He entered the Franciscan order in the convent of Tours, and after extensive studies, he was promoted to Master of Theology at the University of Paris in 1333; he enjoyed a stunning career in ecclesiastical administration, traveling to the East, but forsaking the luxuries of the Khan’s court in Beijing for a bishopric in Malta, and dying in 1343. Historians of philosophy know him for his masterwork; his Philosophia naturalis, composed in the 1330s, pretends to be the first systematic work of explicitly natural philosophy, starting with the science of being qua being in his Metaphysics – indeed, Nicholas was not only the first philosopher in history to write a Philosophia naturalis, but also, in naming the first part of this work, he was also the first person to give the title ‘Metaphysica’ to his own writing. In addition to the Metaphysics, the remaining parts of his natural philosophy are the Physics, the so-called Categories (a series of ten short treatises, one on each of the categories), and the Natural Theology. The entire text is rigorously systematic, with constant cross-references forward and back. He refers to the scholastic theologians of the previous century, such as Thomas Aquinas, Duns Scotus, and others, as ‘recent philosophers’ or ‘philosophers of our religion;’ for Greek and Arabic philosophers, from Plato to Averroes, he uses the

 Schabel 2000, 156. Schabel implicitly presents the second passage as authentic, since, after the part cited above, it continues by addressing objections that would otherwise be left open. This passage appears in five manuscripts, including Paris, Bibliothèque nationale de France, Latin 3066, which Florian Wöller has recently argued is a witness to Auriol’s final revision of book II (Wöller forthcoming). With the reference to the Commentator, the second passage explicitly refers to the first, arguing for its authenticity. Most likely, Peter Auriol had these two passages written in the margin or on easily overlooked cedulae, sometime after the text had begun to circulate. This would explain why the copyist of the only manuscript witness to the first passage, immediately after the first passage, began copying the next question before finding the second passage. That is, in the manuscript Firenze, Biblioteca Nazionale Centrale, Conv. Sopp. B.6.121, f. 21rb, the copyist finished with “ut dictum est.,” the last words of the first passage; he then began copying the next question (“Utrum angeli sint creati in celo empireo sicut in  loco”) before abandoning it (on f. 21va). At that point, the copyist crossed out the text of the new question, then went back and wrote after the “ut dictum est” the beginning of the second passage, namely “Sed secundum phisicam consideracionem,” extending into the margin.

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appellation ‘our ancestors,’ progenitores, and he explicitly portrays himself as building on, continuing, and in part replacing their work.17 His work was as successful as it was audacious. Over a dozen manuscript copies of the entire Philosophia naturalis survive, and even more of its individual parts; the Metaphysica, for example, survives in over 40 manuscripts and became part of the standard curriculum in some of the mendicant studia. For example, when a Franciscan went to study philosophy in the provincial studium in Strasbourg, his first-year course consisted in Bonet’s Metaphysica. Generations of Franciscans learned metaphysics not from Aristotle, but from Bonet. This historical importance has philological consequences: many of the extant  manuscripts were copied by scholars in their early years of philosophical study and in connection with the classroom, leading to a rather rich variance among the surviving copies. The philosopher Lorenzo Venier, editor of the 1505 edition of Bonet’s work, probably repaired the text in key places himself, and the result is that, until a critical edition of Bonet’s work is produced, his text should be reconstructed with reference to both the printed edition and several manuscripts, as is done here.18 Bonet’s thinking has attracted the attention of historians of science ever since Pierre Duhem pointed to his defense of atomism and the opinion of Democritus, or at least what Bonet thought Democritus’ opinion was. Duhem saw him as a pure philosopher, pursuing principles to their often absurd consequences: Bonet excels in discovering within each doctrine principles that can produce extreme consequences; he presses these principles and forces them to bring to light the corollaries hidden in their shadows. In his hands, the characteristics of a theory become so prominent that the author of the theory would not always recognize the legitimate offspring of his thought.19

Since then, generations of scholars have confirmed Bonet’s importance for discussions of atomism: Anneliese Maier, John Murdoch, and most recently Christophe Grellard and Aurélien Robert.20 The last two place Bonet’s work in the context of contemporary atomists such as Henry of Harclay, Gerald Odonis, and Nicholas of Autrecourt. In one such study, Grellard points to a connection between atomism and doctrines of space as three-dimensional extension, arguing that Bonet’s atomism is undergirded by a theory of abstraction combined with a distinction between mathematical and physical place. In brief, Grellard argues that, by appealing to a mathematical place as an abstraction from physical place, Nicholas Bonetus the atomist can avoid all arguments that appear to go against his doctrine. For example, while a  On Nicholas Bonet, see Duba 2014, 464–492. Goris 2015, 102–141.  In what follows, therefore, in addition to the 1505 edition, the following manuscripts are used: Paris, Bibliothèque nationale de France, Latin 6678 (=P, Metaphysica and Physica); Paris, Bibliothèque nationale de France, Latin 16132 (=S, Metaphysica and Physica, the copy from the library of the Sorbonne); Città del Vaticano, Bibliotheca Apostolica Vaticana, Vat. lat. 3040 (=V1, Metaphysica) and Vat. lat. 3039 (=V2, Physica, the copies used by Francesco della Rovere, later Pope Sixtus IV). 19  Duhem 1956, 259; English translation: Duhem 1985, 229. 20  Maier 1949, 177–179, Murdoch 1984, 45–66, Grellard 2004, Grellard and Robert 2009, and Robert 2012. 17 18

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physical thing can only be divided a finite number of times along an axis, the mathematical abstraction of that thing is capable of infinite division.21 In fact, Bonet’s distinction between mathematical and physical considerations is not just a means to support his atomism; it plays a central role in his philosophical system and in his mission, which is fundamentally syncretic and compatibilist. The challenge is that the distinction between an imaginary consideration – a mathematical sense – on the one hand, and a natural one – a physical sense – on the other, long predates Bonet and Scholastics in general. Indeed, Aristotle, in book IV of the Physics, extensively argues against the ‘common-sense’ notion of place as three-­ dimensional extension, pointing out that, if place had three-dimensional extension, then it would be a body over and above the body actually in place; rather, Aristotle founds place on the inside surface of the containing body; he likewise argues against time as a continuum independent of existing things and ties it directly to motion. Thus, the idea of mathematical place itself can be found in Aristotle, as the ‘common-­ sense’ notion of place as three-dimensional extension, a notion that he rejects, mirroring his rejection of time as an absolute continuum. Bonet’s contribution lies in defending this idea of mathematical place (and time) and in applying it systematically. Specifically, he develops a doctrine of mathematical abstraction, and inspired by what we might call a variant reading of Averroes’ discussion of time, applies it first to time and then to place, the latter by means of Scotus’ doctrine of equivalent places. That is, Bonet develops a twofold notion of time, encompassing both natural time, rooted in external reality, and mathematical time, an abstraction from that reality with purely conceptual existence; he credits Averroes with the term ‘mathematical time’; and he extends this natural/mathematical divide to motion and place. A consummate syncretist, he melds this Pseudo-Averroan term with the notion of equivalence poached from Scotus, and he relies on the doctrine of abstraction to fend off accusations of making time, place, and motion mere fictions. Nicholas Bonet’s doctrine of abstraction follows his presentation of the Platonic and Peripatetic doctrines of universals, a presentation that is so idiosyncratic that the editor of the 1505 Venice edition feels the need to refute Bonet’s ‘Peripateticism’ in the margins.22 After claiming that Aristotle’s universals have real, extramental existence in singulars, and can exist in separation from them, Nicholas describes the process of ‘mathematical separation,’ that is, of abstraction, beginning with magnitudes, such as those involved in spatial extensions or temporal durations. Relevant to his doctrines of place and time, Bonet argues that the purely mental abstraction of particular magnitudes is possible: For the intellect can abstract a particular magnitude objectively from every subject, because a quantity can have cognized being without the subject in which it exists having cognized being. And so, to abstract is nothing other than to consider this-besides-this (hoc preter hoc). And this is not a falsehood (mendacium) of those who abstract, and such an abstraction

21 22

 Grellard 2004, 189, citing Nicholas Bonetus, Physica IV, c. 2 (see below, n26).  Duba 2014, 480–484.

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of quantity from every sensible subject and matter is properly mathematical. For mathematicians consider the quantities of bodies without caring in what matter they exist.23

Of any given reality, the mind can consider a quantity by itself. Echoing Aristotle’s comments in Physics II, c. 2, Bonet is quick to insist that such an abstraction is not a pure fiction (mendacium), since it is abstracted from reality in the manner of hoc praeter hoc.24 These terms will surface again, precisely when Nicholas describes the distinction between physical and mathematical place. Nicholas Bonet hints at the central role of this distinction in the first mention of his doctrine of mathematical being, which occurs in the next section of the Philosophia naturalis, the Physica. In book IV, while defending his doctrine of atomism, Bonet confronts the objection that Aristotelian continua are infinitely divisible: But there is a doubt concerning these statements about the reality of motion, since to say such things is to contradict Aristotle, as is clear in the entirety of Physics VI. [To this,] it is said that Aristotle spoke of motion, time, and place mathematically, but not physically, or he spoke of motion only in conceivable being, but not in real being. But it is granted that in conceivable being motion has divisibility, continuity, and perhaps infinity, and so too the other properties that will be described in Physica VIII; but it does not have them in real being.25

While in the extramental world motion can be divided into a finite number of indivisible mutata esse, in conceivable being, that motion can be infinitely divided. Aristotle’s discussion of motion, time, and place mixes conceivable being and real being, and for this Bonet appeals forward to his Physica VI, where he discusses time, and to the ‘other properties’ of motion that he will discuss in his Physica VIII, that is, the culmination of his Physica, his discussion on place. 23  Nicholaus Bonetus, Metaphysica VIII, c. 2 (1505, ff. 42vb-43ra; P, f. 102r-v; S, f. 77va; V1, f. 78v): “Post hec autem de separatione mathematica est dicendum, et primo de separatione mathematicorum a sensibilibus, et primo quantum ad magnitudines, postmodum autem de numeris fiet sermo. Separatio autem mathematicorum potest intelligi tripliciter. Prima separatio magnitudinis singularis. Secunda universalis magnitudinis a singularibus. Tertia universalis magnitudinis ab omni subiecto, et in quolibet ordine potest intelligi separatio fieri vel apud intellectum in esse cognito, vel extra intellectum et in esse reali. – Dicamus igitur in primis de separatione mathematicorum in esse cognito quod in isto triplici ordine separatio possibilis est; potest namque intellectus abstrahere magnitudinem particularem ab omni subiecto obiective, quia quantitas potest capere esse cognitum absque hoc quod subiectum in quo est capiat esse cognitum. Et sic abstrahere nihil aliud est nisi considerare hoc preter hoc. Et talium abstrahentium non est mendacium, et talis abstractio quantitatis ab omni subiecto et materia sensibili proprie est mathematica. Considerant namque mathematici quantitates corporum non curantes in qua materia existant.” 24  Cf. Aristoteles, Physica II, c. 2 (193b 34–35); Auctoritates Aristotelis (ed. Hamesse 1972, 145 n57): “Abstrahentium non est mendacium.” 25  Nicholaus Bonetus, Physica IV, c. 2 (1505, f. 60rb; P, f. 142va; S, f. 111rb; V2, f. 76r-v): “Habet autem dubitationem circa ista dicta de realitate motus, quoniam sic dicendo est dimittere Aristotelem in contradictione, ut patet VI Physicorum per totum. Fertur quod locutus est Aristoteles de motu, tempore, et loco mathematice, non autem physice, vel tantum de motu in esse conceptibili, non autem in esse reali. Concessum est autem quod in esse conceptibili motus habet continuitatem, divisibilitatem, et forte infinitatem, et sic de aliis proprietatibus que VIII Physicorum scribuntur, non autem habet illa in esse reali.”

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In book VI of the Physica, Nicholas Bonet distinguishes between the physical and mathematical considerations of time and the present instant of time, the now (nunc). He begins by arguing that each motion has its own time, and therefore its own now. That leads to an objection, namely that, according to this sense, two events cannot happen at the same time: And if you argue, “therefore in the same now in which I eat someone else does not live, and in the same now in which I speak, the Seine does not flow,” I reply: not in the same now really, but in the same equivalently, by which I understand a now measuring extrinsically and not intrinsically. You have to observe carefully that it is not the same now according to physical consideration, but according to mathematical consideration it is the same now in number, as will be said below concerning time. And if you should say: “You contradict your ancestors,” I reply: in this matter, they spoke about time and the now mathematically, abstracting the now by the intellect from a given mutatum esse in this motion and [from another mutatum esse] in that motion, and as such it is the same now, at least equivalently. Our ancestors also held it to be absolutely impossible for there to be many worlds and consequently many equally-first motions, therefore there are many times together and many nows; but we deviate from our ancestors in this principle, therefore we must also deviate from them in the conclusion that follows necessarily from that principle.26

Duhem sees here further proof of the revolutionary nature of the Condemnation of 1277; since Bonet recognizes that he cannot share the same assumptions as his philosophical predecessors.27 Beyond this discussion of principles, however, Bonet explicitly brings in Scotus’ notion of equivalence, and by equivalence he means the equivalence achieved by mentally abstracting the nows from the motions in which they inhere. Unlike Scotus, however, Bonet does not ground this equivalence in the sense of being numerically different but specifically the same; equivalence for Bonet means that the two items can become numerically one via abstraction, when considered mathematically. Bonet clarifies the two ways of considering time in the next chapter, explicitly citing Averroes: We should investigate the parts of time as well as the unity of time. To the evidence of which, it should be understood that there are two considerations of time: one natural and the  Nicholaus Bonetus, Physica VI, c. 1 (1505, f. 67rb; P, f. 161r; S, f. 127ra-b; V2, f. 54v): “Et si arguas ‘ergo in eodem nunc in quo comedo alius non vivit, et in eodem in quo loquor, Secana non currit,’ respondeo: non in eodem realiter, sed in eodem equivalenter, per quod intelligo nunc mensurans extrinsece et non intrinsece. Debes diligenter advertere quod nunc secundum considerationem physicam non est idem; secundum considerationem tamen mathematicam est idem nunc numero, sicut dicetur inferius de tempore. – Et si dicas: ‘contradicis progenitoribus tuis,’ respondeo: illi loquti sunt in hac materia de tempore et de nunc mathematice, abstrahendo nunc per intellectum ab isto mutato esse in hoc motu et in illo, et ut sic idem nunc est saltem equivalenter. Progenitores etiam nostri habuerunt simpliciter pro impossibili plures esse mundos et per consequens plures esse motus eque primos, ergo plura tempora simul et plura nunc; nos autem ab eis deviamus in hoc principio, ergo et oportet deviare in conclusione necessario sequente ex illo principio.” 27  Duhem 1956, 431: “En affirmant que Dieu peut, s’il lui plaît, créer plusieurs Mondes, Étienne Tempier a ruiné le fondement qui portait la théorie peripatéticienne du temps; de même en affirmant que Dieu peut imposer à l’Univers un mouvement de translation, il avait privé de base la théorie péripatéticienne du lieu.” The condemnation Duhem has in mind is of the doctrine that God cannot move the universe rectilinearly; see Piché-Lafleur 1999, 96 n49. 26

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other mathematical. Therefore, the simultaneity and unity of time should be spoken of in one way according to natural being and in another way according to mathematical being, and this is what that Commentator, Averroes, says in Physics IV, the chapter on time, comment 131, that time is said to be related outside the soul in the same way, similar to place, and he adds: “this consideration of time is mathematical and not natural”: one manuscript has the reading “mathematical,” another “divine,” another has “philosophical.”28

Averroes defended a notion of time according to which time has actual existence only in the mind; in the world, it only has potential existence in the individual movements. Therefore, outside the mind, time only resembles the perfect, that is, the actual. The quotation of Averroes that Bonet makes at the end of the passage is intriguing: in the Juntina edition, the text reads, “in this way time is said to have existence outside the soul similar to the actualized (simile perfecto), even if it is not actualized. And this investigation of time is more philosophical than natural.”29 Here, Bonet’s text seems to corrupt the first part to associate time with place (notably changing simile perfecto to simile loco),30 and Bonet himself selects the reading that says that this investigation “is mathematical and not natural,” admitting that there are other variants, namely “divine” and “philosophical.” Bonet appeals to Averroes for the division between “mathematical” and “physical” (or “natural”). His doctrine uses the “physical” sense to absorb theories associating time and the instant with motion. He then guarantees that there is a single time for all things through a curious mix of Averroes’ conceptual notion of time, Scotus’ doctrine of equivalence, and an appeal to mathematical abstraction based on a variant reading of Averroes. Nicholas Bonet crowns his Physica with a discussion on place in the eighth and final book. There, in the last chapter, Bonet pulls together the strings and ascribes to Aristotle and Averroes the distinction between mathematical and natural place: The final saying of our ancestors on the immobility of place is: there are two kinds of speculation concerning place: one mathematical and the other natural. Aristotle had the mathematical consideration of place in mind when he defines place saying that it is primarily the 28  Nicholaus Bonetus, Physica VI, c. 2 (1505, f. 67vb; P, f. 162r-v; S, f. 128rb-va; V2, f. 55r): “De simultate autem partium temporis est inquirendum et de eius unitate. Ad cuius evidentiam est intelligendum quod consideratio de tempore est duplex: una naturalis et alia mathematica. Ideo aliter est dicendum de simultate et unitate temporis secundum esse naturale (naturale] nature mss.), aliter secundum esse mathematicum, et hoc est quod dicit Commentator ille Averroys, 4 (4] 8 P, 2 V2) Physicorum, capitulo de tempore, commento 131, dicens quod tempus eundem modum dicitur habere esse extra animam simile loco (eundem ... loco] secundum hunc modum dicitur inesse extra animam simile perfecto etsi non sit perfectum 1505), et addit: ‘ista consideratio de tempore magis est mathematica quam naturalis.’ Una littera habet ‘mathematica,’ alia ‘divina,’ alia habet ‘philosophica.’” 29  Averroes, Physica IV, comm. 131 (1562, f. 202vaH): “Secundum igitur hunc modum dicitur tempus habere esse extra animam simile perfecto, etsi non sit perfectum. Et ista perscrutatio de tempore magis est philosophica quam naturalis.” 30  Of the texts I consulted, only the 1505 edition has the correct reading for the first part of the text (simile perfecto), and this may be the corrective work of the editor. Cf. Duhem 1956, 432: “C’est ce que dit le Commentateur d’Aristote au commentaire 131 sur le huitième livre des Physiques: il remarque que la façon dont le temps se comporte hors de l’esprit est analogue à celle dont se comporte le lieu.”

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immobile surface of the containing body; but the natural consideration of place would define place thus: that it is primarily the mobile surface of the containing body. For a natural philosopher, as natural philosopher, does not consider the definition of place (ratio loci) properly speaking, but the definition of vessel (ratio vasis). But every place that has the definition of vessel is mobile.31

Nicholas Bonet echoes Peter Auriol’s presentation of place, emphasizing that Aristotle’s reference to the vessel indicates that the discussion concerns physical place. Yet, he states what Auriol does not, namely that physical place is primarily mobile place. Further, he ascribes the mobile/immobile place distinction to “our ancestors,” but his definition according to the “natural consideration of place” is explicitly hypothetical; no ancestor actually made such a statement. Nicholas Bonet differs from Auriol concerning the non-natural consideration of place as well: Auriol’s metaphysical place is tied to the quiddity of place, that is, to the notion of what place is, while Nicholas Bonet discusses mathematical place not with the terminology of quiddities, but with the terms he used earlier in defining abstraction: Therefore, you have to diligently observe that mathematical consideration of place is the consideration of the primary containing surface of the body without considering the natural body to which that surface belongs. Thus a mathematician considers the surface of air that immediately surrounds and contains you, without caring in what body it exists, be it air or something else; he considers precisely that surface, and, as it is abstracted from every natural body, it is immobile, because all mathematical beings are immobile, because they abstract from motion and from sensible matter. Nor is there a falsehood (mendacium) in such an abstraction, because what is considered is this-besides-this (hoc praeter hoc), not this-without-this. Thus place, as a mathematician considers it, is entirely immobile. Hence the surface of air that surrounds and contains you, when it is considered as if separate from the air (and from other bodies through the variation of the natural body that contains you) never changes. For since the surrounding surface, as considered mathematically, is always considered as one, therefore place is entirely immobile according to mathematical consideration; but according to natural consideration it is mobile and only has the definition of a vessel, because natural place is considered, namely as the surface is in this and that natural body, and that surface is certainly mobile, both subjectively and objectively, just as its natural body is mobile, in the way that the parts of the river continually vary according to the natural being of the river, and consequently so do the surfaces of those bodies as they are considered under natural being, but not as they are mathematically considered.32  Nicholaus Bonetus, Physica VIII, c. 4 (1505, f. 75rb; P, f. 183r; S, f. 145vb; V2, f. 80r): “Ultimum autem dictum nostrorum progenitorum de immobilitate loci est istud: quoniam de loco est duplex speculatio, una mathematica et alia naturalis. Consideratio autem mathematica de loco fuit apud Aristotelem cum diffinit locum dicens quod est superficies corporis continentis immobilis primum. Consideratio autem naturalis de loco sic diffiniret locum: quod est superficies corporis continentis mobilis primum. Naturalis enim ut naturalis est non considerat proprie rationem loci, sed rationem vasis; omnis autem locus qui habet rationem vasis mobilis est.” 32  Nicholaus Bonetus, Physica VIII, c. 4 (1505, f. 75rb; P, f. 183r; S, ff. 144vb-145ra; V2, f. 80r): “Debes igitur diligenter advertere quod mathematica consideratio de loco est consideratio de superficiei corporis continentis primum, absque hoc quod consideretur corpus naturale cuius est illa superficies. Unde mathematicus considerat superficiem aeris te ambientem et continentem immediate, non curando in quo corpore existat, sive sit aer vel aliquid aliud, sed precise considerat illam superficiem, et, ut sit abstracta ab omni corpore naturali, immobilis est, quia omnia mathematicalia (]mathematica mss.) sunt immobilia, quia abstrahunt a motu et a materia sensibili. Nec in tali abstractione est mendacium, quia consideratur hoc preter hoc, non autem hoc sine hoc. Ideo

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Finally, Bonet supports his argument with an appeal to Averroes; more specifically, he cites the same passage he used in support of mathematical time, where he managed to introduce the word ‘mathematical’ through a variant reading. Now, however, he presents a manifestly perverse citation: But this is clear according to the Commentator, Physics IV, comment 131, since the consideration of place is more mathematical than natural. Let us conclude therefore that this was the intention of our ancestors concerning the immobility of place, and who should not be content with this aforesaid threefold immobility can go look elsewhere.33

Bonet’s mathematical place is the only sense in which place is immobile, and mathematical place exists in conceivable being, not in reality. He claims it is not a pure fiction because of its tie to reality via abstraction. While the physical place of a non-­ moving object may change, its mathematical place does not, and this occurs because the mind understands the equivalence of the disparate physical places. But this raises the question: with respect to what external reality are two equivalent places equivalent?

5.5  Conclusion Aristotle’s doctrine of container-place has long caused perplexity, and especially when the container itself moves, leading to the problem of mobile place. To resolve this issue, John Duns Scotus appealed to a doctrine of equivalent place, according to which two numerically distinct container-places can be said to be one if they have the same relation to the universe. Peter Auriol simplified the appeal, and claimed that place in the proper sense was metaphysical place, understood as position in a three-dimensional extension, and consigned container-place to an accidental sense, “place according to physical consideration.” Nicholas Bonet might have been inspired by Peter Auriol’s claim that Aristotle spoke of place in two senses, and only one sense was physical. For Bonet, however, the defining feature of physical place locus, ut de eo mathematicus considerat est omnino immobilis. Unde superficies aeris te ambiens et continens considerata quasi separata ab aere et ab alio corpore per variationem corporis naturalis continentis numquam mutabitur. Superficies enim ambiens ut mathematice considerata, quoniam semper consideratur ut una, ideo locus est omnino immobilis secundum considerationem mathematicam; secundum autem considerationem naturalem, mobilis est et tantum habet rationem vasis, quia consideratur locus naturalis, ut scilicet superficies est in corpore naturali isto et illo, et illa superficies bene est mobilis et subiective et obiective, sicut et corpus naturale cuius est, sicut partes fluvii continue variantur secundum esse naturale fluvii, et per consequens superficies illorum partium ut sub esse naturali considerantur, non autem ut mathematice considerantur.” 33  Nicholaus Bonetus, Physica VIII, c. 4 (1505, f. 75rb; P, f. 183r-v; S, f. 145ra, V2, f. 80r): “Palam autem secundum Commentatorem, IV Physicorum, commento 131, quoniam consideratio de loco est magis mathematica quam naturalis. – Concludamus ergo quod ista fuit intentio progenitorum nostrorum de loco immobilitate, et qui ista triplici immobilitate predicta non fuerit contentus, querat aliam.”

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was that it was mobile, and the other sense of place was certainly not metaphysical, giving place-as-extension ontological priority over physical place, but rather mathematical, in the sense of considering magnitudes independently of the subjects that they inhere in, and therefore making place-as-extension derive from physical place. In this way, he tried to place Scotus’ kernel of a doctrine of equivalent place in fertile ground, although unlike Scotus’ teaching, Bonet’s identity by equivalence is a numeric identity enabled by abstraction. Bonet, however, never explains the frame of reference according to which two places can be equivalent. In these aspects, Bonet’s use of abstraction plays a central role in his physics, serving equally well in his discussion of place as in his treatment of atomism, and of time. To answer the question of influence, Bonet was explicitly influenced by Scotus, possibly influenced by Auriol, and absolutely faithful only to himself. Influence and irreverence mark Bonet’s attitude towards the ancient Greek and Arabic philosophers, those Bonet calls his ‘predecessors.’ Conscious that his philosophical point of departure differed from that of his predecessors, Bonet sought nevertheless to engage them in dialogue, explaining their positions, and to take the mantle as their equal and interlocutor. Yet, over the course of the Physica, his dialogue with the philosophers becomes increasingly warped by his own philosophy, to the point that, at the end, he claims that his views find support in the very words of his predecessors, words that those predecessors might never have written. His ventriloquist act reveals in the extreme the radical solitude of the philosopher, who can only participate in a perennial tradition by constructing a monologue with the past.

References Averroes. 1562. Quartum Volumen Aristotelis De physico auditu libri octo cum Averrois Cordubensis variis in eosdem commentariis, Quae omnia, a summis huius aetatis Philosophis a mendis quamplurimis expurgata cernuntur. Marci Antonij Zimarae Contradictionum in eosdem Libros Solutiones. Venetiis apud Iunctas (USTC 810959, v. 4 = Physica). Cross, Richard. 1998. The Physics of Duns Scotus. Oxford: Oxford University Press. Duba, William. 2014. Three Franciscan Metaphysicians After Scotus: Antonius Andreae, Francis of Marchia, and Nicholas Bonet. In A Companion to the Latin Medieval Commentaries on Aristotle’s Metaphysics, ed. Fabrizio Amerini and Gabriele Galluzzo, 413–493. Leiden: Brill. Duba, William, and Chris Schabel. 2017. Remigio, Auriol, Scotus, and the Myth of the Two-Year Sentences Lecture at Paris. Recherches de Théologie et Philosophie Médiévales 84: 143–179. Duhem, Pierre. 1956. Le système du monde: Histoire des doctrines cosmologiques de Platon à Copernic. Vol. 7. Paris: Hermann. ———. 1985. Medieval Cosmology. Theories of Infinity, Place, Time, Void, and The Plurality of Worlds, trans. Roger Ariew. Chicago: University of Chicago Press. Goris, Wouter. 2015. Transzendentale Einheit. Leiden: Brill. Grellard, Christophe. 2004. Les présupposés méthodologiques de l’atomisme: La théorie du contenu de Nicolas d’Autrécourt et Nicolas Bonet. In Méthodes et statut des sciences à la fin du Moyen-Âge, ed. Christophe Grellard, 181–199. Paris: Presses Universitaires du Septentrion. Grellard, Christophe, and Aurélien Robert, eds. 2009. Atomism in Late-Medieval Philosophy and Theology. Leiden: Brill.

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Hamesse, Jacqueline. 1972. Les Auctoritates Aristotelis: Un florilège médiéval. Étude historique et édition critique. Louvain: Université Catholique de Louvain. Ioannes Duns Scotus. 1973. Ordinatio. Liber Secundus. Distinctiones 1–3, ed. Carolus Balič. Vatican City: Typis Polyglottis Vaticanis. Maier, Anneliese. 1949. Die Vorläufer Galileis im 14. Jahrhundert. Rome: Storia e Letteratura. ———. 1968. Zwei Grundprobleme der Scholastischen Naturphilosophie. 3rd ed. Rome: Storia e Letteratura. Murdoch, John. 1984. Atomism and Motion in the Fourteenth Century. In Transformation and Tradition in the Sciences: Essays in Honor of I.  Bernard Cohen, ed. Everett Mendelsohn, 45–66. Cambridge: Cambridge University Press. Nicholaus Bonetus. 1505. Habes Nicholai Bonetti viri perspicacissimi quattuor volumina: Metaphysicam videlicet naturalem phylosophiam praedicamenta necnon theologiam naturalem, Venice, (USTC 816175 = Philosophia naturalis (Metaphysica, Physica, Praedicamenta, et Theologia naturalis). Petrus Aureoli. 2000. In II Sententiarum, d. 2, pars 3, q. 1, ed. Chris Schabel. In Chris Schabel, Place, Space, and the Physics of Grace in Auriol’s Sentences Commentary. Vivarium 38:117– 161, at 143–154. Piché, David, and Claude Lafleur. 1999. La condamnation parisienne de 1277: Nouvelle édition du texte latin, traduction, introduction, et commentaire. Paris: J. Vrin. Robert, Aurélien. 2012. Le vide, le lieu et l’espace chez quelques atomistes du XIVe siècle. In La nature et le vide dans la physique médiévale, ed. Joël Biard and Sabine Rommevaux, 67–98. Turnhout: Brepols. Schabel, Chris. 2000. Place, Space, and the Physics of Grace in Auriol’s Sentences Commentary. Vivarium 38: 117–161. ———. 2011. The Reception of Peter Auriol’s Doctrine of Place, with Editions of Questions by Landulph Caracciolo and Gerard of Siena. In Représentations et conceptions de l’espace dans la culture médiévale: Colloque Fribourgeois 2009, ed. Tiziana Suarez-Nani and Martin Rohde, 147–192. Berlin: De Gruyter. Wöller, Florian. Forthcoming. Inaugural Speeches by Bachelors of Theology: Principial Collationes and their Transmission (1317–1319). In Principia on the Sentences, eds. Monica Brînzei and William Duba. Turnhout: Brepols.

Chapter 6

Space, Imagination, and Numbers in John Wyclif’s Mathematical Theology Aurélien Robert

Abstract  The aim of this paper is to show that John Wyclif’s theory of space is at once an interpretation of the Platonic theory of place and a Neopythagorean conception of magnitudes and numbers. The result is an original form of mathematical atomism in which atoms are point-like entities with a particular situation in space. If the core of this view comes from Boethius’ De arithmetica, John Wyclif is also influenced by Robert Grosseteste’s metaphysics, which includes the Boethian number theory within the Christian tale of the creation of the world ex nihilo. John Wyclif, however, adds some novelty to this theory concerning the epistemological status of this hypothetical description of the creation of the world out of atoms. First, according to Wyclif, whereas geometry is concerned with sensible and imaginable beings, arithmetic, which is purely intellectual, has access to the deep mathematical structure of the universe. He then suggests a subordination of geometry under arithmetic, which he considers the most solid basis for his metaphysics. As a result, with the attribution of numbers and units to every level of reality, it becomes possible to reform our natural imagination, so that it can imagine the atomic structure of matter and space.

6.1  Introduction It has long been thought that medieval philosophers were not able to conceive space as a three-dimensional, absolute and infinite space, because they predominantly adopted the Aristotelian cosmos together with its conception of place as the two-­ dimensional surface of the surrounding body.1 Edward Grant went as far as to con1  For an account of the Aristotelian notions of place and space see Algra’s Chapter 2 in this volume.

A. Robert (*) Centre d’Études Supérieures de la Renaissance, CNRS, Université de Tours, Tours, France e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_6

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clude that theories of abstract and mathematical space found no support between the sixth century, with John Philoponus, and the sixteenth century, with Francesco Patrizi – with some rare exceptions, such as the Jewish philosopher Hasdai Crescas in the fourteenth century.2 In recent decades, however, new interesting examples have been discovered within fourteenth-century Western philosophy, of thinkers such as Walter Chatton, Guiral Ot, William Crathorn, Nicolas Bonet, Nicole Oresme, and John Wyclif, who tended to reduce place to space or, at least, to a position in space, even though they did not replace the Aristotelian cosmos with a Euclidean absolute and infinite space.3 What is interesting with regard to these newly explored cases is that, with exception of Nicole Oresme, they all defended a specific form of atomism, according to which a body is ultimately constituted of indivisibles. And except for Nicolas Bonet and Nicolas of Autrécourt, who sometimes considered indivisibles as minima or corpuscles, all others defended a mathematical atomism in which indivisibles are point-like entities. These two aspects, the theory of place and atomism, are directly connected with each other insofar as geometric space is thought of as composed of surfaces, lines and points (mathematical atoms). John Wyclif (ca. 1330–1384) is one of the most intriguing figures of this group of philosophers. While best known today for his opinions on the reform of the Church, he also wrote several philosophical treatises in which he defended an interesting theory of place and space inspired by the Platonic and Neopythagorean traditions. As a consequence, Wyclif’s system perfectly illustrates what David Albertson recently called “mathematical theologies,” which correspond to a systematic analysis of the created universe in mathematical terms, based on a Neopythagorean number theory.4 Albertson convincingly shows that this approach continued to be very popular throughout the Middle Ages, from Boethius’ time to the twelfth century at least, and it was then revived in the fifteenth century by Nicolas of Cusa. But, as I have argued elsewhere, this type of theory also continued to be important in the thirteenth and fourteenth centuries, among a range of philosophers and theologians, and more particularly for the atomists listed above.5 The present paper aims to place John Wyclif within this long tradition, and show how he develops it in his own fashion. Here I will focus on John Wyclif’s atomist conception of matter and space in relation to his philosophy of mathematics. Indeed, Wyclif faced a classical problem that concerned all atomists: indivisibles, be they corpuscles or mathematical points, cannot be seen or touched, so that they could be mere fictional entities, or correspond to a mere theoretical hypothesis. An Aristotelian philosopher would argue that intellectual abstraction always depends on sensory cognition and imagination, and that, if indivisibles are not cognized by the senses, there cannot be an accurate  Grant 1976, 138.  On Walter Chatton see Robert 2012; on Guiral Ot see Bakker and De Boer 2009; on William Crathorn see Robert 2009 and Roques 2016; on Nicolas Bonet see Duba’s Chapter 5 in this volume; on Nicole Oresme see Kirschner 2000. We also find this kind of theory in the Arabic tradition, but I will limit this study to the Latin tradition. 4  Albertson 2014. 5  Robert 2017. 2 3

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representation of them in the mind. How can we imagine points independently of other entities? How could one be certain that they exist? John Wyclif was perfectly aware of these problems and tried to find a solution that is coherent with the principles of his Platonic and Neopythagorean metaphysics. According to him, if the senses and imagination have a role in the process of grasping the mathematical structure of the world, only the intellect can ascend to this non-sensible reality, thanks to the science of arithmetic. In other words, whereas the geometer and the natural philosopher heavily depend on sensory cognition, so that they cannot grasp the atomic structure of reality, the metaphysician is able to conceive reality as composed of indivisibles, thanks to the attribution of numbers to all kinds of realities, including matter and space. With this mathematical conception of reality, the intellect is therefore able to correct the senses and gives a new top-down impulse to the imagination.

6.2  John Wyclif’s Mathematical Atomism From his earlier philosophical works in the 1360s to his later theological tracts, John Wyclif constantly asserted that every continuum is ultimately constituted of indivisibles without quantity (non quanta). In a stimulating paper, Norman Kretzmann analysed some of his arguments, but noted that, despite some really innovative philosophical insights into the problem of the continuum, the whole theory seemed to be based on theological assumptions, such as the possibility for God to count the precise number of atoms in a finite continuum of matter, space or time.6 More recently, Emily Michael has also suggested an interpretation of John Wyclif’s atomism as a consequence of his “logic of Scripture,” insofar as it depends on his exegesis of Genesis, based on Augustine’s commentaries.7 They are both absolutely right. It is, indeed, difficult to separate the philosophical arguments supporting atomism from its broader theological context. This is partly due to his methodology, which subordinates philosophical investigation to Scripture and Christian theology, and partly to his metaphysics. This becomes quite clear in the Trialogus, written in 1382 or 1383, in which John Wyclif gives an overview of his system. Following the traditional agenda of medieval theologians, the treatise begins with God’s existence and properties, and then turns to the divine ideas – considered equivalent to Platonic ideas in the Timaeus – which served as models for the creation of the world. The second book deals with the world itself, its unity and composition. At one point Alithia, who speaks for philosophical truth, says that the world seems to be a mere aggregate of creatures, whereas Pseustis, a sceptic of sorts, raises some doubts about this mereological assumption. Finally Phronesis, who represents Wyclif’s own position, defends the unity of the world without denying Alithia’s point of view altogether. Here again,  Kretzmann 1986.  Michael 2009.

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the text is reminiscent of a typically Platonic trend: in the same way as a man is a little world, a microcosm, with a unity due to its substantial form, the bigger and total world, the macrocosm, has a similar unity, which is due to something akin to ‘the soul of the world.’ Unfortunately, Wyclif does not develop this Platonic conception of the unity of the world, but he seems to state that the parts of the universe, including indivisible parts, would be a mere aggregate without a form. He then turns to the composition of created things from indivisibles: Pseustis: You frequently assume what is impossible, that a continuum is composed of instants, for which Aristotle often reproves Plato and Democritus, indeed he teaches this with enduring reason and mathematical demonstration. Phronesis: Certainly it appears to the wise, in geometry and other sciences, as in arithmetic, [that] something with a quantity is composed of [indivisibles] without quantity, which must be the principles of any sort of composite. […] I give this response along with Augustine and faith in Scripture, that just as God saw everything that He made [Genesis 1, 31], so He understands distinctly every part of every continuum, so that there are not given more or other components of that continuum. And in that way the reasoning seems plainly to succeed. And as for the text of Aristotle and his followers, it is clear that it does not produce faith, since it had often erred. But Democritus, Plato, Augustine, and Robert Grosseteste, who thought in this way, are much more distinguished philosophers, and much more brilliant in many metaphysical issues.8

This short sketch reveals the most important features of Wyclif’s mathematical atomism. The first point to be noted here is that, even though atomism is coherent with the principles of mathematics, it cannot be understood without metaphysics and must agree with Scripture, and more particularly with the story of Creation. Wyclif explicitly names his sources, even though we should add some names to this short list, like Boethius. The alleged reason for naming them, i.e. Democritus, Plato, Augustine and Robert Grosseteste, is that these philosophers were much more brilliant than Aristotle on metaphysical issues. This means that what is at stake here does not concern natural philosophy: it is a metaphysical problem connected with the original creation of the material world. John Wyclif’s atomism is also related to his well-known thesis about the sacrament of the Eucharist. In his official condemnation at the Council of Constance (1414–1418), three of the forbidden theses directly concern atomism, and the context suggests that they were considered by the authorities present at the Council as the source of his negation of the dogma of transubstantiation.9 49: God cannot annihilate, diminish or increase the world. 51: Any continuous line is composed of two, three, or four points without intermediate points, or of only an absolutely finite number of points; and time is, was and will be composed of instants without intermediate instants. 52: One has to imagine that one corporeal substance was produced at its beginning as composed of indivisibles, and that it occupies every possible place.10

8  Wyclif 1869, II, ch. 3, 83–84 (for the Latin text), and Wyclif 2012, 76–77 (for the English translation, slightly modified here). 9  Lahey 2009, ch. 4; see Levy 2003 for a general presentation. 10  [Councils] 1973, 426.

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These three assertions give a faithful outline of Wyclif’s atomism. First, God has created the material world with indivisibles or atoms and he cannot change its structure afterwards. Second, what he has created, notably prime matter, has a mathematical structure: it is composed of mathematical atoms, i.e. unextended point-like entities. Third, this is conceivable for us, as soon as we ‘imagine’ (imaginandum est) that God has created the world with these atoms, so that they occupy the totality of the space that is now filled by the world. This space is like a sphere composed of lines – each point in this sphere is the end of one diameter –, which are, in turn, constituted of points. As a system, it certainly allows Wyclif to deny the reality of transubstantiation during the Eucharist, insofar as the official dogma would imply that God must annihilate one substance, or at least its form, in order to create another. But, as it seems, the negation of transubstantiation is only a consequence of this system, not Wyclif’s principle motive to endorse it. The main reason for adopting mathematical atomism is his metaphysics of creation. These three propositions condemned at the Council of Constance almost literally feature in the last part of John Wyclif’s Logica, usually referred to as Logicae continuatio, which is probably one of his earlier philosophical works, together with his commentary on the Physics.11 In these texts, Wyclif does not discuss transubstantiation, or only incidentally, but provides a full-fledged atomistic theory, in which he tackles several important issues, such as the nature of space, the distinction between the continuous and the discrete, and the role of atomism in the description of different kinds of motion. Certainly, the theological aspect of this theory is not totally absent from the Logica, but it is limited to a metaphysical theory of creation largely inspired by the Platonic and Neopythagorean tradition. Indeed, despite his apparent allegiance to Democritus, the doctor evangelicus is by no means a materialist, and he does not limit his ontology to atoms and void. Not only does he deny the existence of void, insofar as the world-space is totally filled with atoms, but he does not restrict his ontology to indivisibles of matter, space and time. As is well known, Wyclif is a realist about universals – they have some kind of existence and unity independently of the singular objects concretely exemplifying them. He also defends a realist analysis of the ten Aristotelian categories – they all have some specific kind of existence and are not mere linguistic or conceptual ways to order the world – and believes in the existence of real counterparts of ­propositions in the world (propositiones in re).12 What is more, he does not only follow Aristotle’s Categories in his own ontology, but also defends hylomorphism: every particular is  It is usually assumed that the third part of the Logica was written between 1360 and 1363, immediately after the first two parts, but the date 1383 is once mentioned in the text. Thomson (1983) considers the possibility that either a copyist changed the original date, or that it is a scribal mistake. Wyclif’s unedited commentary on the Physics survives in only one manuscript (Venice, Biblioteca Nazionale Marciana, MS Lat. VI. 173). Ivan Müller is presently preparing an edition of this text. The two important questions in which Wyclif deals with atomism and the nature of place are the following: Utrum omnia temporaliter existentia sunt in loco (ff. 38ra-40rb); Utrum omne tempus, magnitudo et motus diversificate se invicem consequuntur (ff. 52vb-55ra), and many arguments are similar to the ones developed in the Logica. 12  Conti 2006 and Cesalli 2005. 11

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constituted of matter and forms (substantial and accidental). As a consequence, matter is composed of indivisibles, but a particular piece of matter is also informed by elemental forms (earth, fire, water and air) and by their mixture before it receives substantial and accidental forms.13 Another important departure from Democritus is that Wyclif’s atoms are absolutely indivisible, i.e. physically and conceptually. They are not corpuscles with a shape and figure, but point-like entities. What is more, they do not play any causal role in natural phenomena. Indivisibles of matter, form, space, time and motion rather serve as units of measurement for natural phenomena, at least from the point of view of God, who has created the world according to these units. This very rich ontology led Wyclif to give a new interpretation of Aristotle’s Categories, which is central for his atomism. Indeed, in the first part of his Logica and in his De ente praedicamentali, John Wyclif describes the presence of indivisible units in several categories, not only in the category of quantity. In every category there must be one principle, which is the metre and the measure of all the things contained in this category: the first principle in the category of substance is God, who is superior to all created substances; the first principle in the category of quantity is the unit, because unit is the principle of continuous quantity as well as discrete quantity; the first principle in the category of quality is the degree, because every latitude of a quality is composed of degrees; the first principle in the category of relation is dependence; the first principle in the category of action is the contemplation of an intelligence, because every action will be performed by this action; the first principle in the category of passion is the reception of prime matter; the first principle in the category of ‘where’ is the situation (situs) of a point, because the whole situation (situs) of the world is composed of punctual situations (ex sitibus punctalibus); the first principle in the category of ‘when’ is the indivisible instant, because in the same way as the world is composed of punctual entities, time is composed of instants; the first principle of position (positionis) is the situation of its centre (situs centri), because position is a relation (respectus) between a body and this situation.14

A material substance is composed of matter and form, and its matter is reducible to the atoms from which it has been created. Substantial forms are indivisible by themselves and exemplify a universal form, which is like a unit in God’s mind. Concerning accidental categories, the most important one is quantity, insofar as every material substance is quantified and is composed of indivisible units, which are numbers for discrete quantities and points for continuous quantities. Other accidental beings belonging to the categories of quality, where, and when, are based on quantity insofar as they only inhere in a quantified substance, and insofar as they are themselves quantified, i.e. measurable with absolute units. And it is a general principle that in every category there is some indivisible principle.

 Michael 2009.  Logica, I, ch. 4, in Wyclif 1893 13; see also De ente praedicamentali, 1, 3, in Wyclif 1891. The references to the Logica are from the nineteenth-century edition whenever the text is correct, but when it is not, in particular for the Logicae continuatio (henceforth LC), I will give my own transcription of MS Assisi, Biblioteca Communale 662 (now A), dating from c. 1385, which gives a better version.

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Taking this general framework as a basis, John Wyclif gives a very long exposition of his atomism in his Logicae continuatio (third treatise, chapter 9), in an analysis of propositions in which the term ‘where’ (ubi) occurs. This logical pretext is rapidly abandoned for a general presentation of his theory of place (locus) and situation (situs). His aim is to show that locus and situs can be analysed in terms of the situation of atoms, so that atomism follows from a more general theory of place, and not the contrary. It is not surprising, then, that this chapter of the Logicae continuatio precisely begins with something similar to the first of the three propositions condemned at Constance: Although the term ‘place’ is equivocal, it is sufficient for now to know what place is when understood as situation. In order to know what it is, it is worth noticing that the world is composed of a fixed number of atoms and that it cannot be increased or diminished or locally moved along a straight line or changed in its figure, so that, from natural and immutable causes, its continuous quantity and figure follows from the number of atoms. Otherwise, indeed, the world would not be at its maximal capacity and would not be maximally harmonious relatively to its figure. The situation and dimension15 of the world follow from these [indivisibles]. This is why, when Aristotle mentions continuous quantities, he names the different species in a certain order: line, surface and body, and beyond this, place and time; and the point is the principle for all, and the unit is the principle of the point. And place follows matter to such an extent that wherever there is this maximal matter (maxima materia) of the world there is a place. As a consequence, even if it were – per impossibile – moved locally along a straight line in an infinite void space, its situation would be continuously the same, insofar as the extension of this matter is sufficient to individuate its situation. […] And this was Plato’s opinion, who called matter ‘hyle,’ ‘vacuum,’ ‘a forged craftiness enveloped by thick darkness.’16

In his very useful study on John Wyclif’s theory of matter, Zenon Kaluza has shown that the specific vocabulary used in this text clearly echoes Plato’s Timaeus and Chalcidius’s commentary, even though the Platonic Chôra is sometimes identified with Augustine’s materia informis and Aristotle’s prime matter.17 What is important here is that the place of the world and its parts can be understood without reference to something external to the world itself, even if we imagine that there is an infinite void space all around. According to Wyclif, absolute space, such as the Euclidean infinite geometrical space, cannot help us to describe the place and motion of bodily entities in our world, insofar as we always need some fixed referential for locating something relatively to something else, or in order to describe the motion of a mobile. For this reason, the notions of place and situation are intimately related. The place of a body is the totality of the situations of its atomic parts. In an earlier chapter of the Logicae continuatio (III, 7) Wyclif explained that in all natural phenomena there must be minima and maxima. This is also true for place: the indivisible is a minimum and the totality of the world is a maximum. From this result two possibilities for apprehending the place of a body in the inner space of our closed world: we can either consider the place of a body relatively to a  The edition has duratio but the MS A has dimensio.  LC, III, ch. 9, in Wyclif 1899, 1–2. 17  Kaluza 2003. 15 16

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point or a series of points, or relatively to the totality of the world. On the one hand, Wyclif asserts that to every point of matter a punctual situation (situs punctalis) corresponds, so that the situation of a particular body corresponds to the totality of the situations of the points from which it is composed. But, on the other hand, human beings cannot use these units of measurement, because they do not have access to these indivisibles of matter and space.18 As a consequence, we have to situate bodies relatively to the totality of the world, by their distance to fixed points like the Poles, the centre of the world or a precise point on the Equator.19 As a whole, the perfect sphere of our material world constitutes a fixed spatial framework of points, always full of matter, but it can be thought of abstractedly as a mathematical, empty, spherical space. When a body moves from one place to another, a part or the totality of its points change from one situation to another.20 The place of a particular body is, therefore, equal to the part of space it occupies, together with a specific position relative to fixed points, even though we cannot know the precise position and number of all of its points. In spite of our natural incapacity to cognize points, Wyclif says, it is still possible to use different descriptions of place. One can say, for instance, that place is a continuous quantity, immobile, permanent, in which a body is formally located (a definition inspired by the Liber sex principiorum) or that place is the extremity of the surrounding body (a definition inspired by Aristotle). The first definition, attributed to Gilbert de la Porée, fits better with Wyclif’s own position, but even the Aristotelian definition can be used to describe the place of a body, although the situation of the surface of the surrounding body should be determined by the position of the lines and points from which it is composed, relatively to other fixed points in the universe. What is important for Wyclif is that there exist absolute units of measurement in our world, which are independent of our conventions for measuring distances, time, and speed, even though we cannot know them and are forced to use conventional systems. After he has presented his theory of place and local motion, John Wyclif asks whether the continuum is composed of indivisibles. Naturally his answer is positive. Indeed, despite our incapacity to know exactly the number and location of all the atoms composing a particular body, we can “imagine,” Wyclif says, this composition from a metaphysical point of view, starting from the indivisible points up to composite lines, surfaces, and bodies. The first step consists in accepting that the point enters into the definition of the line (a line is defined by at least two points). For this reason, points belong to the essence of the line, which for Wyclif means that it is ontologically prior to the line, as its cause. In this context, the main argument he gives rests on an analogy between time and numbers: points are the principles and causes of a line, in the same way that instants are the principles of time, and in the same way that units are the principles of numbers.21 The example of time is  LC, III, ch. 9, 2.  LC, III, ch. 9, 3–4. 20  LC, III, ch. 9, 11–29. 21  LC, III, ch. 9, 30. 18 19

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crucial in Wyclif’s mind, insofar as it seems to be the case that only indivisible instants exist (the present) and that time is, nonetheless, continuous (there is no gap between the past, the present and the future). What is more, Aristotle himself was not very clear about the status of time, since he seems to say that continuous time is also a number, not only in the subject who measures time (numerus numerans), but also in the reality measured by time (numerus numeratus).22 In the case of spatial continua all the indivisibles exist, and they exist in a certain number. Wyclif adds further arguments. If this were not the case, he continues, it would be possible to remove one point from a line, for instance the last one, without changing its nature, and, by way of consequence, this would be also true if we removed a larger number of points, and, per impossibile, an infinite number of points. This would have strange consequences for geometry, according to Wyclif, if we accept that a segment of a straight line is defined by its first and its last points. On the contrary, Wyclif’s theory holds that the place of a line corresponds to a series of indivisible situations in the world, which changes as soon as one or several points are removed from or added to the entire line. And what is true for indivisible situations must be also true for their material counterparts, because to every punctual situation (situs punctualis) in the world corresponds a point of matter, which Wyclif sometimes refers to as an atom. According to Wyclif, one must conclude that a line is a series of points situated next to each other, with distinct positions in space. Two points can be situated immediately next to each other, exactly like two instants in time are successive without any gap. It would be reasonable to think that these points have, in reality, some kind of extension in order to explain how they can be real parts of the continuum, but this is apparently not necessary for Wyclif. Indeed, he frequently repeats that these points have no quantity: they are non quanta. If I understand his position correctly, he means to say that, if according to Aristotle’s criteria in the Categories (4b20 sq.) quantitative parts are continuous – i.e. if their extremities are ‘together,’ and if they have distinct positions in space  – then the extreme points of these quantitative parts are also in a relation of continuity, insofar as they must touch each other in some way and have distinct positions in space. Indeed, if we can imagine that (1) when two segments of a straight line are continuous, then their extremities are points, which are immediately contiguous, without any gap; and (2) that there are points everywhere in a line; then (3) we can imagine that all these points are continuously situated next to each other, without interruption, insofar as each pair of these contiguous points can be considered as a pair of extremities of two distinct segments of that line. If we can imagine that, then we can also imagine that the line is at the same time continuous and composed of points. Wyclif’s global strategy therefore consists in demonstrating that we can derive all kinds of magnitudes, in different categories, from indivisible units. For spatial continua this means that geometric figures are derived from unextended points and their indivisible situations. For instance, a minimal line is made of two points, a minimal surface is a triangle made of three points, and a minimal body is a pyramid

22

 See Annas 1975.

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made of four points, etc.23 Larger figures are always multiples of these minimal ones. This typically Neopythagorean way of describing geometric figures is omnipresent in Wyclif’s works, and is reinforced by his Platonic theory of place. Because of the limits of our cognitive faculties we are forced to start with the world as a whole before we divide it into parts, so that we are naturally inclined to consider division never to stop. If we could cognize all the indivisibles, as well as their situation and their number, we would be able to conceive the world differently. We cannot cognize points directly through the senses, but we can nonetheless imagine how the continuum – the whole world and its quantitative parts – is composed from the addition of points and indivisible situations thanks to a thought experiment involving God’s absolute power (potentia Dei absoluta): In the same way, as I believe, no theologian would deny that God can produce a punctual substance by his absolute power, either by condensation or by causing a new entity, or by producing a spirit in a punctual site and annihilating all the other creatures except this spirit, keeping it in its site without movement. It is evident in this case that punctuality or point, which for a substance means being punctual, is an act that is posterior to that substance, be it separable or inseparable. Therefore a point can exist. There is no more doubt that if God can produce a punctual being, he can juxtapose many of them. And there is no doubt that their sites would be correspondingly juxtaposed next to each other, insofar as site is the subject of what is situated. It is therefore evident that God can produce a quantified being from these non-quantified beings […]. God could create a punctual substance in every indivisible site of the world and annihilate every continuous substance, conserving punctual substances immobile. It is obvious that thus far God acts on24 as much place as there was in the beginning, so that such an amount of place exists, or at least it may happen that such an amount of place is produced from indivisibles as it was in the first place. […] Therefore, once every accident of continuity is posited, one must posit the existence of a continuous subject of this [continuum], which would be composed of punctual beings, because they would be its intrinsic principles. There is no doubt that, once such a possibility is admitted, no philosopher in the world would have infallible evidence for the conclusion that it is not actually the case.25  LC, III, ch. 9, 49, 55, 59–61.  The Latin has est (God is in as much place…), but in this context it is difficult to understand how God can be in this place. 25  LC, III, ch. 9, 33–34, corrected with MS A, f. 72ra: “Similiter, ut credo, nullus theologus negaret quin Deus de potentia absoluta potest facere substantiam punctalem vel condensando vel noviter causando vel tertio faciendo spiritum esse in situ punctali et annihilando omnem aliam creaturam preter talem spiritum servatum immotum. Et tunc patet quod punctalitas vel punctus que est huiusmodi substantiam esse punctalem est accidens posterius illa substantia, sive sit separabile sive inseparabile. Punctus ergo potest esse. Nec dubium quin si Deus potest unum punctale producere potest et quodlibet iuxtaponere. Nec dubium quin situs essent correspondenter iuxtapositi, cum situs sit subiectum situari. Et ultra patet quod Deus potest ex talibus non quantis facere unum quantum […]. Creet substantiam ad omnem situm punctalem mundi unam substantiam punctalem et annihilet post omnem substantiam continuam servando punctales substantias immotas. Et patet quod Deus est adhuc per tantum locum sicut fuit in principio et per consequens est tantus locus vel saltem contingit tantum locum fieri ex illis punctalibus sicut prius. […] Posito ergo quocumque tali accidente continuo oportet ponere subiectum eius continuum et illud esset compositum ex punctalibus, quia illa forent eius principia intrinseca. Nec dubito quin admisso hoc pro possibili omnes philosophi mundi non haberent infallibilem evidentiam ad concludendum quod non est sic de facto.” 23 24

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To sum up: since the material world is composed of atoms which fill the totality of atomic situations in space, it could certainly be discrete; but this is not the case, because (1) every indivisible site is filled with a point-like entity, so that there is no gap or void space in our world, and (2) the totality of the world was created from indivisibles, and as a continuum, from the beginning. Later, in the Logicae continuatio, Wyclif explains this point more precisely with a proposition that is very similar to proposition 52, which had been condemned at Constance: One has to imagine a unique corporeal essence produced in the first instant, composed from indivisibles, occupying every possible place, not corruptible according to any of its parts, except by the division and separation of one part from another. But, since it must be the case that this total essence has every one of its indivisible parts in a relation of continuity, it is obvious that such an essence is absolutely incorruptible. And this essence is first conceived in a confused way under the notion of being, absolutely, i.e. neither as fire or air, or whatever genus or species […]. But philosophers, who further consider that each such essence which qualifies to be the subject of accidents is absolutely one, attribute substantiality to it. After that, once it is considered in its extension, they attribute corporeity to it, which the Bishop of Lincoln [Robert Grosseteste] calls light. Third, they attribute to it the form of its proximate genus, such as animality, ‘stone-ness’ or whatever else. Fourth, considered under the aspect of its species, they attribute to it its most specific form. Therefore, philosophers say that in a substance, the matter, the form and the composite are distinct.26

Here John Wyclif seems to follow Avicenna’s emanatist metaphysics, in which the form of corporeity (forma corporeitatis) is the first form of material substances – a form which is already present in their material substratum before they receive substantial and accidental forms. It corresponds to the extension of material substances insofar as it is the necessary condition for having a certain quantity. As we shall see, Robert Grosseteste actually interpreted this claim as meaning that the world was created in the first place as one material and corporeal substance, together with its extension or form of corporeity, thanks to the multiplication of a single point of light in all directions. Wyclif believes that it is possible to conserve the conceptual apparatus of Aristotle’s Physics within a more general and Platonic scheme. The concepts of matter and form, of the four elements, of substance and accidents, are still efficient and valuable, but the arguments against atomism are not, because they only concern sensible reality, not the deep ontological structure of the continuum.27 For example,  LC, III, ch. 9, 119, corrected with MS A, f. 88ra-b: “ymaginandum est igitur unam essentiam corpoream in principio productam, ex indivisibilibus compositam et occupare omnem locum possibilem, nec esse secundum eius partem aliquam corruptibilem nisi forte per divisionem et separationem unius partis a reliqua. Sed cum oportet illam totam essentiam habere quamcumque talem partem aliqualiter continuatam, patet quod illa essentia est simpliciter incorruptibilis et illa essentia primo confuse concipitur sub ratione qua [est] ens simpliciter, et nec ut ignis vel aer vel cuiuscumque alterius generis vel speciei […]. Sed philosophi ulterius considerantes quamlibet talem essentiam esse unum absolutum cui per se competit substare accidentibus attribuunt sibi substantialitatem. Et postmodum considerata eius extensione attribuunt sibi corporeitatem quam Lincolniensis vocat lucem. Et tertio formam generis proximi, ut animalitatem, lapiditatem vel aliud huiusmodi. Et quarto considerata ratione speciei attribuunt sibi formam specialissimam. Ideo dicunt philosophi quod substantiarum alia est materia, alia est forma, alia compositum ex hiis.” 27  LC, III, ch. 9, 35. 26

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in response to Aristotle’s argument that two points cannot touch, so that they cannot form a continuous quantity, Wyclif replies that he cannot conceive the spatial ordering of points because his concept of contact is derived from sensible realities. With the hypothetical model based on arithmetic and God’s absolute power, it is perfectly imaginable for Wyclif that points can touch in a broad way (large loquendo), insofar as every point occupies a distinct position in space and that the totality of place is occupied.28 Before we turn to the epistemological problem raised by the role of imagination in the foundation of this mathematical model it is important to indicate where Wyclif borrowed the main tenets of his Platonic and Neopythagorean doctrine.

6.3  The Platonic and Neopythagorean Background The possibility of deriving spatial magnitudes from points equivalent to numerical units with a particular position in space was one of the central ideas of Pythagoreanism, at least in its late development in the Neoplatonic and Neopythagorean traditions.29 The first major synthesis happened thanks to Nicomachus of Gerasa in the second century A.D., in his treatise On arithmetic.30 In brief, Nicomachus explains Plato’s conception of the creation of the world in the Timaeus with a theory of numbers: mathematical beings are not only mediating entities between humans and a world of ideas, as is usually the case in Plato’s dialogues, but they rather reflect an actual correspondence between God’s mathematical ideas and the structure of the material world. As a consequence, arithmetic is not only a practice that helps us to ascend to divine reality, but it is also the key for our understanding of every natural phenomenon, together with geometry, music and astronomy. In order to grasp these numbers in material reality, one has to consider points equivalent to numerical units with a particular position in space. Geometric figures are, therefore, structured with numbers, and geometry must be subordinated to arithmetic. At a higher level, music and astronomy allow us to grasp the harmony between the different levels of creation. A noteworthy consequence of this theory is that matter and space have exactly the same structure, like the Chôra in Plato’s Timaeus, but this structure is primarily of a numerical order. In other words, the analysis of geometric three-dimensional solids as composed of surfaces, lines and points does not only hold for idealized figures – in God’s mind or in a human intellect – but also for concrete and material bodies. It gives the ontological structure of both geometric space and of material bodies occupying this space. This theory was widely known in the Middle Ages thanks to ancient sources such as Macrobius, Cassiodorus, or Martianus Capella, but the most important of these was Boethius’ treatise On arithmetic, which is a Latin translation of Nicomachus of  LC, III, ch. 9, 35–36.  See Philip 1966, Burkert 1972, Zhmud 2012, Cornelli 2013; Horky 2013. 30  For a general introduction to Nicomachus’s arithmetic, see Levin 1975. 28 29

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Gerasa’s work, with only small additions and modifications. Like its Greek model, this text deals not merely with mathematics, but endeavours to show that a good grasp of the ontological organization of the material world requires the finding of units, numbers and relations between numbers in all kinds of realities within the created world. For this reason the science of arithmetic antecedes the other sciences of the quadrivium (geometry, music and astronomy), and it is also, and more generally, the basis of all kinds of philosophical reasoning. As Boethius says, “whoever puts these matters aside has lost the whole teaching of philosophy,” because with mathematics in general, and arithmetic in particular, “we bring a superior mind from knowledge offered by the senses to the more certain things of the intellect.”31 This intellectual grasp of higher realities through arithmetic and numbers is useful for the other mathematical sciences, but also, by way of consequence, for physics and metaphysics. As Boethius puts it, [arithmetic] is prior to all not only because God the creator of the massive structure of the world (mundanae molis) considered this first discipline as the exemplar of his own thought and established all things in accord with it; or that through numbers of an assigned order all things exhibiting the logic of their maker found concord; but arithmetic is said to be first for this reason also, because whatever things are prior in nature, it is to these underlying elements that the posterior elements can be referred. Now if posterior things pass away, nothing concerning the status of the prior substance is disturbed […]. The same thing is seen to occur in geometry and arithmetic. If you take away numbers, in what will consist the triangle, quadrangle, or whatever else is treated in geometry? All those things are in the domain of number.32

While Plato’s Timaeus tends to limit its description of the mathematical structure of matter and place to geometric figures, Nicomachus and Boethius ascribe numerical values to geometric figures, in such a way that they can be analysed in terms of multiples of more basic units, i.e. points. For instance, the first line is made of two points, the first triangle of three points, the first square of four points, and so forth, and larger figures are multiples of these numbers. Mathematical atoms as building blocks of spatial figures are not only units of measurement, they are also the ultimate metaphysical constituents of material realities, and at the same time, the ultimate constituents of space in which matter exists. As Boethius says: It is necessary that whatever solid body may exist, it should have length, width, and depth, and whatever contains these three in itself, that thing is by its very name called a solid. These three things are concerned with each other by an inseparable connection, in every body, and it has been so constituted in the nature of bodies. If anything should be lacking in one of these dimensions, that body is not solid. That which maintains only two intervals is called a surface; every surface is contained only by width and breadth. […] The line, to which has been attributed the nature of one dimension, is exceeded by the surface in one dimension and is exceeded by the solid in two dimensions. The point is exceeded by the line in one dimension, that which remains, length. If a point is superseded by one dimension in a line, it is exceeded in a surface by two dimensions; a point is removed from solidity by three dimensions of intervals, and so it is that a point exists without magnitude or a body or

31 32

 On Arithmetic, I, i, in Boethius 1983, 73.  On Arithmetic, I, i, in Boethius 1983, 74.

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dimension of an interval. It is bereft of length, width, and depth. It is the principle of all intervals and indivisible by nature, and the Greeks call it “atom” (atomon).33

A point, despite its non-quantitative nature, is therefore the metaphysical principle of all spatial dimensions, and consequently of every material and quantified being. The rest of book II is therefore dedicated to demonstrating this equivalence between numbers and geometric figures. David Albertson has brilliantly shown that this Neopythagorean conception of geometric space remained very important during the Middle Ages, at least in the twelfth century.34 But there is no reason to think that this Neopythagorean model that Boethius transmitted did not continue to be a common matrix for many philosophers and theologians in the thirteenth and fourteenth centuries, despite the constant refinements in natural philosophy and mathematical theories after the arrival of the Aristotelian corpus and its Arabic commentators. As I have shown elsewhere, the Neopythagorean derivation of spatial magnitudes from points was reworked by many of those who defended mathematical atomism in the thirteenth and fourteenth centuries.35 And there is no doubt that John Wyclif also belongs to this long tradition. To put it briefly, before the reception of Aristotle’s Physics in the West, medieval philosophers discussed the composition of the continuum and the nature of place in their commentaries on Aristotle’s Categories and Boethius’s De arithmetica. Indeed, when Aristotle distinguishes discrete and continuous quantities in the Categories (4b20 sq.) the criteria he uses are, at least partly, compatible with the Neopythagorean model.36 He simply says that a continuous quantity has its parts ‘together’, so that they touch at a common limit or extremity, and that, except for time, these parts occupy distinct positions in space. If points can be thought of as occupying distinct positions in space without any gap in a finite line, and as touching each other, then it is possible for a continuum to be ontologically composed of indivisibles. The problem for twelfth-century commentators was that Boethius defends the Neopythagorean thesis in his De arithmetica, whereas he seems to affirm the opposite view in his commentary on the Categories, where he follows Aristotle and says that points cannot be parts of a line, a surface or a body, because they are only the extremities of a continuous line. Some twelfth-century readers of Aristotle and Boethius, such as William of Champeaux and Peter Abelard, argued for the necessity to accept the positive existence of points as intrinsic metaphysical parts of the line and, transitively, as metaphysical constituents of surfaces and bodies.37 And it is worth noticing that Peter Abelard’s arguments in his Dialectica and his Logica ingredientibus are similar in many respects to Wyclif’s own arguments in his Logica: (1) a quantity is a complex being composed of simple entities; (2) these  On Arithmetic, II, iv, in Boethius 1983, 130 (trans. slightly modified).  Albertson 2014. 35  Robert 2017. 36  On this point see Mendell 1987. 37  King 2004. 33 34

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simple entities must be considered parts of the whole quantity; (3) each time we divide a line into quantitative parts, new points arise from the division, and since division is possible everywhere, there are points everywhere in the line; (4) when a line is divided into two parts, for instance, the end-points of each part are next to each other before the division, so that it is possible to imagine points everywhere in the line with distinct, though immediate, positions in the line; (5) these points cannot be mere accidents of a continuous quantity, because they define a line and are parts of its essence. Other commentators on the Categories in the thirteenth and fourteenth centuries, such as Albert the Great or Walter Burley, continued Peter Abelard’s effort to give an ontological status to the points, opposing the Categories to the Physics. After the reception of Aristotle’s Physics and De generatione et corruptione in the thirteenth century, medieval philosophers had to take into account new arguments – notably concerning the infinite – against physical and mathematical atomism, and a majority of them were convinced by these arguments. Furthermore, mathematical arguments based on incommensurability or on the impossibility to ascribe a precise number of parts to a continuum came into the picture at this time, with some Arabic texts (like Avicenna and Al-Ghazali’s) newly translated into Latin. So, from the thirteenth century onwards, the problem of the continuum was deeply transformed by these novelties.38 Nevertheless, despite these new trends in mathematics and physics, some thinkers continued to defend the old Neopythagorean mathematical atomism.39 This is notably the case for Robert Grosseteste, who is one of the most important sources of John Wyclif.40 In his treatise On light Grosseteste describes the creation of the world out of nothing in terms of an “infinite multiplication” (replicatio infinita) of an original point of light in every direction, so that it finally forms a perfect sphere.41 This process of emanation of light gives rise to the corporeal form of the world together with its definitive extension. Light is therefore the first form of the created prime matter, and it is what philosophers like Avicenna called “corporeity.”42 But this theory was “the meaning of the philosophers positing that everything is composed of atoms and saying that bodies are composed of surfaces, surfaces of lines, and lines of points.”43 Indeed, Grosseteste says, from this multiplication of a point of light results an infinite number of points in the total extension of the world. It is, thus, possible to analyse different portions of matter as different numbers of atoms or points, i.e. as different ‘infinities,’ in Grosseteste’s terminology. Indeed, he believes in the possibility of comparing different infinite numbers of points in the same way as we, for instance, compare the series of natural numbers with the series of even numbers

 See Maier 1949, Murdoch 1974 and 1982.  See fn. 1. 40  See Robson 2008, 26–31. 41  Trans. Lewis 2013. 42  On light, in Grosseteste 2013, 239–240; see Panti 2012. 43  On light, in Grosseteste 2013, 242. 38 39

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(according to him these series or sets of numbers do not have the same number of elements). What is new in Grosseteste’s account, apart from his metaphysics of light, is that he endeavours to respond to the classical arguments based on incommensurability with his original conception of the infinite. In each part of the world, he says, there is an infinite number of points, and if a line is twice as long as another, it contains twice as many points as the first. This allows Grosseteste to state that there can be different ratios between magnitudes, exactly like there are ratios between different series of numbers.44 Those ratios can be rational or irrational, as is the case for the side of a square and its diagonal. It is, therefore, possible to say that the continuum is infinitely divisible. As Neil Lewis puts it, in Grosseteste’s Notes on the Physics, “a typical strategy is for him to hold that Aristotle’s theories are of limited ambition, and that his own account locates Aristotle’s views within a broader picture.”45 More precisely, he endeavours to interpret some important propositions of the Physics within the Neopythagorean model previously described. When he comments on book III about the infinite, for instance, he states that the infinite is a principle for natural philosophers, even though it is not their task to deal with the infinite as such. It is a principle because, “according to what Plato and Augustine say about number, number and wisdom are the same, and the wisdom of God is an infinite number, and there is an infinite number of ideas, i.e. reasons of things (rationes rerum) in divine wisdom.”46 It is not only compatible with the famous dictum of Wisdom 11, 21 (God disposed everything in number, weight and measure) as interpreted by Augustine, it is also confirmed by Plato and “the Pythagoreans, who posited that an infinite number is the principle of sensible things.”47 These philosophers did not refer to a divine number, according to Grosseteste, but to numbers expressing the infinite multiplication of matter (replicationem materiae infinitam), which is a passive property of matter.48 As far as forms are concerned, except for the form of corporeity, one has to turn to Plato and Augustine. The first relation between divine ideas and the material world is precisely the derivation of geometric figures from points, which Grosseteste describes exactly like Boethius in his De arithmetica: “indeed, in the same way as different species and figurations of numbers are produced from the additions of different finite numbers, it is also the case for infinite numbers. The triangular infinite number, which exists in multiplied matter and form, is the principle of sensible triangulation in a body in the same way as the squaring in the infinite number is the principle of squaring in a body, and the cube in number for the bodily cube, and the pyramid for pyramid, etc.”49 To sum up, all figures are multiples of minimal figures as well as multiples of numbers. Since the world is composed of an infinite number  On light, Grosseteste 2013, 241–242.  Lewis 2005, 160. 46  Grosseteste, Commentarius in VIII libros physicorum, III, in Grosseteste 1963, 54. 47  Grosseteste 1963, 54. 48  Grosseteste 1963, 54. 49  Grosseteste 1963, 55 (see also 93). 44 45

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of points, it is not a problem to affirm, like Aristotle, that the continuum is infinitely divisible. Many commentators pointed out the originality of Grosseteste’s conception of the infinite, especially his views on the comparison of different infinities. But if we look closer, sometimes he uses the term infinitus with the meaning of ‘infinite’ in the mathematical sense, sometimes with the meaning of ‘indefinite,’ i.e. uncountable. For instance, in his commentary on the Physics he affirms that we say that the number of points is ‘infinite’ only because we are unable to count these uncognizable points.50 In other words, what is infinite for us always corresponds to a definite number for God, who can count everything he has created (sicut enim vere in se finita nobis sunt infinita, sic que vere in se infinita sunt, illi sunt finita). Therefore, we should not overestimate Grosseteste’s theory of the infinite, and John Wyclif was perfectly conscious that it was sometimes a mere figure of speech. For this reason he abandoned the idea of an ‘infinite multiplication’ of points and renounced to the comparison of infinites. Even if we cannot know the exact number of points in a line, such a number exists, at least in God’s mind, and it is necessarily finite for Wyclif. It is clear from the texts quoted above that John Wyclif borrowed from Robert Grosseteste the main lines of his interpretation of the Neopythagorean and Boethian derivation of magnitudes from indivisibles. For instance, when he asks us to ‘imagine’ how God could create the world out of atoms, his description is very similar to Grosseteste’s theory in his treatise On light, except for his finitism. Now the question is: what does he exactly mean when he says that we must imagine this (imaginandum est…)? In comparison with earlier authors in the long tradition briefly sketched above, John Wyclif’s account of the epistemological foundation of his Neopythagorean conception of matter and space provides quite a lot of details concerning the role of the senses, imagination and intellect.

6.4  T  he Epistemological Foundation of Mathematical Atomism and the Role of Imagination In his Logica John Wyclif has frequent recourse to imaginary situations either as an illustration of a philosophical point, or as a counterfactual argument or thought experiment confirming a previous assumption. For instance, when he defends his theory of place, he suggests that the reader imagine a giant whose head is at the Antarctic Pole, his feet at the Arctic Pole, with one of his arms directed to the West, the other to the East, and says that from the position of this giant we would be able to locate other bodies and the imaginable sphere he embraces.51 Elsewhere, he asks us to imagine what would happen if the world were turned the other way round.52  Grosseteste 1963, 91–93.  LC, III, ch. 9, 6. 52  LC, III, ch. 9, 19. 50 51

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But when Wyclif says that we have to imagine that God created the world from points, in the same way as we can imagine that He can juxtapose points in every possible place in the world with to His absolute power, this is neither a mere illustration, nor a simple thought experiment, because this form of imagination is already grounded in a complex theoretical argument. It is surprising, at first sight, that Wyclif uses the term ‘imaginatio’ in this context, insofar as he is convinced of the weakness of simple sensible imagination. What sort of imagination is he referring to here? The problem is that points and their punctual situations cannot be cognized by the senses, and that imagination depends on sensible contents. As soon as we endeavour to imagine or represent these non-quantified entities we are forced to represent them with some quantity, in the same way as geometric figures drawn in the sand are supposed to represent solids, surfaces, lines and points. According to Wyclif, this is the reason why geometry and natural philosophy cannot deal with the atomic constitution of continua. Natural philosophy, in which the cause is demonstrated by the effect with a factual demonstration (demonstratio quia est) based on experience or the senses, does not have to deal with punctual parts. A point is neither sensible nor imaginable. Therefore, its treatment neither comes down to the geometer in particular, who is only directly concerned with imaginable entities, nor to the natural philosopher, but must be reserved to the metaphysician and the arithmetician.53

In the same vein as Nicomachus and Boethius, the evangelical doctor praises metaphysics and arithmetic because they are purely intellectual approaches to reality. An Aristotelian philosopher would object that mathematical beings are mere abstractions, which must be based in some way on sensible cognition. But Wyclif contends that the role of the intellect in the science of arithmetic and metaphysics is precisely to transcend sensible and imaginable beings. And this intellectual work does not always correspond to the Aristotelian conception of abstraction, since the intellect is able to understand something that totally contradicts the information delivered by the senses or shaped by the imagination. As he puts it: Imagination is not sufficient to understand these things […]. One has to ascend higher up to the gaze of the intellect in order to conceive correctly the composition of the continuum from entities without quantity. It is important to do so, because the imagination acts upon the intellect in the apprehension of imaginable objects; and since [imagination] does not discover such a composition of parts in the contours of its object, it is not surprising that it does not assent to it. But the intellect says to itself that another composition of indivisible parts must be accepted, on which [imagination] cannot say anything.54

 LC, III, ch. 9, 36, corrected with MS A, f. 72rb: “non interest tractare de partibus punctalibus in philosophia naturali in qua demonstratur causa per effectus demonstratione quia est., cuius principium est experientia vel sensus. Punctus autem non est sensibilis vel ymaginabilis, ideo tractatus eius non specialiter pertinet geometre qui solum de ymaginabilibus pertractat directe, sicut nec naturali philosopho. Sed illud conservandum est metaphysico et arithmetico.” 54  LC, III, ch. 9, 45, corrected with MS A, f. 73va-b: “Ymaginatio autem non sufficit ista capere […]. Ideo oportet superius ascendere ad aciem intellectus in recte concipiendo compositionem continui ex non quantis. Quod grave est facere ex hoc quod ymaginatio coagit intellectum in appre53

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By analogy, Wyclif continues, in the same way as the intellect of someone who knows the principles of optics is able to correct sensible errors and illusions, it is possible for the intellect to correct our sensible image of the continuum and geometric figures.55 The intellect is certainly naturally inclined to conceptualize what is given to sensory cognition and the imagination, but it is precisely the metaphysician’s task to disconnect his reasoning from these sensible images. This is the force of mathematics, and of arithmetic in particular. According to Norman Kretzmann, Wyclif would endeavour to show that continuity is a mere illusion delivered through the senses  – as happens today when we watch a movie, for instance  – whereas real things are discrete and composed of indivisible units.56 It is, indeed, true that when Wyclif deals with the variation of speed in motion, he affirms that there is only one speed corresponding to continuous motion (when the ratio is equal to one atom of space for one instant of time), which is the maximal speed achievable by a mobile, whereas the other speeds have imperceptible times of rest and are, therefore, discontinuous in some way. But this only means that motion can be discontinuous, when a mobile stays in one place for some imperceptible duration of time, not that matter, space, and time are discontinuous. Even in a discontinuous motion there is no gap or jump, only times of rest. Indeed, as we have seen, Wyclif believes in the existence of continuity in the material world, which makes his position quite difficult to understand from our modern point of view. Matter, space and time are continuous and composed of indivisibles, exactly like a line is continuous and ontologically composed of points. The central idea here is that it is always possible to attribute numbers, i.e. a discrete quantity, to continuous realities, and that there exist absolute units of measurement, conceptually and mathematically indivisible, which are beyond the scope of humanly sensible cognition, but can be conceptualized with mathematics. What Wyclif suggests is that we enlarge our natural and sensible imagination with the principles of arithmetic. This intellectual exercise has its limits, as we have seen, and Wyclif agrees with Robert Grosseteste that we cannot know exactly the number of points in a line.57 Only God knows the precise number of atoms present in the world and each of its parts. This is not a problem for Wyclif’s theory, since it is sufficient for the mathematician to recognize that the relations between continuous quantities correspond to relations between numbers. For instance, if one cuts a line in two equal parts, there will be the same number of points in both parts, whatever the precise number of these points. What about the incommensurability between one side of a square and its diagonal? Here again, Wyclif says that we have to go beyond the senses and the imagination on which geometry is based.

hensione cuiuscumque ymaginabilis. Et cum in toto ambitu sui obiecti non reperit compositionem huiusmodi partium, non est mirabile si dissentit. Sed intellectus dicit sibi quod est dare partium indivisibilium compositionem aliam quam non est suum discutere.” 55  LC, III, ch. 9, 40 and 58. 56  Kretzmann 1986, 43–44. 57  LC, III, ch. 9, 35–37.

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All [the conclusions of geometry], as I said, are conceived for lines, angles and figures that lie in the imagination, but we are talking about [figures] that can be cognized by the intellect only, as Augustine teaches in his On the quantity of the soul. If someone said that all the conclusions of geometry are proved in the same way for pure intelligible and imaginable beings, it is a casual discourse pronounced without the force of a proof. No one would believe it without further proof. And if someone says that Campanus [of Novara] and other commentators on Euclid affirmed this, [I say that] many others, like Pythagoras, Democritus, Plato, and more recently Robert Grosseteste, with others who followed the path of the truth, constantly affirmed the contrary. Therefore, as far as doctrine is concerned, these topical arguments lacking additional demonstrations are the sign of a garrulous defect of arguments. Consequently, I say that there is no demonstrable conclusion for continua that is not demonstrable for numbers, but the reverse is probably not true, because of the scope of the former object. It is obvious that the conclusions of arithmetic do not demonstrate precisely, but only without sensible error, as I said about the division of any given line or angle in two equal parts. […] The geometer is not certain about the quantity and proportion of the intelligible diameter [with the side of a square], since, according to Robert Grosseteste, the number of punctual beings that compose this is unknown to him. He has probable conjectures or true ones or near the truth about the sensible diameter, which cannot be corrected by the senses. The certitude of science is located in the numbers cognized by the blessed, whereas the erroneous and confused idleness is located in the sensible.58

Geometry, as he says elsewhere, only has a conditional necessity (ex suppositione), whereas arithmetic is absolutely necessary.59 For Wyclif, if we follow the axioms of geometry and the proofs deduced from sensible beings and drawings, we must conclude that the continuum is infinitely divisible, because every sensible being has a quantity and is divisible. In the same way, we must conclude that the ratio between the diagonal and the side of a square is, in fact, incommensurable, because it is not possible to express this ratio with natural whole numbers. But we can still imagine that God created the world with atoms, and this is coherent with the principles of arithmetic according to Grosseteste and Wyclif. What is more, with this theory Wyclif believes he can respond to the classical arguments based on incommensurability. Indeed, what seems incommensurable for us is, in fact, commensurable from  LC, III, ch. 9, 109, corrected with MS A, f. 86ra-rb: “Omnes, ut dictum est., intelliguntur de lineis angulis et figuris ymaginacioni subiectis, nos autem loquimur de illis que a solo intellectu cognosci possunt, ut docet Augustinus in De quantitate animae. Quod si aliquis dicat quod eque verificantur omnes conclusiones geometrice de puris intelligibilibus, sicut de ymaginabilibus, leve verbum est et sine probacionis efficacia eructatum. Ideo non credetur nisi efficaciter comprobetur. Quod si dicatur Campanum et multos alios expositores Euclidis illud asserere, revera multi expositores, ut Pitagoras, Democritus, Plato et inter moderniores Lincolniensis cum aliis sequentibus tramitem veritatis constanter asserunt oppositum. Ideo tales topice raciones in materia doctrinali deficientes demonstraciones adducte indicant defectum garulum argumentorum. Et sic dico quod nulla est conclusio demonstrabilis in continuis quin sit demonstrabilis in numeris, sed forte econtra propter amplitudinem obiecti prioris. Et patet quod conclusiones arismetice non demonstrant cum precisione, sed cum exclusione erroris sensibilis, ut dictum est de divisione cuiuscumque date linee vel dati anguli in duo [A: f. 86rb] equalia. […] incertum est cuilibet geometro de quantitate et proporcione intelligibilis dyametri, sicut, secundum Licolniensem, incognitus est sibi numerus punctalium componencium. Et de dyametro sensibili habet coniecturam probabilem vel veram vel veritati propinquam a sensu incorrigibilem. In numeris autem cognitis a beatis consistit certitudo sciencie et in sensibilem langor erroneus et confusus.” 59  LC, III, ch. 9, 57. 58

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the point of view of God’s knowledge of the real number of points in lines and figures. If the Boethian model of derivation of magnitudes from points is valid, there are minimal figures for which the theorems of geometry do not work (like for the minimal square of four points in which the diagonal is equal to the side of the square). If all magnitudes are multiples of these minimal figures, and they are limited by the maximal size of our material world, then every ratio between magnitudes will be expressible with numbers, and every magnitude will be only finitely divisible.60 It is only because we do not cognize the real number of parts that we call these numbers “infinite.”

6.5  Concluding Remarks: Wyclif and Proclus The first aim of this paper was to show that Wyclif’s theory of three-dimensional space as composed of surfaces, lines and points consists of a Neopythagorean interpretation of Plato’s theory of place in the Timaeus. The main source of this mathematical atomism is Boethius’ De arithmetica, from which he takes the idea of the derivation of all magnitudes from indivisibles. He applies this model to the totality of the world and replaces Aristotle’s conception of place with a new one based on two concepts: spatial occupation, and situation. The place of a body is not the surface of the surrounding body but corresponds to the situation of all of its points, i.e. to the portion of space it occupies, which can be located relatively to fixed points. But more important for Wyclif is Robert Grosseteste’s interpretation of this model: Grosseteste includes this in a Neoplatonic metaphysics of light, which explains the creation of the world in terms of a multiplication of a single point of light in all directions in space. The second aim of this paper was to show that Wyclif adds some novelty to this model. Indeed, he is conscious of the fact that Robert Grosseteste’s metaphysics of light is an intellectual construction, and that its force rests on its capacity to provoke the imagination: we can imagine the original diffusion of light from a single point in all directions. Whereas Boethius, like Plato and his followers, simply praises the intellect and depreciates the sensible, Wyclif tries to assign a role to imagination, which stands in between the two. The result is a clear articulation between the sciences and the cognitive faculties, similar in some respect to Proclus’ vision of mathematics, which was not disseminated in Latin in Wyclif’s time. According to Proclus, theology is a higher kind of knowledge, which uses the nous or simple intellectual grasp in order to know forms and divinity. At a lower level, mathematics only uses judgments (dianoia), and physical sciences deal with sensible objects and are limited by sensation. Like Nicomachus of Gerasa, Proclus places arithmetic at the primary stage of mathematical sciences, before geometry, 60

 LC, III, ch. 9, 55–58.

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music and astronomy. This is so, he says, because a unit is simpler than a point, which is a unit with a position in space. Numbers are prior to the ratios between continuous magnitudes, and they correspond to the order imposed to the world by the Demiurge.61 In material reality, a point is therefore the instantiation of a numerical unit. What is interesting for us is that in his commentary on the first book of Euclid’s Elements Proclus famously adds that geometrical reasoning belongs to the domain of intellectual judgement (dianoia), but is assisted by imagination (phantasia). Ian Mueller sums up this theory as follows: imagination “serves as a kind of movie screen on which dianoia projects images for mathematical reflection.”62 Imagination gives to mathematical objects something equivalent to what Aristotle used to call “intelligible matter,” which is a kind of imaginary space in which figures can be represented, multiplied or divided. For Proclus, the Pythagoreans defined the point as a unit with a position in space, in order to distinguish the unit as a pure object of thought and the point as an object of thought and of imagination. The point acquires a kind of spatial individuation when it is projected in imagination. What does it mean to have a representation of a point in the imagination? Proclus says that imagination naturally moves from the whole to its parts, but when it is informed by the intellect, imagination can go the other way round, from the indivisible to the divisible, from points to extended magnitudes, so that “the point is projected in imagination and comes to be, as it were, in a place and embodied in intelligible matter.”63 With this intellectualized imagination, we can therefore imagine lines as “the flowing of a point.” As Proclus puts it: “This line owes its being to the point, which, though without parts, is the cause of the existence of all divisible things; and the flowing indicates the forthgoing of the point and its generative power that extends to every dimension without diminution and, remaining itself the same, provides existence to all divisible things.”64 Without any direct knowledge of Proclus’s commentary, Wyclif attributes to the imagination the same kind of role: when imagination is informed by the intellect and the principles of arithmetic, it can imagine the flowing or the multiplication of a point in space. Wyclif, however, would not agree with Proclus on several issues. For instance, in his commentary on proposition 10 of book 1 of Euclid’s Elements, Proclus assumes the infinite divisibility of a finite straight line.65 Therefore, like Robert Grosseteste, he tries to reconcile Aristotle’s theory of the continuum in book VI of the Physics with his own metaphysics inspired by Plato and the Neopythagoreans. That the number of points is infinite in a finite continuum is, apparently, not a problem for Proclus, whereas the evangelical doctor believes that this number is only indefinite, but actually finite for God. Wyclif would also disagree with Proclus about the epistemological status of arithmetic, since the latter affirms that  Proclus 1970, 30.  Proclus 1970, XX. 63  Proclus 1970, 78. 64  Proclus 1970, 79–80. 65  Proclus 1970, 216–217. 61 62

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arithmetic is more precise than geometry, for its principles are simpler. A unit has no position, but a point has; and geometry includes among its principles the point with position, while arithmetic posits the unit. […] Nevertheless they have certain community with one another, so that some theorems demonstrated are common to the two sciences, while others are peculiar to the one or the other. The statement that every ratio is expressible belongs to arithmetic only and not at all to geometry, for geometry contains inexpressible ratios.66

On the contrary, John Wyclif states that arithmetic is no “more precise” than geometry, because we are incapable of attributing precise numbers to geometric figures. Its force rather resides in the fact that it does not depend on the senses. He also disagrees with Proclus on inexpressible ratios, since he believes that every ratio would be expressible if we knew the precise number of indivisibles in every magnitude. Since Alexandre Koyré’s works on the importance of Platonism for the rise of modern science at the time of Galileo were published it has been a commonplace to affirm that the translation of Proclus played a significant role – which is certainly the case – and that the mathematization of space began slowly in the Renaissance with Nicolas of Cusa, or later with Giordano Bruno. But the most important element in modern science may not only be the influence of Platonism or Pythagoreanism – we have seen that they were already influential in the Middle Ages – or the mathematization of space, but the conception of space as absolute and infinite. Nevertheless, even though they were still attached to the Aristotelian finite cosmos, John Wyclif and many other medieval atomists certainly played a crucial role in this long story of the transformations of the concept of space.

References Albertson, David. 2014. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford: Oxford University Press. Annas, Julia E. 1975. Aristotle, Number and Time. The Philosophical Quarterly 25: 97–113. Bakker Paul, J.J.M., and Sander W. De Boer. 2009. Locus est spatium: On Gerald Odonis’ Quaestio de loco. Vivarium 47: 295–330. Boethius. 1983. On Arithmetic. Trans. Michael M. In Boethian Number Theory: A Translation of the De institutione arithmetica. Amsterdam: Rodopi. Burkert, Walter. 1972. Lore and Science in Ancient Pythagoreanism. Harvard: Harvard University Press. Cesalli, Laurent. 2005. Le ‘pan-propositionnalisme’ de Jean Wyclif. Vivarium 43: 124–155. Conti, Alessandro. 2006. Wyclif’s Logic and Metaphysics. In A Companion to John Wyclif, ed. Ian C. Levy, 67–125. Leiden: Brill. Cornelli, Gabriele. 2013. In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin: Walter de Gruyter. [Councils]. 1973. Conciliorum oecumenicorum decreta, ed. Giuseppe Alberigo et  al., 3rd ed. Bologna: Istituto per le scienze religiose.

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Grant, Edward. 1976. Place and Space in Medieval Physical Thought. In Motion and Time, Space and Matter, ed. Peter K. Machamer and Robert G. Turnbull, 137–167. Columbus: Ohio State University Press. Horky, Phillip S. 2013. Plato and Pythagoreanism. Oxford: Oxford University Press. John Wyclif. 1869. In Trialogus, ed. Gotthard V. Lechler. Oxford: Clarendon Press. ———. 1891. In De ente praedicamentali, ed. Rudolf Beer. London: Trübner for the Wyclif Society. ———. 1893–1899. Tractatus de logica. 3 vols., ed. Michael H. Dziewicki. London: Trübner for the Wyclif Society. ———. 2012. Trialogus. Trans Stephen Lahey. Cambridge, MA: Cambridge University Press. Kaluza, Zénon. 2003. La notion de matière et son évolution dans la doctrine wyclifienne. In John Wyclif: Logica, politica, teologia, ed. Mariateresa Fumagalli Beonio Brocchieri and Stefano Simonetta, 113–151. Florence: Edizioni del Galluzzo. King, Peter. 2004. The metaphysics of Peter Abelard. In The Cambridge companion to Abelard, ed. Jeff Brower and Kevin Guilfoy, 65–125. Cambridge: Cambridge University Press. Kirschner, Stefan. 2000. Oresme’s Concepts of Place, Space, and Time in His Commentary on Aristotle’s Physics. Oriens – Occidens: Sciences, mathématiques et philosophie de l’antiquité à l’âge classique 3: 145–179. Kretzmann, Norman. 1986. Continua, Indivisibles, and Change in Wyclif’s Logic of Scripture. In Wyclif in his Times, ed. Anthony Kenny, 31–65. Oxford: Clarendon Press. Lahey, S.E. 2009. John Wyclif. Oxford: Oxford University Press. Levin, Flora R. 1975. The Harmonics of Nicomachus and the Pythagorean Tradition. University Park: American Philological Association. Levy, Ian C. 2003. John Wyclif: Scriptural Logic, Real Presence, and the Parameters of Orthodoxy. Milwaukee: Marquette University Press. Lewis, Neil. 2005. Robert Grosseteste and the Continuum. In Albertus Magnus and the Beginnings of the Medieval Reception of Aristotle in the Latin West, ed. Ludger Honnefelder, Rega Wood, Mechthild Dreyer, and Marc-Aeilko Aris, 159–187. Münster: Aschendorff. Lewis, Neil. 2013. Robert Grosseteste’s on light: An English translation. In Robert Grosseteste and his intellectual milieu, ed. John Flood, James R. Ginther, and Joseph W. Goering, 239–247. Toronto: Pontifical Institute of Mediaeval Studies. Maier, Anneliese. 1949. Kontinuum, Minimum und aktuell Unendliches. Die Vorläufer Galileis im 14. Jahrhundert, 155–215. Rome: Edizioni di Storia e Letteratura. Mendell, Henry. 1987. Topoi on Topos: The Development of Aristotle’s Theory of Place. Phronesis 32: 206–231. Michael, Emily. 2009. John Wyclif’s Atomism. In Atomism in Late Medieval Philosophy and Theology, ed. Christophe Grellard and Aurélien Robert, 183–220. Leiden: Brill. Murdoch, John E. 1974. Naissance et développement de l’atomisme au bas moyen âge latin. In  Cahiers d’études médiévales, 2:  La science de la nature: Théories et pratiques,  11–32. Montreal: Bellarmine. ———. 1982. Infinity and Continuity. In The Cambridge History of Later Medieval Philosophy, ed. Norman Kretzmann, Anthony Kenny, and Jan Pinborg, 564–591. Cambridge, MA: Cambridge University Press. Panti, Cecilia. 2012. The Evolution of the Idea of Corporeity in Robert Grosseteste’s Writings. In Robert Grosseteste His Thought and Its Impact, ed. Jack P. Cunningham, 111–139. Toronto: Pontifical Institute of Mediaeval Studies. Philip, James A. 1966. The ‘Pythagorean’ Theory of the Derivation of Magnitudes. Phoenix 20: 32–50. Proclus. 1970. A Commentary on the First Book of Euclid’s Elements. Trans. Glenn Morrow, with a foreword by Ian Mueller. Princeton: Princeton University Press. Robert, Aurélien. 2009. William Crathorn’s Mereotopological Atomism. In Atomism in Late Medieval Philosophy and Theology, ed. Christophe Grellard and Aurélien Robert, 127–162. Leiden: Brill.

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———. 2012. Le vide, le lieu et l’espace chez quelques atomistes du XIVe siècle. In La nature et le vide dans la physique médiévale: Etudes dédiées à Edward Grant, ed. J. Biard and Sabine Rommevaux, 67–98. Turnhout: Brepols. ———. 2017. Atomisme pythagoricien et espace géométrique au moyen âge. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe–XVIe siècles), ed. Tiziana Suarez-­ Nani, Olivier Ribordy, and Antonio Petagine, 181–206. Turnhout: Brepols. Robert Grosseteste. 1963. Commentarius in VIII libros physicorum Aristotelis, ed. Richard C. Dales. Boulder: University of Colorado Press. Robson, John A. 2008. Wyclif and the Oxford Schools: The Relation of the Summa de ente to Scholastic Debates at Oxford in the Later Fourteenth Century. Cambridge, MA: Cambridge University Press. Roques, Magali. 2016. Crathorn on Extension. Recherches de Théologie et Philosophie médiévales 83 (2): 423–467. Thomson, Williell R. 1983. The Latin Writings of John Wyclif. Toronto: The Pontifical Institute of Medieval Studies. Zhmud, Leonid J. 2012. Pythagoras and the Early Pythagoreans. Oxford: Oxford University Press.

Chapter 7

Francisco Suárez and Francesco Patrizi: Metaphysical Investigations on Place and Space Olivier Ribordy

Abstract  At the threshold of the modern period the intense discussions generated by Aristotelian arguments on place and space gave birth to new scholastic syntheses, such as that of Francisco Suárez (1548–1617), but also some innovative theories, as can be found in the works of the humanist Francesco Patrizi (1529–1597). Suárez shares Patrizi’s critical stance on the Aristotelian definition of place as the surface of the surrounding body, but both thinkers derive widely divergent conclusions from this common starting-point. Patrizi favors a Neoplatonist cosmology that allows for the existence of void between bodies within the outermost sphere, as well as beyond it; Patrizi considers void as the essence of space. He defines three-­ dimensional space as true place (locus verus), which can receive bodies. According to Patrizi’s theory, immobile space is, as it were, the condition of the reception of bodies. While Patrizi supports a conception of space as existing prior to bodies, Suárez opts for a place that inheres in bodies, the ubi intrinsecum, and distinguishes it from the locus extrinsecus. Rejecting any definition of ubi focused on exteriority – be it as an enveloping surface, a physical limit, an external form or even bodily space to be filled – Suárez argues in favor of place’s interiority and brings localization back within the realm of being.

7.1  Introduction On the eve of the modern period, Aristotelian theories of place and space provoked intense reflection that favored the development of new scholastic syntheses, such as those of the Jesuit Francisco Suárez (1548–1617), as well as of innovative lines of argumentation, such as those of the humanist Francesco Patrizi (1529–1597). Given I would like to thank Bill Duba for the English translation of the text and his precious additions, and the editors for their useful remarks. O. Ribordy (*) University of Fribourg, Fribourg, Switzerland e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_7

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the scientific and astronomical observations that had occurred in this period, was it still imaginable to maintain the Aristotelian description of place, or was it necessary to find another definition and develop different cosmological models? Should the localization of beings be understood as an essential and intrinsic characteristic of every being, or rather as an accident? What distinctions must one make between mind and body with respect to space? And how does an immaterial mind relate to a place? This paper first sketches Francisco Suárez’s theses on localization that he presents in his Metaphysical Disputations, finished at Salamanca ca. 1597, and which finds an echo in the treatise De angelis, published posthumously in 1620. Then it puts Suárez’s arguments on place in perspective by considering the very different, but almost precisely contemporary, doctrine presented by Francesco Patrizi in his De spacio physico et mathematico (Patrizi 1587). The humanist Patrizi incorporated his doctrine in his subsequent Nova de universis philosophia (Ferrara 1591, Venice 1593), which he defended before the Inquisition.1 The comparison of these two authors opens new interpretive perspectives on early modern theories of space: Suárez’s ontological model, the product of a detailed analysis of Aristotelian metaphysics, focuses on the characteristics of being (ens inquantum ens) and holds that being is intrinsically in space. Patrizi’s model, however, criticizes Aristotle and prefers a doctrine inspired by Plato, according to which there is a primary space that precedes everything. A contrast of these two models, the first representing a scholastic reading, the second associated with the Humanist movement, not only illustrates the richness of ‘pre-modern’ discussions of Aristotelian place, but also shows the degree to which the Aristotelian category of place (ubi) can be clarified: in Suárez’s case, in the wake of the intense scholastic debates among the Coimbra Jesuits, through the distinction between locus extrinsecus and ubi intrinsecum. By contrast, Patrizi, inspired by a Neoplatonic system of thought, proposes going beyond the Aristotelian categories to add space (spatium), which precedes substance in existence and which genuinely receives all bodies, including the world.

7.2  Localization and Space According to Francisco Suárez Recent research has focused on the coherence of Suárez’s theses on space, particularly as expressed in the Metaphysical Disputations [=DM], as, for example, in Castellote Cubells’ study on the connections between divine immensity (DM XXX), imaginary space and possible worlds.2 In this respect, how the ubi intrinsecum, which Suárez considers in Disputation LI, relates to other works, such as the De angelis, needs to be investigated. In describing the capacity of separate substances to bring changes about, Suárez addresses three aspects: the intellect, the will, and  See Puliafito Bleuel 1993, VII and 45–58. See Deitz 1999, 140, with a summary of the author’s six principal theses. For a precise overview, see De Risi 2016 and infra n42 sqq. 2  Castellote Cubells 2015. 1

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above all the transitive power, in other words, local motion. In the fourth book of his massive De angelis, Suárez investigates a separate substance’s capacity of bringing about local motion; through this capacity a separate substance, like an angel, can move itself, but it can also act on other entities. With respect to the question of a separate substance’s movement, Suárez first focuses on the motive power according to which an angel can move itself.3 He then addresses an angel’s capacity to act on other angels, on the separated soul, on man, and on the soul joined to the body. Finally, he considers an angel’s capacity for moving other corporeal realities. Note that there are two lines of investigation: one with respect to the angel itself and one with respect to external realities. Decisive in this context are a precise definition of the notion of place for a material substance and an explanation for how an angel can be present somewhere. In the question on the localization of an immaterial being, Suárez underscores a central distinction between extrinsic place (locus extrinsecus) and intrinsic ubi. That we should show this truth by reason, and lest the ambiguity of expression give rise to error, it should be noted that two things are to be distinguished in a thing that is in place, namely, extrinsic place, in which it is said to be, and intrinsic ubi, by reason of which it is said to be here or there.4

In his discussion in his treatise on angels, Suárez takes care to maintain the theses that he had established in detail in his Metaphysical Disputation LI on the ubi of material bodies and of immaterial beings. I dealt with this question at length in my Metaphysics, disputation 51, section 3 and 4 [...]. Nevertheless, I will take care to dispatch these matters briefly and without repeating myself, to the degree that I am able. But that the sense and the point of the question be understood, I observe that in a body existing in place two aspects can be considered: one is the extreme surface of the surrounding body, inside which the body is contained; the second is the presence or way of existing that a body has in the space stretched between the sides of the containing body, which fills space. But in angels that are in place, the extreme surface of the containing body is not considered, because an angel is not contained nor is circumscribed in place. Whence, with respect to an angel can be considered, as its extrinsic place, that body in which it intimately and quasi-penetratively exists, according to what was said in the previous chapter.5

Suárez first discusses corporeal ubi before identifying the characteristics of spiritual ubi. In fact, while the body, having dimensions, is surrounded by place, the spirit is not surrounded by place. Just as the corporeal ubi is material and implies that every 3  Suárez 1856, vol. 2, 421: “Et ideo in hoc libro prius dicemus de potestate, quam Angelus habet ad movendum seipsum motu locali. Supponimus enim extra cognitionem, et affectum, Angelum non esse capacem alterius mutationis praeter localem, quia neque augeri potest, aut minui, nec ad qualitates alias, praeter eas, quae intellectui, aut voluntati deserviunt, et in eis recipiuntur, transmutari potest.” 4  Ibid., vol. 2, 422 (cap. 1, §3): “Ut ratione veritatem hanc declaremus, et ne verborum ambiguitas sit errandi occasio, advertendum est, in re existente in loco duo esse distinguenda, scilicet, locum extrinsecum, in quo esse dicitur, et intrinsecum ubi, ratione cujus res hic, vel ibi esse dicitur” (our italics). 5  Suárez 1856, vol. 2, 427–428 (De angelis, lib. IV, cap. 2, §1).

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body excludes every other body from the place that it occupies, the ubi of an angel is spiritual and permits an angel to occupy the same space as a body. In spite of these differences, all beings, corporeal and spiritual, have an ubi intrinsecum according to Suárez. Let us observe in greater detail which theses about the ubi of bodies Suárez criticizes, and which arguments he calls to support his position, before considering his statements on the ubi of separate substances. In order to do so, we must follow Suárez’s own advice and consult DM LI.

7.2.1  O  pinions that Suárez Discusses Concerning the ubi of Bodies From his sources Suárez presents three solidly documented positions on the ubi of bodies. He rejects them all and proposes a fourth position, his own, which is not supported by any explicit source, but rather by an array of arguments. Suárez’s discussion of the ubi of bodies moves from the external to the internal, and he organizes his presentation of positions accordingly. In effect, Suárez begins by considering the exterior envelope of bodies and then gradually focuses on the intrinsic ubi. Suárez holds that ubi is a real and intrinsic mode of the body, and his exposition of the four positions can be presented schematically.6 1. According to the first position, ubi is described as an extrinsic form; thus a thing is said to be something in virtue of a determination.7 This position comes from Aristotle’s famous description of place in Physics IV (4, 212a20) as the surface of the containing body (locus est superficies ultima corporis continentis immobilis).8 2. According to the second position, ubi is not an extrinsic form or the containing surface, but rather is what in some way remains in a localized body considered independently of place.9 Suárez clarifies that, in this case, the extrinsic form certainly does not constitute the ubi, but, in leaving its traces on the ubi, the extrinsic form remains the foundation for it. This position, which suggests that the external container leaves a residue in what it contains, was notably defended  This description is a synthesis of a more detailed survey: Ribordy 2017.  For the suarezian formulation of these four theses, see Suárez 2013 (DM LI, sect. I, §§2–13): “Prima est ubi esse formam quamdam extrinsecam et extrinsece denominantem rem quae alicubi esse dicitur, nimirum superficiem ultima corporis continentis. Quae fundari potest primo, quia esse alicubi nihil aliud est quam esse in aliquo loco; ergo forma huius praedicamenti qua res ubicatur (liceat sic loqui ad rem declarandam), non est nisi locus quo circumscribitur vel continetur.” 8  Aristotle 1983, 28: “So that is what place is: the first unchangeable limit of that which surrounds.” For an account of the Aristotelian notions of place and space see Algra’s Chapter 2 in this volume. 9  Suárez 2013 (DM LI, sect. I, §§2–13): “Secunda sententia est ubi non esse ipsam formam extrinsecam seu superficiem ultimam continentem, sed esse quippiam intrinsecum passive relictum in locato ex circumscriptione loci.” 6

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in the Book of the Six Principles attributed to Gilbert of Poitiers and according to which locus is in the containing body and ubi is in the contained body.10 During the discussion of this second position, Suárez raises the issue of the relation between the contained body and the containing place; specifically, he rejects the theory that John Duns Scotus defended in Quodlibet, q. 11, that place is understood as a relationship with the container, that is, as an extrinsic accident.11 3. According to the third position, ubi is not in any way the containing surface or something that comes from it, but rather ubi is the space filled by the body that is said to be somewhere. The position seems to suggest a three-dimensional ubi. One will note here that, alongside other sources, like Simplicius (Physics IV, ad. c. 5),12 one finds John Philoponus, whose Physics commentary was just then available in Latin.13 4. Having rejected the three preceding positions, Suárez arrives at the fourth position, which he supports: Therefore the fourth position is the one that asserts that what is formally the category of ubi is a certain mode that is real and intrinsic to that thing that is said to be somewhere, from which mode such a thing has that it is here or there. This mode does not essentially depend on the surrounding body, nor on anything else that is extrinsic, but depends only materially on the body that is somewhere, while it effectively depends on the cause that constitutes or conserves that body there.14

Suárez pulls the following lessons from this discussion of the opinions on the place of bodies15: First, in every body there is an intrinsic mode that is distinct from its  See Gilbert of Poitiers 1953 (§5 De ubi, 20–24), at 20: “Ubi vero est circumscriptio corporis a loci circumscriptione procedens, locus autem in eo quod capit et circumscribit. Est igitur in loco quicquid a loco circumscribitur. Non est autem in eodem locus et ubi, sed locus quidem in eo quod capit, ubi vero in eo quod circumscribitur et complectitur.” The work attributed to Gilbert of Poitiers would serve as a source for Albert the Great, who also produced a Liber sex principiorum, a text that Suárez mentions in DM LII (Suárez 1965), sect. II, §4. Moreover, Suárez himself produced an analysis of De sex ultimis praedicamentis, which he also had the opportunity to teach in Segovia. I would like to thank Daniel Heider for this information. Although Suárez refers to this analysis in his De anima, he does not make any mention of it in DM LI, which is our concern here. 11  Duns Scotus 1895, 457–460. 12  Simplicius 1992a, 86–101. See also Simplicius 1992b. 13  Patrizi himself translated the Commentary on the Metaphysics ascribed to Philoponus, while he likely knew Philoponus’ Physics commentary, as it was translated in Latin twice in the sixteenth century, by Guglielmo Doroteo (first printed in Venice, 1539) and by Giovanni Battista Rasario (first printed in Venice, 1558). See Henry 1979, 556–557, who further specifies that Philoponus held space to be “incorporeal space,” described in his Physics commentary as “pure dimensionality void of all corporeality” (Philoponus 1888, 567). See also Lohr 2000, 33–34 and De Risi 2016, 77, as well as Section 2.3 of Algra’s Chapter 2 in this volume. 14  Suárez 2013 (DM LI, sect. I, §13): “Est ergo quarta sententia quae affirmat id quod est formale in praedicamento ubi esse quemdam modum realem et intrinsecum illi rei quae alicubi esse dicitur, a quo habet talis res quod sit hic vel illic. Qui modus per se non pendet a corpore circumscribente neque ab aliquo alio extrinseco, sed solum materialiter a corpore quod alicubi est, effective autem ab ea causa quae tale corpus ibi constituit vel conservat” (our italics). 15  See Suárez 2013 (DM LI, sect. I, §§14–22): “Dico ergo primo esse in quolibet corpore proprium quemdam modum intrinsecum, ex natura rei distinctum a substantia, quantitate et aliis accidentibus corporis, a quo modo essendi formaliter habet unumquodque corpus esse praesens localiter 10

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substance.16 Second, every body is locally present here or there by this intrinsic mode. Consequently, the presence of a body to place cannot be formally explained by any cause external to the body. Certainly, Suárez does not deny that a body is normally surrounded by another body; rather, he rejects that local determination is caused by something external to the determined body. To show this, he brings up the case of the outermost celestial sphere, which, since it is not surrounded by any other body, constitutes an exception. He concludes that this outermost celestial sphere certainly has a real presence there where it is and that it has this presence without any surface surrounding it. Having considered the totality of bodies including the highest, that is, the celestial sphere, Suárez establishes that all bodies have an intrinsic ubi. It now remains to decide the question for separate substances, and therefore to return to it in the De angelis.

7.2.2  S  uárez’s Characterization of the Place of Angels (ubi angelicum) In the treatise De angelis Suárez writes that one can certainly say that an angel is in a place (esse in loco), but only if one understands that the angel is really present there and that it has no distance with respect to its place, even a corporeal place. Echoing John Damascene’s treatment of the question (De fide orthodoxa, I, 17 and II, 3),17 Suárez furthermore deplores the frequent use of imprecise language. For example, when one says that the angels are in the Empyrean Heaven, the expression used is ‘are in,’ which signifies a presence, but the meaning given to it by some authors is ‘have a formal disposition (habitudo) with respect to.’18 Building on such terminological qualifications, Suárez can now maintain that an angel is not, properly speaking, in an extrinsic place, but rather that one must hypothesize, beyond place and every action in it, an accidental mode that is intrinsic to the angel, that is, the ubi angelicum.19 The ubi angelicum however is not similar to a substance, but adds to it “a certain intrinsic, accidental mode.” alicubi seu ibi ubi esse dicitur. Dico secundo: hic modus praesentiae non solum non provenit formaliter ab extrinseco corpore vel superficie ambiente, verum etiam nullo modo ex circumscriptione illius resultat nec per se illam requirit, quamvis ob naturalem ordinem corporum universi nunquam sit sine illa, praeterquam in ultima sphaera caelesti.” 16  According to Suárez 1861 (DM XXXIV, sect. 4, §23), an intrinsic mode is a formal and ultimate determination of existence, adding a modification to being, for example, providing localization. Thus, by an intrinsic mode can a being be individuated and recognized as such. See Coujou 2001, 47–48. On the modus, see Suárez 1976 (DM VII). For a comparison between Suárez (DM VII) and Descartes (PP I, 60–62), see Glauser 2000, 417–445, at 419, 439; Ariew 2012, 38–53. 17  Damascene 1955, 2010, 229–231. 18  On the Empyrean Heaven, see Mehl 2017b. 19  Suárez 1856, vol. 2, 429 (De angelis, lib. IV, §2): “[Prima conclusio] Nihilominus dico primo, Angelum non esse in extrinseco loco, quin praeter illum, et omnem actionem in illum, supponatur in ipso Angelo aliquis intrinsecus modus accidentalis, et ex natura rei a substantia distinctus.”

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Thanks to this notion of an ubi intrinsecum, Suárez can explain a large number of problems relating to the localization of angels. By their intrinsic spiritual ubi, angels can indeed be in a space at the same time that a body is already there, because separate substances do not require extension.20 Moreover, the ubi intrinsecum allows an angel to be present not only to a real place, but also to have a presence to an imaginary space. An angel can be somewhere, even if no surrounding body exists.21 Angels, owing to their intrinsic ubi, seem to be able to keep their localization in just about any situation. To show this, let us consider some of the paradigmatic cases that are particularly telling for scholastic thinkers.

7.2.3  H  ypothetical Cases and Thought Experiments that Appeal to the Imagination Hypothetical cases or thought experiments test the value of the proposed model, in this case, Suárez’s ubi intrinsecum. These hypothetical situations allow complex questions to be investigated, chiefly the localization of an immaterial being (such as a spirit), the bilocation of a being, or the interpenetration of many spirits. 1. In the first case, Suárez seeks to determine if two angels can be in the same place at the same time. Owing to the intrinsic ubi proper to each angel, two angels can simultaneously have the same place, since each one of them would be there according to the spiritual ubi proper to it. Secondly, it should be said, speaking of extrinsic place, that many angels can be at the same time in the same suitable place, according to the condition and ability of each one. [...] Because two angels do not naturally exclude each other from the same place by reason of their substance or by reason of the mode by which they are in a body or even in space, therefore there is no reason why being in the same place is incompatible with them, if they so wanted.22

 Suárez 1856, vol. 2, 423 (De angelis, lib. IV, §2), 2013 (DM LI, sect. IV, §36): “Ratio vero a priori est, quia haec propinquitas, seu indistantia non requirit commensurationem, vel extensionem, aut contactum quantitativum, sed solum simultatem (ut sic dicam) seu quasi penetrationem duarum entitatum in eodem spatio, quod ad rem explicandam nos concipimus, et ideo imaginarium vocatur: spiritus autem capax est hujus existentiae intimae, seu penetrationis cum corpore, imo solus ille hanc naturalem capacitatem habet, quia quantitate caret; ergo.” 21  Suárez 2013 (DM LI, sect. IV, §37). On various aspects of imaginary space, in particular as an example of an ens rationis, see infra n28 sqq. 22  Suárez 1856, vol. 2, 459 (De angelis, lib. IV, §9): “Secundo dicendum est, loquendo de extrinseco loco posse plures Angelos esse simul in eodem loco adaequato, juxta conditionem, et capacitatem uniuscujusque. […] Quia duo Angeli non se excludunt naturaliter ab eodem loco, ratione substantiae suae, nec ratione modi, quo sunt in corpore, vel etiam in spatio, ergo non est cur repugnet naturaliter esse in eodem loco, si velint.” 20

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2. Suárez likewise cites another hypothetical case used by medieval, and later by modern thinkers such as Thomas Hobbes23 or Pierre Gassendi,24 that of the annihilatio mundi. Suárez asks if an angel can keep its localization, even if all bodies were annihilated and then re-created. Here too, thanks to its intrinsic ubi, an angel can keep its localization, independent of the space that surrounds it, be it real, corporeal, empty, even non-existent.25 According to Suárez an angel would keep the same intrinsic mode of existing here, the same substantial presence, before, during and after the destruction of the bodies. Indeed, an angel has in itself an intrinsic mode of localization, even when the neighboring space remains empty. Such an ubi therefore does not depend in itself on a corporeal space. An angel would maintain a presence even in an imaginary space and could be localized thanks to its intrinsic ubi. In fact, the subject of imaginary space was above all explored in Metaphysical Disputation XXX,26 dedicated to divine immensity, to the point that Suárez treats imaginary space rather summarily in his discussion on the place of angels in DM LI. In this context, imaginary space corresponds to a place that can be filled by a body or by a quantity.27 Nevertheless some details on imaginary space can be gleaned from DM LIV, concerning entia rationis. For example, in the category of substance, there is conceived a chimera or similar monsters of reason, which are conceived in the manner of substance inasmuch as they are not fabricated as attributes of other things but imagined as beings by themselves. In the category of quantity, first there seems to be imaginary space, which we conceive as a kind of extension; and also that quantity which we conceive, for instance, in a chimera is a being of reason (ens rationis).28

In this remark, Suárez first of all makes use of the intellectual process of comparison, by which we can positively conceive of a being stripped of a given attribute; in  Leijenhorst 2002, 111–123; Suarez-Nani 2017, 93–107.  See Bellis’ Chapter 11 in this volume. 25  Suárez 2013 (DM LI, sect. IV, §10): “nam corpus annihilatum fuit sine mutatione reali angeli, et consequenter reproductum fuit sine reali additione facta in angelo; ergo omnis modus realis qui reperitur in angelo ante annihilationem illius corporis et post reproductionem eius, perseveravit in angelo toto eo tempore quo corpus illud fuit annihilatum et spatium vacuum. Ergo ubi angelicum, quantum est de se, aeque potest conservari, sive spatium sit reale et corporeum, sive inane, seu nihil praeter ipsum angelum.” 26  Concerning Suárez DM XXX, see the study of Beltrán 1999. For a study of the connections between divine immensity and possible worlds, see Castellote Cubells 2015, 219–235 – an analysis accompanied by a critical survey of contemporary studies of imaginary space, possible worlds, and the links between the Jesuits and Galileo. See also Leijenhorst 1996. 27  Suárez 2013 (DM LI, sect. IV, §29), (infra n31). 28  Suárez 2001 (DM LIV, sect. IV, §1): “Ut in substantia concipitur chymaera, aut similia monstra rationis, quae per modum substantiae concipiuntur; non enim finguntur ut adjacentia aliis, sed ut entia per se ficta. In quantitate videtur esse imprimis spatium imaginarium, quod per modum cujusdam extensionis nos concipimus; quantitas etiam illa, quam in chymaera, verbi gratia, concipimus, ens rationis est.” On DM LIV, see Coujou 2001 and for the quoted English translation Suárez 1995, 90. 23 24

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this case, conceiving of an imaginary space without extension amounts to conceiving it as like an extension. It is only through recourse to positive knowledge of extension that it is possible for us to act as if imaginary space also had dimensions. This example of imaginary space is thus just an illustration of the principle adopted at the beginning of DM LIV, where a being of reason is “forged according to the modality of being” and presents itself as an object to the mind.29 Over the course of the disputation, Suárez adds still more details concerning imaginary space. First, he underscores that “although it is true that this space so conceived is a being of reason, nevertheless, it falls under negation or privation considered extensively. For this space, when abstracted from its dimensions, is something negative.”30 Second, Suárez observes that it is out of the question to fill imaginary space: for example, it is an error to fill it with shadows. To liken imaginary space to shadows amounts to not taking seriously the privation represented by an empty space, for it amounts to filling the space. In other words, it amounts to giving a fictional being an imaginary or invented privation; filling an imaginary space could be compared to creating a blind chimaera, where one adds an invented privation – blindness – to the fictional being that is a chimaera. Third and finally, Suárez explains that purely fictional beings without basis in reality can encompass all the categories (quantity, quality, relation, position, action, passion, etc.) and even be multiplied to infinity, while beings of reason that have a basis in reality cannot embrace all the categories. Imaginary space, as a negation, can embrace several categories, but particularly that of quantity. Suárez had already investigated the links between substance and quantity in Metaphysical Disputation XL. The question then became whether imaginary space, as a being of reason, is exhausted by the category of quantity. Related questions, on the possibility of hypothetically having distances in imaginary space, and which deserve further development, bring us to the third thought experiment. 3. The third hypothetical case is that of a supposed distance between two angels. According to this hypothesis, one admits the existence of two angelic substances, between which there will be a distance, without however a real quantity being there. Since therefore in that argument it is inferred that there can be a distance between essentially (secundum se) spiritual beings, those particles in themselves can be taken in different ways [...]. Whence another sense can be between angels in themselves, that is, between angelic substances alone there can be distance, even if there were no quantity in reality; and we believe this sense to be true, because for there to be distance, it suffices for there to be the imaginary space, which we conceive as something suited to be filled with quantity. For  Suárez 2001 (DM LIV, sect. II, §16): “quamprimum concipitur per modum entis quod vere non est ens, jam intelligitur fabricatum ens rationis” and DM LIV, §2: “Hoc igitur modo metaphysicae proprium est agere de ente rationis ut sic, et de communi ratione, proprietatibus et divisionibus ejus, quia hae rationes suo modo sunt quasi transcendentales, et intelligi non possunt nisi, per comparationem ad veras et reales rationes entium, vel transcendentales, vel ita communes, ut sint proprie metaphysicae; nam quod fictum est, vel apparens, per comparationem ad id quod vere est, intelligi debet” (our italics). 30  Suárez 2001 (DM LIV, sect. IV, §7). 29

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two angels can have two ubis, by reason of which they ground between them a relation of distance, because they can so relate to each other that between them so large a body could be placed without their changing, which is enough for distance, even if, in fact, such a body were not placed.31

Unsurprisingly, according to this hypothesis, the ubis of the two angels constitute the foundation of the relation of distance between them – it scarcely matters whether a body is placed or not in the imaginary space that separates the two angels. The ubi suffices to explain the presence of the first angel to the second. In all the hypothetical cases cited, the key to interpretation lies in the ubi intrinsecum32: a real mode, intrinsic to all beings – corporeal and spiritual – and which guarantees their being localized. Criticizing the Aristotelian definition of place that emphasizes the external limit, Suárez’s model ends up privileging the interiority of place and re-establishing localization inside beings by means of the intrinsic ubi. In the Baroque period, the discussion of Aristotelian place saw other, very different doctrines come to the fore, which doctrines clarify from a different perspective Suárez’s synthesis: this is the case with Patrizi’s theses.

7.3  P  utting in Perspective: Aspects of Patrizi’s Investigations of Place and Space The works of Francesco Patrizi hold a particularly meaningful spot in philosophical investigations into place and space conducted at the end of the sixteenth century. As Hélène Védrine has shown, Patrizi severely criticized Aristotelian positions in his Peripatetic Discussions (Discussionum peripateticorum libri IV, Basel, 1581), in  Suárez 2013 (DM LI, sect. IV, §29): “Cum igitur in illo argumento infertur posse esse distantiam inter res spirituales secundum se, variis modis accipi potest illa particula secundum se […]. Unde alius sensus esse potest inter angelos secundum se, id est, inter solas substantias angelicas posse esse distantiam, etiamsi nulla realis quantitas sit in rerum natura; et hunc sensum verum esse credimus, quia ad hoc sufficit spatium imaginarium, quod nos concipimus ut aptum repleri quantitate. Possunt enim duo angeli habere duo ubi, ratione quorum fundent inter se relationem distantiae, quia possunt ita se habere ut inter eos possit tantum corpus interponi sine eorum mutatione, quod satis est ad distantiam, etiamsi de facto tale corpus interpositum non sit.” 32  In his Commentary on the Physics (1640), Francisco de Oviedo also mentions the ubi intrinsecum (Liber quartus physicorum, Controversia XV, De loco et vacuo, punctum IV, at 310–312. Refusing to describe place as an extrinsic denomination or as the result of circumscription, Oviedo prefers the opinion that designates the ubi as a real form and a physical accident added to the localized thing. Among those who hold this position, Oviedo mentions Suárez explicitly. In the same Physics commentary, Oviedo – who goes beyond the Aristotelian definition of place – describes imaginary space as a certain capacity; for, according to him, before a body can acquire presence in a place, a certain capacity (for localization) must be pre-existing in the place. Imaginary space moreover seems not to fall into the customary categories and rather to be neither a created being nor an uncreated being, but rather just a capacity. Certain related topics (for example on space preceding the localization of a body) emerge from Patrizi’s other texts. See infra Section 7.3.3. 31

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particular those on the enigmatic distinction between non-localized prime matter and localized determinate matter.33 His speculation on infinity, place, and the void also contains a criticism of major Aristotelian theses. Looking to propose a better physical model than that set out by Aristotle, Patrizi introduces four new constitutive principles of the universe: space, light, heat and fluor (a sort of material principle).34 If the first principle, space, is, according to Patrizi, both corporeal and incorporeal, we will note that the second principle is also both corporeal and incorporeal.35 In an innovative work, De spacio physico et mathematico, published 6  years later, Patrizi achieved a cosmological synthesis inspired by Neoplatonism and further criticized the Aristotelian doctrine of place. The De spatio physico et mathematico, along with a new introduction, would later be included in the Nova de universis philosophia, published in 1591 in Ferrara, where Patrizi taught Platonic philosophy, and again in 1593 in Venice, where he had to face the Inquisition. In the Nova de universis philosophia, one finds similar formulations applied to space and to light, such as “spatium sit corpus incorporeum et incorporeum corpus”36 and “Lumen corpus est incorporeum et incorpor[e]um corpus.”37 Nevertheless, as John Henry’s analysis has shown, space is primordial, preceding all being, including light: “space is created first as a theatre in which all following events take place.”38 In any case, light shares an important characteristic with space: it does not have resistance. These aspects allow Patrizi to distinguish space from natural bodies. Citing the three fundamental forms of space (tria spatia), namely “length or the line, width or the surface, and depth or the body,” Patrizi states that a natural body  These observations come from Hélène Védrine’s introduction to Patrizi 1996, 24. She also cites Patrizi 1571, 1581 on 396. See also Patrizi 1581, 246–250 (Discussionum peripateticorum), where, on the topics of locus, vacuum, tempus, and coelum, Patrizi systematically prefers Platonic explanations to Aristotelian ones. I would like to thank Filip Karfik for drawing my attention to this text. 34  Cf. Patrizi 1996, 27, 1591 (Pancosmia, liber XIII, f. 92v): “Spacium, quo trino omne corpus constat. Lumen, quod corpora omnia se ipso inficit. Fluor, qui corpora omnia constituit. Et calor, qui corpora omnia a fluore constituta et format et vivificat.” 35  Patrizi 1591b (Panaugia, liber I, f. 2v): “Lux ergo & incorporeorum, & corporum aeque, simulachrum est. & imago, & medium quoddam inter divina incorporea, & corporum naturam”; ibid., f° 10r°: “Inter quae dicimus, lumen esse corpus incorporeum, & immateriale, trine dimensum.” In a recent study, Delphine Bellis examines these same passages from Patrizi and observes that the mathematician and astronomer Ismaël Boulliau (1605–1694) gives a similar description in his De natura lucis, 1638 (theorema, p. 62): “Lux est substantia media proportionalis inter corpoream substantiam et incorpoream.” Boulliau explicitly cites Patrizi in the De natura lucis, p.  121: “Asserit deinde illam esse mediam, inter corpus, & incorporeum in sole & astris, corpus est quia in his habet molem, & trinam dimensionem, incorporea est quia est forma solis.” While in his Questiones celeberrimae in Genesim (1623), Mersenne would criticize Patrizi’s description, Descartes rather would target Boulliau. See Bellis Forthcoming. 36  Patrizi 1591, f. 68v. 37  Ibid., f. 74v. 38  Henry 1979, at 556: “Light is for him [Patrizi], the nearest analogy to God, and it is what he calls a corporeal incorporeal: corporeal because it is extended, but incorporeal because it has no resistance, no density, and is instantly propagated.” 33

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includes resistance (antitypia) over and above these three dimensions.39 He then argues that, since bodies have these three dimensions, so does place. Patrizi singles out an inconsistency in Aristotle’s teaching: on the one hand, Aristotle states that place has three dimensions (Physics IV, 209a); on the other, inasmuch as place is the surface of the containing body, place seems to have two dimensions and to lack depth (Physics IV, 212a).40 Patrizi resolves this aporia by making two counter-claims: (i) place has depth, and in this sense he defines place as a three-dimensional space that is immobile and capable of receiving different localized bodies; and (ii) place is distinct from body, in order to allow, at least at different times, two bodies to have the exact same place.41 Patrizi therefore establishes a subtle balance between localizing body (locans corpus), immobile space, and localized body (locatum). When it moves, the localizing body, having three dimensions, leaves behind it a free space, which the localized body can occupy. Therefore it is necessary that the localizing body (locans corpus), when it receives the localized body (locatum), leave in its entirety from there, and the space that is immobile there leave of itself a vacuum, so that it may be filled by the entering body.42

7.3.1  Definition of True Place Patrizi defines as true place the immobile and three-dimensional space that is called upon to be filled by a body. Therefore, he maintains that, just as the localized body has its proper place, the immobile space where a body could enter also has its proper place. Nevertheless, while three-dimensionality remains an accident of a localized 39  Patrizi 1996, 40, 1591, f. 61v. With respect to mathematical space, Patrizi states that minimum space is constituted by a line and not by a point, which is stripped of all dimensionality. Apart from a straight line, he also admits a circular line that can simply do without points. See Patrizi 1996, 33. 40  Aristotle 1983, 21: “It has three dimensions, length, breadth, and depth, by which every body is bounded.” Ibid., 1983, 28 (see supra n8). 41  In the part of his study dedicated to Patrizi’s criticism of Aristotle, John Henry (1979, at 559– 566) simply regrets that Patrizi had not developed theoretical arguments for explaining “the possibility of motion in a void,” which would have allowed him to refute Aristotle, who held such motion to be impossible. Henry concludes: “this is one of the major failings of his otherwise comprehensive critique” (ibid., 563). 42  Patrizi 1591, f. 62v: “Ergo necesse est, ut locans corpus, dum locatum recipit, ipsum totum inde discedat, & spacium quod ibi immobile est, relinquat se ipso vacuum, ut ingrediente corpore impleatur.” After emphasizing the originality of Patrizi’s positions, Hélène Védrine, (Patrizi 1996, 28), qualifies his conception of space: “Audacieuse par ses implications cosmologiques et sa critique physique, cette tentative reste parfaitement simpliste dans ses conséquences opératoires et mathématiques.” In his very rich study, De Risi 2016, at 83, highlights Patrizi’s originality on three points of the metaphysics of space: the conception of space as “the foundation of the quantification and extension of everything which exists in it,” the formulation of “a new epistemology of geometry as the science of space,” and the “thesis that space is directly quantified” (and also “the idea that the world is mathematizable”).

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body, it constitutes immobile space. In this context, Patrizi’s insistence on the equivalence between three-dimensional space and place becomes more understandable43: Therefore, place, because it is not a body, will necessarily be space endowed with three dimensions: length, width, and depth, by which it receives and grasps the length, width, and depth of the located body (corporis locati). And such a threefold space is true place, different from the localized body, in itself immobile, and in every aspect equal to the localized body. Place therefore has its own space, which is different from the proper space of the body. Rather, this threefold space truly is place, and place truly is threefold space. For space is accidental to place just as it is accidental to body [...] but this place is none other than those distances. And space is true place. And place is true space.44

One of Patrizi’s most striking achievements was to have “directly quantified space” – and not substance or matter – and to have “geometricized space.”45 De Risi underscores with emphasis the evolution that Patrizi imposes from a geometry that had been, until then, based around quantified matter to a geometry that turns on concepts of localization, a geometrical science based on logical principles to be found by the intellect and not on the construction of imaginary figures.46 Furthermore, he indicates that arithmetic, which according to Aristotle held first place, so-to-speak gives way to another mathematical science, geometry. Indeed, from a physical perspective, Patrizi considers space a first principle, prior to all beings, and, from a mathematical perspective, he integrates space into the field of geometrical investigations. A possible mathematical echo of his approach occurs several years later, in 1657, when, in his Introduction to Geometry, Blaise Pascal states that “the object of pure geometry is space, which it considers according to its triple extension in three different directions, which we call dimensions.”47 Patrizi’s conception of space from a physical perspective had an even greater influence than his mathematical reflections. For example, Gassendi accepts the idea that the study of space precedes that of physical bodies. Even if Gassendi, unlike Patrizi, defines space as quantity, he still maintains, along the lines of Patrizi, the priority of space, for example arguing that the space occupied by a city was there before the city, and that this immobile space would stay the same should the city need to be transferred or rebuilt. By going beyond the Aristotelian definition of place and developing his understanding of  And yet, space, which precedes all things, remains prior with respect to place, since place is just a part of space. 44  Patrizi 1996, 44; 1591, f. 62v, our italics. The cited passages were translated from the Latin text; for an English translation of part of the Nova de universis philosophia (Pancosmia. Liber primus: De spacio physico and also excerpts of Book II: Liber secundus: De spatio mathematico) see Patrizi 1943, 224–245, here 225: “[Patrizi] can thus claim to be the ancestor of the Absolute Space of early modern science. Patrizi first elevated Space to that metaphysical pre-eminence which More and Newton emphasized.” See also Muccillo 2010 and Leinkauf 1999. 45  De Risi 2016, 79, 97. 46  Ibid., 79–83, 90–93, at 80: “The element of exceptional novelty in Patrizi’s theory of space, namely, is that it envisages the idea of a quantitative extension without any substrate at all, neither substantial nor material.” See also Patrizi 1586 (infra n71 sqq.). 47  The passage from the Introduction to Geometry – a work that we know about only from some of Leibniz’s notes – is signalled by De Vittori 2010, 25. See also Itard 1969. 43

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place as primary, abstract, three-dimensional, immobile, and capable of receiving all bodies, including the world, Patrizi seems to have provided Gassendi with key arguments, and to have laid the groundwork for Newton’s absolute space. Moreover, he seems to have bequeathed a field of research to the critics of Descartes, including the Cambridge Platonist Henry More.48 Henceforth the question became whether space, conceived as capable of being infinite and prior to all beings, represents a physical limit for God.49 In addition to the definition of three-dimensional space as true place, another thesis appears in Patrizi’s text: his claim, at first glance disconcerting, that space can be both finite and infinite in actuality.

7.3.2  Finite and Infinite Space The space that contains the world is finite, while the space of the universe beyond the world is both finite – insofar as one of its parts touches the world – and infinite. In spite of this difference, these two spaces, in the world and outside the world, share certain basic characteristics: “they both are suited to receive bodies” and “they both have three dimensions.”50 In this way Patrizi emphasizes that both kinds of space allow “the shifting of bodies and their movement, which is proper to both kinds of space.”51 Patrizi undertakes to show “by almost tangible arguments”52 the existence of a space outside the world, by means of (i) investigations on the signs of the Zodiac, (ii) the natural philosophers’ theories of the conflagration of the world, and (iii) various thought experiments, which call upon the imagination. Thus, according to  Muccillo 2010, 56–64, quoting Gassendi, Syntagma philosophicum (Lyon, 1658), 182A: “certe illud Spatium sive intervallum quod, occupat Turris, erat ibi priusquam illa conderetur: quae etiam, si dirui, reaedificari, aut transferri intelligatur, semper tamen idem spatium, sive intervallum immotum consistet.” Muccillo 2010, 49, likewise indicates that Descartes is the author of a “radicale geometrizzazione dello spazio, che viene così privato di tutte le qualità che non siano quelle della materia stessa.” On the connections between matter and extension, see also Kambouchner 2015. 49  Muccillo 2010, 59. The debate revolves around Descartes’ thesis of a dichotomy between res extensa and res cogitans, implying the exclusion of any spiritual principle, and thus of God, in the physical world. It would focus precisely on the conception of space and the question of God’s relation to the world. According to More, to avoid having to affirm (with Descartes) that God is nowhere in the world, it is legitimate to attribute to God a local presence and a certain specific extension (purum subiectum mensurabilitatis). While the extension of bodies makes them impenetrable and tangible, the extension attributed to God permits Him to be everywhere. On this debate between More and Descartes, see Suarez-Nani Forthcoming. 50  Patrizi 1591, f. 64v. 51  Ibid., f. 64v: “Neutrum ipsorum corpus est: utrumque corpus recipere est aptum, utrumque corpori cedit: utrumque trine est dimensum; […] neutrum corporibus resistit […]. Sic spacii utriusque proprium est, cessio corporibus, eorumque motibus praestita.” 52  Ibid., f. 63v: “Sed rationibus fere sensatis, extra mundum spatium esse, illud inane demonstremus.” 48

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Patrizi, (i) the finite space, 30° long and 20° wide, occupied by a sign of the Zodiac in the internal surface of the heavens can be easily extended by lines into the contiguous and empty external space beyond the world. (ii) The hypothetical explosion of the world – (conflagratio) an argument used by Stoics, such as Cleomedes53 – would mean that the vapors it emitted would expand into the currently empty space that surrounds it, thereby proving the existence of a void space around the world. (iii) To support the thesis of a void space outside the world, Patrizi uses the following thought experiments: If the mind imagines the whole world to move from its place, it [viz. the whole world] would necessarily fill that empty space [into which it moves] – which now is just empty space because it contains no body – and make that space its place. Moreover, if this world were made by God to shrink to a smaller size, part of its place that now exists will be left as empty space, not to speak of those cases that some people will allow in thinking of a man standing on top of heaven, or who stretches an arm outside.54

7.3.3  Space as First Principle Although Aristotle, in presenting the categories, certainly mentioned place (ubi), to Patrizi’s eyes he did not treat space with the required precision.55 In his cosmological model, Patrizi emphasizes above all that space precedes all being56: “Since no other beings in nature exist beyond these four: space, place, body, quality, but body is prior to quality, and place to body, and space to place, without doubt, space is the first of all things.”57

 See Edelheit 2009, 247–248.  Patrizi 1591, f. 63v: “Si mundus universus mente cogitetur suo loco moveri, inane illud spacium, necessario replebit, locumque in eo sibi efficiet, quod nunc, quia corpus nullum continet, spacium tantummodo est inane. Praeterea si mundus etiam hic, in minorem a Deo contrahatur molem, eius loci qui nunc est, vacuum remanebit spacium, ut ommittamus, quae, aliqui de homine in supremo cœlo stante, vel brachio extra porrecto cogitatione admiserunt.” These examples have a long history, and were freely used, particularly in the medieval period: e.g. Oresme 1968; 1997, 317 (Quaest. In Phys. IV, q. 1), where he specifies that “place is the space between the extremities of the container.” This space would be “void if there were no body there, and full if a body filled it”: a notion that evokes parallels to Patrizi’s theses. For these observations, see Suarez-Nani 2004, 107–109. See also Oresme 2013, at 423–428. 55  Patrizi’s criticism of Aristotle is sometimes quite strong. See Patrizi 1591, ff. 67v-68a (De spacio mathematico): “Therefore, all the artifice of this man, by which he strives to ruin the indivisible line and minima, using sophisms dressed as war machines, appears to us to be extremely futile. Thus it leads us to ask how something so pointless could have created such tumult in philosophy and mathematics. May this fiction, may this lie, be expelled from the school of the truth.” See Deitz 2007 and infra n82. 56  See Prins 2015. 57  Patrizi 1591, f. 65r: “At cum entia nulla alia in natura sint praeter haec quatuor, spacium, locus, corpus, qualitas; corpus autem qualitate prius est; & corpore locus, & loco spacium, spacium nimirum rerum omnium primum est.” 53 54

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Echoing to some degree Plato’s Timaeus (52b) – where space (χώρα) is described as “providing a situation for all things that come into being”58 – Patrizi considers space as a first principle that precedes everything in nature.59 Space exists even before the creation of the world; space provides, so to speak, the conditions for the localization of the world. According to Patrizi, the case of the annihilatio mundi confirms this hypothesis: “For if the world were corrupted or reduced to nothing [which certain well-known Ancients have claimed], then the space in which the world is localized would be left empty.”60 In any case, space is merely a simple empty envelope, a simple capacity to receive bodies, characterized by having dimensions, by being immobile. Moreover, this description is not incompatible with the distinction made above between the space “that localizes the world, which is full of the body of the world, just as the other space [outside the world] is empty of all body. The latter also differs from the former in the fact that it is at once finite and infinite while the other is entirely finite.”61 In spite of their difference, these two spaces share a capacity to receive bodies. Nevertheless, the void is essential to space.

7.3.4  Empty and Full Space While Patrizi denies the existence of a large void in the space that contains the world (such as, according to some, the air of the heavens), he does admit the existence of small voids and minima of space between bodies.62 He appeals to the observable example of a portion of water that, when it contracts by half, neither disappears by half, nor occupies the other half, but rather densifies, occupying the empty spaces that it contains in itself.63 Therefore, there exists a void between bodies, and the void is even more essential to space than is the plenum64: “For this reason, if being a  Plato 1989, 122–125.  This parallel is highlighted by Henry 1979, 554. 60  Patrizi 1591, f. 65r. 61  Ibid., f. 64v. 62  Ibid.: “Illud enim inane, ac vacuum totum est, quantumcumque est. Hoc vero plenum mundo est, ac mundi corporibus omnibus, minutis tantum inter corpora intervalli vacui distinctum.” 63  Ibid., f. 63r. He invokes other examples and experiences to confirm the presence of tiny void spaces in the world, such as an airtight vase filled with water that, when exposed to cold air, produces a void. Similar problematic examples often represent thought experiments. See De Vittori 2010, 4–5: “l’eau est incompressible. De même Patrizi annonce que la glace a un volume moindre que l’eau (c’est de l’eau contractée), or c’est le contraire. L’argumentation est faible mais les idées avancées sont d’une importance capitale pour la compréhension de la suite de la démarche de l’auteur.” Thus Patrizi ends up supporting the presence of the void and the plenum in the world, and calls into question Aristotle’s model of place. 64  See the remark by Védrine, in the introduction to her edition of Patrizi’s text, (Patrizi 1996, 31): Void space exists prior to the body. In any case, space is not “un vide absolu, puisque l’espace est parcouru par la lumière, la chaleur et le fluor. Ici, vide signifie seulement absence d’antitypie, 58 59

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plenum is accidental to this mundane space, being a vacuum will belong to its essence. For both half of mundane space is a vacuum and the universe outside mundane space is empty.”65 In this way, Patrizi posits a void around the last sphere, such that the enclosed world, finite and full of bodies, is surrounded by another space, void, and both finite and infinite.66 Extra-mundane space, which in itself is unlimited, can be described from two angles, according to whether it touches the edge of the world or stretches to infinity67: Taking another way, we say that the space that is outside the world is both finite and infinite. For it is finite by that part that is contiguous with the outermost surface of the world, not indeed by its own proper and natural boundary, but rather by the ends of the world. But by that part by which it departs from the world and stretches away from it, it goes on to infinity.68

7.3.5  Definition of Space In order to philosophize correctly about space, Patrizi proposes going beyond the Aristotelian categories, since space precedes all of them. Space is neither accident nor substance, but “the substantial [hypostatica] extension that is self-subsisting, depending on nothing” (De spatio physico, §9). Patrizi then gives a demonstration of his thesis that space transcends all of Aristotle’s definitions of substance. According to Patrizi, space is certainly a substance in the sense that it “subsists by itself,” “exists by itself,” “maintains itself under everything,” “has no need of others in order to be,” “is found before everything,” but space – inasmuch as it is “more substance than any other substance” – is prior to the category of substance. In other words, space includes all the characteristics of substance, but simply is not a substance. Indeed, space “is not an individual substance, because it is not composed of matter and form [...] and it is not a genus, because it is not predicated of species or of singulars.”69 c’est-à-dire de résistance matérielle. Aussi n’est-il pas étonnant que l’espace contienne tous les corps, mais les pénètre également et soit pénétré par eux. En somme, l’espace se réduit à l’extension suivant les trois dimensions, mais il possède, comme toutes les réalités ‘médiatrices,’ une sorte de privilège qui le fait participer au corporel et à l’incorporel.” 65  Patrizi 1591, f. 64v: “Quare si plenum esse, spacio huic mundano accidit; vacuum esse ad essentiam eius pertinebit. Nam, & dimidia mundani spacii pars vacua est, & universum illud extra mundanum est inane.” 66  Patrizi 1996, 29. 67  Patrizi 1591, f. 64r: “Neque ergo a se ipso, neque a mundo, spacium, quod a mundo est. procul, terminatur. […] A corpore ergo nullo, vel finito, vel infinito, spacium illud primum, a mundo abiens terminatur, aut terminari potest.” 68  Ibid.: “Nos alia ingredientes via, dicimus, spacium quod est extra mundum, & finitum esse, & infinitum. Finitum quidem ea parte, qua mundi extimam superficiem contingit, non quidem proprio, & naturali fine suo, sed mundi terminis. Qua vero digreditur a mundo, ab eoque proculabit, in infinitum transit.” 69  Ibid., f. 65r.

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Transcending the categories of substance and accident, space cannot be described only as a body or as incorporeal. Indeed, space has three-dimensionality like a body but, like a spiritual being, it lacks resistance. It is at once body and incorporeal, to the point that Patrizi defines it as corporeal non-body (noncorpus corporeum) and incorporeal body (corpus incorporeum), perfectly immobile.70 Moreover, in his Italian-language work, Della nuova geometria, Patrizi summarizes some of the major results obtained in the De spatio physico et mathematico, notably including the characteristics of space, this time conceived from a mathematical perspective. Thus he states that “space is extension, and extension is space,” that “all space is either long, or long and wide, or long, wide, and deep.”71 From this geometrical perspective, Patrizi insists on the priority of space with respect to any element that is placed in it, and he particularly emphasizes that space is prior to a point. A point, which does not have quantity, is thus not a space, but is in space. From this, the first magnitude is the line. The line is continuous and in actuality – and it is not infinitely divisible, contrary to the claims of mathematicians from Antiquity, including Euclid. Patrizi states that a line is not composed of points; it is simple, primary, and minimal.72 As De Vittori explains in his analysis of this treatise, one of Patrizi’s goals is to philosophically found the geometrical principles that Euclid simply presupposed without giving them the necessary demonstrations. According to Patrizi’s reasoning, thus, every mathematical object is defined with respect to space; his project of ‘geometricizing space’ does not consist in abstracting geometrical figures from sensible objects, but rather in discovering within space (understood as first principle) the connections between geometric figures.73 For example, a line is ‘delimited’ at its extremities by points, but not insofar as the human mind would perceive points, but in virtue of the intrinsic connections between these mathematical objects placed in space. Thus the line can be finite and limited (by these points), all while being stretched to infinity.74 Finiteness and extension to infinity can perfectly well be admitted at the same time for the smallest  Ibid., ff. 65r-65v: “Itaque corpus incorporeum est, & noncorpus corporeum. […] Itaque nec toto, nec partibus movetur. Est ergo & immotum prorsus, & omnino immobile.” See also Védrine, (Patrizi 1996, 30): “Comme espace de l’univers, il est vide, infini; comme espace du monde, il est fini et rempli de corps. Simple et homogène sous sa première forme, il est complexe sous la seconde. Divisé par les corps, les contenant tous et les limitant, l’espace du monde perd, dans une certaine mesure, sa pureté originelle, bien qu’il reste fondamentalement, comme l’espace de l’univers, ‘corpus incorporeum’.” On the strong links between Patrizi and Proclus, who had described space as “immaterial body,” see Deitz 1999, at 155. 71  For the discussion that follows, see De Vittori 2010, 1–28, at 9–10, 20–25; Patrizi 1586, lib. I, 3. 72  Patrizi 1586, lib. III, 49 (Book III, conclusion of the XVII first propositions). 73  Although Makovský 2014, 294–295, 307–310 acknowledges that, in his Della nuova geometria, Patrizi includes in his discussion of space relational aspects (between geometrical figures), he is highly critical of the work, recalling Leibniz’s judgment that “the preface to his New Geometry, dedicated to the Duke of Ferrara, is admirable, but the content is deplorable” (Leibniz 1999, A VI, 4A, 966). See also De Risi 2016, 92–96. 74  As shown by De Vittori 2010, 23. Patrizi 1586, lib. III, 50–51 (“risoluzione delle seconde XVI proposizioni”): “E cio perche la linea si puo allungare in infinito […] E cio perche due punti estremi, da ambi i lati la fan finita” (our italics). 70

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spatial entity, the minimal line. On the other hand, the infinite division (in potency) of a minimum constitutes a physical barrier, which, to Patrizi’s eyes, mathematics – a domain that he is less familiar with – does not seem to be able to cross.75 It is above all in his study of space from a physical perspective that Patrizi reveals his undeniable originality in describing immobile space as both finite and infinite,76 full and empty, corporeal and incorporeal. Nevertheless, he leaves one issue open: space cannot be understood as a whole, composed of finite parts  – as the author himself recognizes in his final chapter (De spacio physico, §10). For space, the cost of its transcendence (finite/infinite, full/empty, corporeal/incorporeal) is a certain lack of uniformity77 – even if the two types of space identified by Patrizi, namely the space of the world and the space of the universe, share three-dimensionality and the capacity for receiving bodies. And yet the enclosed, finite world is not replaced by the infinite universe. Stoic authors in Antiquity and various Platonizing authors in the Renaissance believed that they coexisted in and often supported an enclosed world inside an infinite universe.78 For the immobility of the universe allows one to think of a delimited world within. An author steeped in the Renaissance of Platonic sources, Agostino Steuco, described in his Philosophia perennis (1540, published in 1591) the world as a ­particle drowning in an infinite universe.79 Patrizi shares Steuco’s claim of the compatibility between the infinite universe and the enclosed world.80  See Védrine (Patrizi 1996, 33–34), who emphasizes Patrizi’s “réalisme mathématique” and his less detailed mathematical hypotheses, contrasted with physical and ontological barriers: he accepts the infinitely large in actuality, but holds that it is impossible for a minimum to be infinitely divisible, even in potency. “Patrizi […] s’arrête à un géométrisme simpliste lié à des spéculations physiques sur l’élément ultime de l’espace” (ibid., 33). 76  This notion, developed in a Stoic vein, would be criticized by Giordano Bruno, without, however, targeting Patrizi by name, as shown by Del Prete 1999, 42 (with reference to Bruno 2006, 60–66). See also infra n82. 77  Muccilllo 2010, 64, states that Patrizi’s doctrine of space, considered from a mathematical perspective, appears as homogeneous, infinite, and isotropic. For Patrizi space stays the same, for geometry as for physics, as emphasized by Makovský 2014, 302. On the mathematical implications of Patrizi’s actually infinite space, and on his rejection of mathematical constructivism, that is, his refusal to resort to the imagination to construct figures, see De Risi 2016, 90–91. 78  For this line of argument, see the study by Mehl 2017, 229–248, at 233. For the Stoics see also Section 3.2.2 of Bakker’s Chapter 3 in this volume. 79  Mehl emphasizes that, without doubt ascribing to Empedocles a thesis that he did not hold, Agostino Steuco had tried to show that the world was included like a particle in the infinite universe, assimilated to God. In support of his reasoning, Mehl cites Steuco 1591, vol. 3, f. 50v (Philosophia perennis III, 8): “Cum vero dicat tantum interesse inter universum ac mundum, quantum inter immensum quiddam ac brevem particulam, palam fit, hoc universum, aliquid a mundo diversum eum sensisse. […] Ergo superiorum Philosophorum vestigia sequutus Empedocles, ipsum universum dicebat Deum, cuius quasi particula esset iste mundus.” Steuco understands space both as a representation by a subject and as an interval between two realities. 80  Even more stunning, the Philosophia perennis appears among the chief sources that Francisco Suárez mentions in the proemium to his De angelis – at the moment when he reveals his project and indicates that a study of spiritual creatures belongs to natural theology or metaphysics, and that such a study is also important for natural philosophers, since it bears on the movement of celestial 75

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7.4  C  oncluding Remarks: Different Approaches to Place and Space If Suárez shares with Patrizi the criticism of the Aristotelian definition of place as surface of the surrounding body, the two thinkers draw from this criticism largely divergent conclusions. The humanist Patrizi favors a Neoplatonic cosmology, which allowed for a void between bodies in the world as well as a void beyond the last sphere81; Patrizi holds that void is the very essence of space. He defines three-dimensional space as the true place (locus verus) that is capable of receiving bodies. While Aristotle, opposed to the very hypothesis of the void, would deny that something incorporeal like the void could have three-dimensionality, Patrizi, to the contrary, emphasizes this aspect and distinguishes corporeity from dimension.82 Patrizi separates Aristotelian locus (defined, incorrectly, according to just the two dimensions of length and width)83 from a notion of spatium, which is three-dimensional and precedes all substances and permits the localization of everything. Space is prior to the categories, prior to substance. It is neither purely a body, because it has no resistance, nor is it completely incorporeal, because it is three-dimensional and is able to bound bodies. More than anything, space is a substance, without belonging to the category of substance (“Spatium maxime omnium substantiam esse, sed non est categoriae substantia illa”).84 Patrizi’s doctrine considers immobile space in some way as the condition for the reception of bodies and souls as animated beings.85 Space is an incorporeal body and a corporeal non-body.

bodies. Suárez 1856, (Prooemium, XII), where, following the aforesaid general passage and after having mentioned several authors who studied separate substances (including Plato, Thomas Aquinas, and Marsilio Ficino), he names Steuco: “Et alia ex Philosophis congerit de Angelis Augustinus Eugubinus, in lib. 8 peren. Philosoph.” 81  See De Risi 2016, 67, which observes that Patrizi admits (i) the microscopic or disseminated void, (ii) the observable, coacervated void, and (iii) the extracosmic void. 82  See Henry 1979, 572: “the first systematic attempt to completely reject Aristotle’s place and to establish the vulgar opinion of space as a philosophically sound, even philosophically necessary concept was made by Patrizi.” By contrast, Giordano Bruno considers Patrizi a “pedant” and judges that he uselessly befouled pages with his Discussiones peripateticae. See Bruno 2016, 165–167: “de quali è un francese arcipedante, ch’ha fatte le Scole sopra le arte liberali e l’Animadversioni contra Aristotele; et un altro sterco di pedanti, italiano, che ha imbrattati tanti quinterni con le sue Discussioni peripatetiche.” See Henry 1979, 551 and Védrine, (Patrizi 1996, 21), who emphasizes that Bruno nevertheless extensively used the results of Patrizi’s research. 83  Patrizi 1591, f. 62v: “Locus ergo integer erit, non superficies ambientis sola, sed profunditas etiam, intra superficiem existens, simul cum illis.” 84  Ibid., f. 65r. 85  Ibid., f. 65v: “immobile autem in mundo nihil est, praeter spacium ac terram.” Cf. ibid., f. 61r: “this must be prior to all else; when it is present all other things can be placed in it, when absent all others are destroyed” (also quoted by Henry 1979, 554).

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While Patrizi favors a space (as true place) that exists before bodies, Suárez prefers a place that inheres in bodies, the ubi intrinsecum,86 and distinguishes it from the locus extrinsecus. Rejecting any model that defines place through an emphasis on exteriority – be this as a containing surface, physical limit, exterior form, or even corporeal space to be filled – Francisco Suárez argues in favor of the interiority of place and brings localization into the heart of the being. Through his analysis of the ubi intrinsecum, he explains localization as common denominator of all creatures, corporeal and spiritual.87 By their diversity and by their speculative density, the models of Suárez and Patrizi illustrate the richness of conceptions of place and space at the dawn of the modern period, and attest to the fruitful debates that built up on the foundation of Aristotelian doctrines.

References Ariew, Roger. 2012. Descartes and Leibniz as Readers of Suárez: Theory of Distinctions and Principle of Individuation. In The Philosophy of Francisco Suárez, ed. Benjamin Hill and Henrik Lagerlund, 38–53. Oxford: Oxford University Press. Aristotle. 1983. Aristotle’s Physics. Books III and IV, trans. with Notes by Edward Hussey. Oxford: Clarendon Press. Bellis, Delphine. Forthcoming. La nature de la lumière entre physique et ontologie: Descartes et Boulliau. In Descartes en dialogue, ed. Olivier Ribordy, and Isabelle Wienand. Basel: Schwabe. Beltrán, Miquel. 1999. El Dios de Suárez y los espacios imaginarios. In Francisco Suárez (1548– 1617), Tradição e Modernidade, ed. Adelino Cardoso, Antonio Manuel Martins, and Leonel Ribeiro Dos Santos, 93–98. Lisbon: Colibri. Boulliau, Ismaël. 1638. De natura lucis. Paris: Louis de Heuqueville. Bruno, Giordano. 2006. Opere Complete/Œuvres complètes, vol. 4: De l’infinito, universo e mondi/ De l’infini, de l’univers et des mondes, text Giovanni Aquilecchia, notes Jean Seidengart, intr. Miguel Ángel Granada, trans. Jean-Pierre Cavaillé. Paris: Les Belles Lettres. ———. 2016. Opere Complete/Œuvres complètes, vol. 3: De la causa, principio et uno/De la cause, du principe et de l’un, text and notes Giovanni Aquilecchia, intr. and notes Thomas Leinkauf, trans. Luc Hersant, new ed. rev. Zaira Sorrenti. Paris: Les Belles Lettres. Castellote Cubells, Salvador. 2015. Francisco Suárez: Teoría sobre el espacio. De la inmensidad y la infinidad de Dios al espacio imaginario y los mundos posibles. Valencia: Facultad de Teología San Vicente Ferrer. Coujou, Jean-Paul. 2001. Le vocabulaire de Suárez. Paris: Ellipses.

 Nevertheless, Patrizi suggests that space certainly has, at least in its infinite part, “the force to localize from the inside what it receives and to surround it on all sides from the outside” (Patrizi 1591, f. 65v). 87  On this point concerning the spatialization of beings, and not only of bodies, see De Risi 2016, at 70: “The Nova philosophia, however, not only provides important details on the use of Patrizi’s concept of space in natural philosophy, but also accomplishes a further, and fundamental, radicalization of the theses of De spacio physico in the form of the statement that all beings, not only bodies, are located in space and thus possess spatial attributes.” 86

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Deitz, Luc. 1999. Space, Light, and Soul in Francesco Patrizi’s Nova de universis philosophia (1591). In Natural Particulars: Nature and the Disciplines in Renaissance Europe, ed. Anthony Grafton and Nancy Siraisi, 139–169. Cambridge, MA: MIT Press. ———. 2007. Francesco Patrizi da Cherso’s Criticism of Aristotle’s Logic. Vivarium 45 (1): 113–124. Del Prete, Antonella. 1999. Bruno, l’infini et les mondes. Paris: PUF. De Risi, Vincenzo. 2016. Francesco Patrizi and the New Geometry of Space. In Boundaries, Extents and Circulations, ed. Koen Vermeir and Jonathan Regier, 55–106. Cham: Springer. De Vittori, Thomas. 2010. La nouvelle géométrie de Francesco Patrizi da Cherso. In HAL archives ouvertes. https://hal.archives-ouvertes.fr/hal-00414155v2. Edelheit, Amos. 2009. Francesco Patrizi’s Two Books on Space: Geometry, Mathematics, and Dialectic beyond Aristotelian Science. Studies in History and Philosophy of Science 40: 243–257. [Gilbert of Poitiers]. 1953. Liber de sex principiis Gilberto Porretae ascriptus, ed. Alban Heysse and Damien van den Eynde. Münster: Aschendorff. Glauser, Richard. 2000. Descartes, Suárez, and the Theory of Distinctions. In The Philosophy of Marjorie Grene, ed. Randall E. Auxier and Lewis E. Hahn, 417–445. Chicago/La Salle: Open Court. Henry, John. 1979. Francesco Patrizi da Cherso’s Concept of Space and its Later Influence. Annals of Science 36: 549–575. Itard, Jean. 1969. L’Introduction à la Géométrie de Pascal. Revue d’histoire des sciences et de leurs applications 15 (3–4): 269–286. John Damascene. 1955. De fide orthodoxa: Versions of Burgundio and Cerbanus, ed. Eligius M.  Buytaert. Saint-Bonaventure/Louvain/Paderborn: The Franciscan Institute/Nauwelaerts/ Schöningh. [John Damascene]. Jean Damascène. 2010–2011. La foi orthodoxe, 2 vols., ed. Bonifatius Kotter, trans. Pierre Ledrux, with Vassa Kontouma-Conticello and Georges-Matthieu de Durand. Paris: Cerf. John Duns Scotus. 1895. Quodlibet. Vol. XI. Paris: Louis Vivès. Kambouchner, Denis. 2015. Descartes n’a pas dit. […] Un répertoire des fausses idées sur l’auteur du Discours de la méthode, avec les éléments utiles et une esquisse d’apologie. Paris: Les Belles Lettres. Leibniz, Gottfried Wilhelm. 1999. Projet et essais pour avancer à quelque certitude pour finir une bonne partie des disputes et pour avancer l’art d’inventer. August 1688 – October 1690. In Sämtliche Schriften und Bände, ed. Berlin-Brandenburgische Akademie der Wissenschaften and Akademie der Wissenschaften in Göttingen (6th series, Philosophische Schriften, vol. 4, part A), 963–970. Berlin: Akademie Verlag. Leijenhorst, Cees. 1996. Jesuit Concepts of Spatium Imaginarium and Thomas Hobbes’ Doctrine of Space. Early Science and Medicine 1 (3): 355–380. ———. 2002. The Mechanisation of Aristotelianism: The Late Aristotelian Setting of Thomas Hobbes’ Natural Philosophy. Leiden/Boston/Cologne: Brill. Leinkauf, Thomas. 1999. Francesco Patrizi (1529–1597): Neue Philosophien der Geschichte, der Dichtung und der Welt. In Philosophen der Renaissance: Eine Einführung, ed. Paul Richard Blum, 173–187. Darmstadt: Wissenschaftliche Buchgesellschaft. Lohr, Charles H. 2000. Renaissance Latin Translations of the Greek Commentaries on Aristotle. In Humanism and Early Modern Philosophy, ed. Jill Kray and Martin F. Stone, 24–40. London/ New York: Routledge. Makovský. 2014. The New Geometry of Francesco Patrizi. In Francesco Patrizi, Philosopher of the Renaissance: Proceedings from the Centre for Renaissance Text Conference (24–26 April 2014), ed. Tomáš Nejeschleba and Paul Richard Blum, 294–312. Olomouc: Palacky University Olomouc. Mehl, Édouard. 2017. Agostino Steuco et la question de l’immensité cosmique entre théologie et science au temps de la Réforme. In Lieu, espace, mouvement: Physique, métaphysique et cos-

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mologie (XIIe–XVIe siècles), Actes du colloque, Fribourg 12-14.03.2015, ed. Tiziana Suarez-­ Nani, Olivier Ribordy, and Antonio Petagine, 229–248. Barcelona/Rome: FIDEM. ———. 2017b. La fiction théologique du ciel empyrée, de Luther à Descartes. Revue des Sciences Religieuses 91 (2): 193–210. Mersenne, Marin. 1623. Questiones celeberrimae in Genesim cum accurata textus explicatione. Paris: Sébastien Cramoisy. Muccillo, Maria. 2010. La concezione dello spazio di Francesco Patrizi (1529–1597) e la sua fortuna nell’ambito della reazione anticartesiana inglese. In Dal cartesianismo all’illuminismo radicale, ed. Carlo Borghero and Claudio Buccolini, 49–71. Florence: Le Lettere. Nicole Oresme. 1968. Le Livre du Ciel et du Monde, ed. Albert D. Menut and Alexander J. Denomy. Madison: The University of Wisconsin Press. [Nicole Oresme]. 1997. Nicolaus Oresmes Kommentar zur Physik des Aristoteles: Kommentar mit Edition der Quaestionen zu Buch 3 und 4 der aristotelischen Physik sowie von vier Quaestionen zu Buch 5, ed. Stefan Kirschner. Stuttgart: Steiner. Nicole Oresme. 2013. Questiones super Physicam (books I–VII), ed. Stefano Caroti, Jean Celeyrette, Stefan Kirschner, and Edmond Mazet. Leiden/Boston: Brill. Oviedo, Francisco de. 1640. Integer cursus philosophicus ad unum corpus redactus in summulas, logicam, physicam… (Liber quartus physicorum, Controversia XV: De loco et vacuo). Lyon: Pierre Prost. Patrizi, Francesco. 1571. Discussionum peripateticarum tomi primi, libri XIII. Venice: Domenico de Franceschi. ———. 1581. Discussionum peripateticorum libri IV. Basel: Perna. ———. 1586. Della nuova geometria, Libri XV. Ferrara: Vittorio Baldini. ———. 1587. De rerum natura, Libri II.  Priores. Alter de Spacio Physico, Alter de Spacio Mathematico. Ferrara: Vittorio Baldini. ———. 1591a. Nova de universis philosophia. Pancosmia. Liber primus: De spacio physico, ff. 61-65b/Pancosmia. Liber secundus: De spacio mathematico, ff. 66-68b. Ferrara: Benedetto Mammarelli. ———. 1591b. Nova de universis philosophia. Panaugia. Liber primus: De luce, ff. 1r-3r. Ferrara: Benedetto Mammarelli. ———. 1593. Nova de universis philosophia…. Venice: Roberto Meietti. ———. 1943. On Physical Space, trans. Benjamin Brickman. Journal of the History of Ideas 4: 224–245. ———. 1996. De spacio physico et mathematico, présentation, traduction et notes par Hélène Védrine. Paris: Vrin. Philoponus, John. 1539. Ioannis Grammatici cognomento Philoponi eruditissima Commentaria in primos quatuor Aristotelis De naturali auscultatione libros, nunc primum e Greco in Latinum fideliter translata…, trans. Guglielmo Doroteo. Venice: Brandino and Ottaviano Scoto. ———. 1558. Aristotelis Physicorum libri quatuor cum Ioannis Grammatici cognomento Philoponi commentariis: Quos nuper ad Graecorum codicum fidem summa diligentia restituit Ioannes Baptista Rasarius…, ed. Giovanni Battista Rasario. Venice: Girolamo Scoto. ———. 1888. Ioannis Philoponi in Aristotelis physicorum libros quattuor priores commentaria, ed. Girolamo Vitelli. Berlin: G. Reimer. Plato. 1989. Timaeus, trans. Robert Gregg Bury. Plato in Twelve Volumes, vol. 9. Cambridge, MA: Harvard University Press. London: Heinemann. Prins, Jacomien. 2015. Echoes of an Invisible World: Marsilio Ficino and Francesco Patrizi on Cosmic Order and Music Theory. Leiden: Brill. Puliafito Bleuel, Anna Laura. 1993. Francesco Patrizi da Cherso, Nova de universis philosophia, Materiali per un’edizione emendata. Florence: Olschki. Ribordy, Olivier. 2017. La localisation comme enjeu métaphysique: Thèses sur le lieu, discutées par Francisco Suárez. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe–XVIe siècles), Actes du colloque, Fribourg 12-14.03.2015, ed. Tiziana Suarez-Nani, Olivier Ribordy, and Antonio Petagine, 249–273. Barcelona/Rome: FIDEM.

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Chapter 8

Giordano Bruno’s Concept of Space: Cosmological and Theological Aspects Miguel Á. Granada

Abstract  Bruno’s concept of space remains constant throughout his entire work. Its main tenets are: (1) the rejection of Aristotle’s concept of ‘place’ as an accident of bodily substance and the ensuing notion of ‘natural places;’ (2) the notion of space as an infinite, homogeneous receptacle of matter; and (3) the idea that void, though conceptually prior to matter, is always and everywhere filled with matter. Edward Grant (in his masterful Much Ado About Nothing, Cambridge, 1981) argued that “the consequences of Bruno’s description of space and the properties he assigned it lead inevitably to an infinite space that is coeternal with but wholly independent of God.” In the present chapter I show that Grant’s conclusion is incompatible with the foundations of Bruno’s ontology. De immenso and Lampas triginta statuarum allow us to establish Bruno’s true concept of the relation between God and space in accordance with the doctrine of the six ‘infigurable’ primary principles distributed in two triads: Mind or Father-Intellect-Spirit; and Chaos or Void-Orcus or Privation-Night or Matter. Both triads represent, in accordance with the ontology of De la causa, the two (non hierarchized) aspects of God’s essence as a coincidence of opposites: potency and act, matter and form, void space and mind. As a consequence, since God is space and matter no less than mind and form, we can confidently say that Bruno – relying on Biblical passages describing God as unity of contradictories – had already gone as far as Spinoza in conflating God, extension, matter, and space.

This article is the result of research conducted within the project “Cosmología, teología y antropología en la primera fase de la Revolución Científica (1543–1633),” funded by the Spanish Government (Ministerio de Economía y Competitividad, Project FFI2015-64498-P for the triennium 2016–2018). I wish to thank Patrick J. Boner for his careful reading and improvements on the original English version of this article, as well as for his aid with the English translations of several passages from Bruno’s Latin works. M. Á. Granada (*) University of Barcelona, Barcelona, Spain e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_8

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8.1  Introduction In his still fundamental From the Closed World to the Infinite Universe, Alexandre Koyré stated that “never before [Bruno] had the essential infinitude of space been asserted in such an outright, definite and conscious manner.”1 Even if he did not consider contemporary authors such as Bernardino Telesio and Francesco Patrizi – as has been objected, among others, by Edward Grant2  – Koyré’s analysis still remains correct if we take into consideration the role that the concept of space plays in their respective cosmologies: in Bruno that of an infinite, homogeneous universe with infinite planetary star-centered systems, as opposed to a finite geocentric universe in a finite space (Telesio) and a finite geocentric universe (Patrizi) in an infinite space filled with spiritual light.3 Bruno’s concept of space pervades almost all his work. We may turn to three telling moments: (1) the Italian cosmological dialogues, in particular De l’infinito, universo e mondi (1584), but also La cena de le Ceneri (also 1584); (2) his Latin poem De immenso et innumerabilibus, published in Frankfurt in 1591; and (3) an intermediary state when, in Germany around 1587, Bruno expands the Parisian Articuli adversus peripateticos of 1586 into the Camoeracensis acrotismus, eventually published in Wittenberg in 1588. This intermediary period (though we should be aware that the composition of De immenso covers an extended period, the beginning of which cannot be fixed exactly) also covers the Lampas triginta statuarum (written in 1587, but not published until the nineteenth century). This last work, unattended by both Koyré and Grant, offers some fundamental insights in its examination of the ‘unfigurable principles’ of Chaos, Orcus and Night (i.e. Void, Appetite and Matter), in connection with the opposite triad of Mind, Intellect and Spirit, particularly into the ontological condition of space and void, as well as their relation to God or the One. Bruno’s concept of space remains basically the same throughout all these works.4 While there is no structural modification in the doctrine, some differences emerge between its presentation in the Italian dialogues and in the writings of 1587, where we find the first occurrence of the doctrine of De immenso. These differences are mainly that the presentation in the Italian dialogues, especially in De l’infinito, focuses on the cosmological aspects of space and the void, as well as on the criticism of the Aristotelian and Stoic doctrine. By contrast, from 1587 Bruno pays more attention to the ontological and theological foundation of space and the void, while he tries to determine the nature of space (and the void) in itself, as well as its relation to God. 1  Koyré 1957, 39. On Bruno’s concept of space and the infinite, homogeneous universe see ibid., 39–55. 2  Grant 1981, xiii, 380 n69, 389 n163. On Bruno’s concept of space see ibid., 183–192. 3  For Telesio’s concept of space see Schuhmann 1992, Grant 1981, 192–-194; Granada 2007, 274. On Patrizi see Grant 1981, 199–206, Henry 1979; Granada 2007, 277 f. 4  See the accurate general presentations of the concept in Amato 2006; Fantechi 2014a. Cf. also Fantechi 2014b.

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8.2  Space in the Italian Dialogues, Mainly in “De l’infinito” In the Italian cosmological dialogues, the main subject of demonstration is the infinity and homogeneity of the universe. This requires the existence of infinite space and as a consequence, in these dialogues (but mainly in De l’infinito) Bruno argues for this premise, which despite its secondary character with respect to the infinite universe, is given wide attention and established in its major cosmological features. Since Bruno is fully aware that Aristotle’s concept of space must be destroyed for the infinite universe to be built, he begins De l’infinito with an outright assault on the Aristotelian concept of place as outlined in the fourth book of the Physics.5 If place is an accident of bodily substance, and more precisely, if it is the unmoved internal surface of the containing body, it follows that the universe (which for Aristotle is necessarily finite) is nowhere or in no place (in the extreme, it is in itself), since there is no body outside to contain it. Accordingly, as the much quoted sentence in De caelo, I, 9 states, “it is obvious that there is neither place nor void nor time outside the heaven, since it has been demonstrated that there neither is nor can be body there.”6 In addition, since the existing intellectual substances (the unmoved movers of the celestial spheres) and the first of them (God in the monotheistic religions) are incorporeal and unextended, they cannot act as place and limit of the world, this task additionally being unworthy of them.7 Against Aristotle, Bruno introduces the old and well-known thought experiment of the hand stretched out beyond the convex sphere of heaven (in the introductory epistle of De l’infinito the Lucretian flying dart thrown against the “furthest coasts” of the world).8 It is unimaginable that either the hand or the dart would be nowhere, and even “would not exist.”9 As a consequence, beyond the purported limit of our world, there is something, namely space, be it void (as the Stoics affirm) or filled with other worlds (as the Epicureans purport), Bruno notably inclining to the latter option10: what is beyond [this surface]? If the reply is nothing, then I call that void or emptiness. And such a void or emptiness hath no measure and no outer limit, though it hath an inner; and this is harder to imagine than is an infinite or immense universe. For if we insist on a finite

5  For an account of the Aristotelian notions of place and space see Algra’s Chapter 2 in this volume. 6  De caelo, I, 9, 279a, 16–18, in Aristotle 1939. 7  De l’infinito in Bruno 2006, 61–67. See also On the Infinite in Bruno 1968, 251–254. 8  See On the Infinite in Bruno 1968, 231 for the quotation of Lucretius (De rerum natura, II, 968– 983), and 253 for the mention of the hand; De l’infinito in Bruno 2006, 11 and 65. For Lucretius’ version of the thought experiment see Section 3.2.2 of Bakker’s Chapter 3 in this volume. 9  De l’infinito in Bruno 2006, 55 and 11; On the Infinite in Bruno 1968, 253 and 231. 10  For an account of Epicurean and Stoic conceptions of extracosmic void see Section 3.2 of Bakker’s Chapter 3 in this volume.

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universe, we cannot escape the void. And let us now see whether there can be such a space in which is naught.11

Space is, then, unavoidable – a prerequisite for the actual or potential presence of bodies. As it is said in Bruno’s final encomium: “an infinite space is not impossible but is necessary.”12 This necessary space is presented in the initial criticism of the Aristotelian concept as an aptitude or ability to contain bodies,13 that is, as a receptacle (continente, ricetto),14 for which Bruno employs a plurality of names throughout this dialogue, unfortunately sometimes translated into English as the generic term ‘space.’15 Space, as a receptacle able to contain bodies, is not a body; it is incorporeal, but has dimensions. The passage in On the Infinite is worth quoting: “that which is not corporeal nor doth offer sensible resistance is wont, if it hath dimension, to be named Void, since people usually understand as corporeal that which has the property of offering resistance.”16 Space is, then, a (three-dimensional) extension or dimension, non-resistant to the presence or motion of bodies because it is incorporeal. For that reason, Aristotle’s argument against three-dimensional space is null, grounded in the erroneous assumption that three-dimensional extension is an attribute unique to bodies and, as a consequence, such a space filled with a body would violate the axiom of the impenetrability of dimensions.17 For Bruno, then, space (as the ability to contain or as a receptacle) and bodies can coexist, since they belong to different genera of being, sharing the common property of three-dimensionality, bodies being received generously by the spatial womb or grembo as a condition for the possibility of bodily presence. The quoted passage clearly shows that, in the  On the Infinite in Bruno 1968, 254; De l’infinito in Bruno 2006, 67–69. For the identification of both positions with those of the Stoics and Epicureans see De l’infinito in Bruno 2006, 115; On the Infinite in Bruno 1968, 272. For the greater plausibility of the filled space see De l’infinito in Bruno 2006, 171–173; On the Infinite in Bruno 1968, 298–299. 12  On the Infinite in Bruno 1968, 377; De l’infinito in Bruno 2006, 369. 13  On the Infinite in Bruno 1968, 254–255; De l’infinito in Bruno 2006, 69: “aptitudine di contenere;” 71: “attitudine alla recepzione di corpo.” This description corresponds closely to the Stoic definition of place. See Algra 1995, 263–281; Alessandrelli 2014. 14  De l’infinito in Bruno 2006, 125: “uno infinito, immobile, infigurato, spaciosissimo continente de innumerabili mobili;” 181: “tutto è un ricetto generale.” For the later Latin works see Acrotismus Camoeracensis in Bruno 1879, 123, art. xxviii: “[Spacium] est igitur receptaculum corporum magnitudinem habentium;” De immenso, IV, 1, in Bruno 1879, 78: “Spacium sane nullum est corpus, sed corporis receptaculum.” 15  Grembo, seno (“infinito spacioso seno,” De l’infinito in Bruno 2006, 175; “infinitely spacious bosom,” On the Infinite in Bruno 1968, 300; campo (“generale e spacioso campo,” De l’infinito in Bruno 2006, 183; “the vastness of universal space,” On the Infinite in Bruno 1968, 302; inane, vuoto, vacuo, etere, cielo (“l’infinito spacio, cioé, il cielo continente e pervagato da quelli [gli astri],” De l’infinito in Bruno 2006, 355; “the infinite space, the heaven comprehending all, traversed by all,” On the Infinite in Bruno 1968, 370. 16  On the Infinite in Bruno 1968, 273, translation modified; De l’infinito in Bruno 2006, 115: “ciò che non è corpo che resiste sensibilmente, tutto suole esser chiamato (se ha dimensione) vacuo: atteso che comunmente non apprendeno l’esser corpo se non con la proprietà di resistenza.” 17  De l’infinito in Bruno 2006, 113: “incompossibilità delle dimensioni di uno et un altro.” 11

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Italian dialogue, Bruno is already acquainted with John Philoponus’ anti-­Aristotelian concept of space, which he will adopt, with explicit reference to the Greek commentator, in the famous chapter of De immenso, brilliantly analyzed by Edward Grant: “Space is a certain physical quantity, continuous and three-dimensional, in which the magnitude of bodies is comprehended.”18 This follows from the fact that bodily dimensions require the previous presence of the dimensional container: “for where there are no dimensions of a body, there shall be the dimensions of space, in which bodily dimensions may be received. Indeed, those [bodily] dimensions can be nowhere without the latter ones.”19 Moreover, many of the attributes of space, indicated and commented by Bruno in the Latin poem after the definition, are already present in the Italian dialogue. Space is the place, but in itself it has no place. The Latin poem says that space is “illocabile” and the Italian dialogue that “this space cannot be conceived as existing within another space.”20 Most importantly, as has often been highlighted as the most significant characteristic of Bruno’s concept, space is identical in all its infinite extension; it is homogeneous or indifferent. Some statements may be cited in support of this interpretation: “the indifference throughout the vast space of the universe;”21  De immenso, I, 8, in Bruno 1879, 231: “Est ergo spacium, quantitas quaedam continua physica triplici dimensione constans, in qua corporum magnitudo capiatur.” See Grant 1981, 186. On this page Philoponus is praised as the commentator who more audaciously (“audactius”) has attacked the Aristotelian concept of place. Bruno may have known Philoponus’ criticism and his novel concept of space directly, since Philoponus’ Commentary on Aristotle’s Physics (containing his “Corollaries on Place and Void”) had been published in Latin translation in eight editions between 1539 and 1581. But he may also have found a sympathetic presentation of Philoponus’ views in Gianfrancesco Pico della Mirandola’s Examen vanitatis doctrinae gentium et veritatis Christianae disciplinae, printed in Basle in 1573, and demonstrably known to him. Philoponus, however, considered that space was finite and coextensive with the finite spherical world of the cosmological tradition; see Philoponus 1991. On Philoponus see Duhem 1913–1958, vol. I, 313–320, Sedley 1987; and Section 2.3 of Algra’s Chapter 2 in this volume. For Gianfrancesco Pico’s presentation of Philoponus’ concept see Schmitt 1967, 138–159. Pico was also the first to present in Latin the concept of space of the Hebrew Hasdai Crescas, whose affinity with Bruno was even stronger, since he stated the reality, beyond the outermost sphere of the world, of an infinite void space, in which God’s omnipotence could have created a plurality of other worlds. On Crescas’ views see Schmitt 1967 (index), and Wolfson 1929. According to Wolfson 1929, 36, “knowing as we do that a countryman of Bruno, Gianfrancesco Pico della Mirandola, similarly separated from Crescas in time and space and language, obtained a knowledge of Crescas through some unknown Jewish intermediary, the possibility of a similar intermediary in the case of Bruno is not to be excluded.” We think, however, that such a possibility is rather remote. Since Pico’s comments on Crescas’ views are rather scarce, we are inclined to consider the striking similarities between Bruno and Crescas an effect of their common knowledge of the Stoic conception of extracosmic infinite void space, and of the assertion in Christian thought after 1279 of the possibility (by God’s absolute power) of a plurality of worlds. 19  De immenso, I, 8, in Bruno 1879, 231: “ubi quippe nullius corporis sunt dimensiones, spacii dimensiones esse decebit, in quibus illae recipi possint. Quinimo illae dimensiones nusquam absque dimensionibus istis esse possunt.” 20  On the Infinite in Bruno 1968, 373; De l’infinito in Bruno 2006, 361. 21  On the Infinite in Bruno 1968, 361; De l’infinito in Bruno 2006, 331: “la indifferenza de l’ampio spacio dell’ universo.” 18

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“since in the immensity of space there is no distinction of upper, lower, right-hand, left-hand, forward or backward;”22 “all the rest of space, which is identical in natural character with our own.”23 There is no difference, therefore, between the region of universal space containing our world and every other region. Space is indifferent with respect to particular matters, elements or bodies, and this implies that elements and composite bodies have no natural places to which they naturally move by virtue of this reciprocal implication of natural places and elementary composition. True, space has an appetite for matter,24 but it is indifferent as to which kind of matter occupies it. This point allows us to perceive the cogency of Bruno’s transition from infinite homogeneous space to the infinitely filled universe. Indifference of space, together with the principle of sufficient reason,25 allows Bruno to deduce from the occupation of a particular portion of space (indifferent to space as a whole) by a world (our world) the convenience and even necessity of infinite space filled with an infinite plurality of worlds (in the sense of planetary systems): “For just as it would be ill were this our space not filled, that is, were our world not to exist, then, since the spaces are indistinguishable, it would be no less ill if the whole of space were not filled. Thus we see that the universe is of infinite size and the worlds therein without number.”26 It is true that Bruno must accept that homogeneity and indifference, along with the principle of sufficient reason, may only allow us to state the possibility and convenience of the existence of infinite worlds in infinite space once the existence of one world in this space is given, but not an absolute necessity of their existence: I declare that which I cannot deny, namely, that within infinite space either there may be an infinity of worlds similar to our own; or that this universe may have extended its capacity in order to contain many bodies such as those we name stars; or again that, whether these worlds be similar or dissimilar to one another, it may with no less reason be well that one than that another should exist. For the existence of one is no less reasonable than that of another; and the existence of many no less so than of one or of the other; and the existence of an infinity of them no less so than the existence of a large number. Wherefore, even as  On the Infinite in Bruno 1968, 362; De l’infinito in Bruno 2006, 333: “nell’immenso spacio non è differenza di alto, basso, destro, sinistro, avanti et addietro.” By contrast, Epicurean space admits an ‘upwards’ and ‘downwards;’ see Epicurus, Letter to Herodotus, 60, and Konstan 1972. 23  On the Infinite in Bruno 1968, 363; De l’infinito in Bruno 2006, 337. 24  De l’infinito in Bruno 2006, 113: “Ora se la materia ha il suo appetito, il quale non deve essere in vano, perché tal appetito è della natura e procede da l’ordine della prima natura, bisogna che il loco, il spacio, l’inane abbiano cotale appetito;” On the Infinite in Bruno 1968, 271. It is important to note that, if space is indifferent to the kind of matter occupying it, it is not indifferent with respect to being occupied or empty, since space desires matter. This point separates Bruno from the triumphant representation of space and matter in the scientific revolution. More in accordance with ancient atomism and Epicureanism, authors like Galileo, Gassendi or Newton will maintain that space is indifferent to being void or filled. For this point of contrast with Lucretius see Fantechi 2006, 579–581. The cause of this divergence is precisely Bruno’s concept of the relation of void space to God, as will be shown in what follows. 25  Cf. Koyré 1957, 44 and 46. 26  On the Infinite in Bruno 1968, 256; De l’infinito in Bruno 2006, 73. 22

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the abolition and nonexistence of this world would be an evil, so would it be of innumerable others.27

However, the fact that for Bruno homogeneous space desires matter indifferently is a powerful argument in favor of the plenitude of space. This trend of thought is, in addition, warranted and brought to fulfillment by two other principles governing Bruno’s thought: the first is the so-called ‘principle of plenitude,’ derived (as sufficiently shown by Arthur O. Lovejoy)28 from the Platonic tradition; the second is Bruno’s rejection of the scholastic distinction between the absolute and ordained power of God (potentia absoluta et ordinata).29 If this distinction had been introduced in the twelfth and thirteenth centuries in order to preserve God’s freedom and the contingency of the creation, its rejection enables Bruno to affirm the necessary derivation of the universe from God’s power, while still not abolishing God’s freedom. De l’infinito makes clear the necessary character of God’s production, but it is in De immenso, where Bruno, after presenting his concept of space with all its attributes, establishes the series of ‘common principles’ (principia communia) granting the absolute simplicity and unity of God’s essence30 and the coincidence of necessity and freedom in His production.31 Accordingly, since all His attributes are coextensive and one, God acts in His one and unique production (the universe) with all His infinite power; and as a result the universe is infinite, eternal, and the infinite space totally filled with informed matter.32 Any presence of empty, or void, should contradict the principle of plenitude, according to which “the Good is diffusive of itself” (bonum est diffusivum sui),33 since it would indicate that infinite divine  On the Infinite in Bruno 1968, 259; De l’infinito in Bruno 2006, 81–83.  Lovejoy 1936, 116–124; cf. also Koyré 1957, 42. Regarding, however, the derivation of this principle also from Aristotle, see Del Prete 2003. Even Epicurus and Lucretius already subscribed to a version of the ‘principle of plenitude’ without giving up the necessity of void; see e.g. Lucretius, De rerum natura, II, 1048–1089. 29  For the history of this distinction see Courtenay 1990. On its rejection by Bruno see Granada 1994, 2002. 30  De immenso, I, 11, in Bruno 1879, 242, principle IV: “Deus est simplicissima essentia, in qua nulla compositio potest esse, vel diversitas intrinsece.” 31  Ibid., 243, principle IX: “Necessitas et libertas sunt unum, unde non est formidandum quod, cum [Deus] agat necessitate naturae, non libere agat: sed potius immo omnino non libere ageret, aliter agendo, quam necessitas et natura, imo naturae necessitas requirit.” Accordingly, the adversary should prove the (impossible) assertion that “necessity in God is different from freedom” (“probandum est adversario: [...] VI. necessitatem in Deo aliud esse a libertate,” ibid., 244). 32  De l’infinito in Bruno 2006, 89: “Qual raggione vuole che vogliamo credere che l’agente che può fare un buono infinito lo fa finito? E se lo fa finito, perché doviamo noi credere che possa farlo infinito, essendo in lui il possere et il fare tutto uno? Perché è immutabile, non ha contingenzia nell’operazione, né nella efficacia, ma da determinata e certa efficacia depende determinato e certo effetto inmutabilmente;” On the Infinite in Bruno 1968, 262: “What argument would persuade us that the Agent capable of creating infinite good should have created it finite? And if he hath created it finite, why should we believe that the Agent could have created it infinite, since power and action are in him but one? For he is immutable, there is no contingency in his action or in his power, but from determined and assured power there immutably do follow determined and assured results.” 33  See Dionysius the Areopagite, On the Divine Names, chap. 4, §20; Saint Thomas Aquinas, Summa theologiae, I, 27, art. 5, obj. 2. Cf. Lovejoy 1936, 49 f. 27 28

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g­ oodness ‘envies being’ (“invidia l’essere”), contrary to Plato’s assertion in Timaios 29e that God, according to the Latin translation by Ficinus (who employs the same term  – invidia  – as Chalcidius, the first Latin interpreter, to translate the Greek φθόνος), “bonus erat. Bonus autem nulla unquam aliqua de re invidia tangitur. Ergo cum livor ab eo alienissimus esset, omnia sibi quantum fieri poterant simillima fieri voluit.”34 Void would also contradict the coextension and identity of power and will in God, since it would entail either that God’s power is finite, or that He does not want to produce all He can produce. At the same time, and because production is, like power and will, an essential attribute of God, the infinite universe is a necessary and free production; and the same applies to infinite and homogeneous space, since it is a necessary condition for the existence of matter and the universe. Moreover, the infinite and eternal universe is not external to God (a creatio ad extra marked by contingency); rather, it has the properties of necessity and infinity governing the generatio ad  intra, that is, the derivation of the Son and the Holy Spirit in the trinitary process. And after the dialogue De la causa, principio et uno has interpreted the (divine) intellect as the most eminent faculty of the universal soul, and the Holy Spirit as this universal soul which is the form of the universe, it can be argued, with Hans Blumenberg, that Bruno (in accordance with his rigorously unitary concept of God) has identified the generatio ad intra with the production of the infinite and necessary universe, and conceived it as an internal process in God. As a result, the universe becomes the Verbum of God and His self-production and explication.35 Infinite void space is therefore filled everywhere with informed matter. First, and immediately, with liquid and continuous pure air, also called ether and even spiritus inasmuch as it penetrates us36; secondly, with stars (suns and planets forming  “He was good; and in the good no jealousy in any matter can ever arise. So, being without jealousy, he desired that all things should come as near as possible to being like himself,” as translated in Cornford 1935, 33. Unfortunately, Cornford’s translation misses the connection with the Latin tradition, preserved instead by Bruno with his terms invidioso, invidia (De l’infinito in Bruno 2006, 85 and 87). The same happens in Singer’s translation; see On the Infinite in Bruno 1968, 260: “remain grudgingly sterile;” 262: “Omnipotence doth not grudge being.” 35  See Blumenberg 1976, 127: “Ein Gott, der realisieren muss, was er kann, bringt sich selbst noch einmal hervor. Zeugung und Schöpfung fallen zusammen. Wo die Schöpfung die hervorbringende Macht Gottes erschöpft, kann für den trinitarischen Prozess kein Raum mehr sein. Wenn aber, und das ist der nächste Schritt, die absolute Selbstverwirklichung der göttlichen Allmacht ‘Welt’ ist und nicht ‘Person,’ dann muss der Charakter der Personalität auch schon dem sich selbst reproduzierenden Grunde abgesprochen werden;” 179, n148: “Bruno hat eine der dunkelsten Unterscheidungen der Dogmengeschichte nicht mitgemacht, die von generatio und creatio: die Hervorbringung des Gottessohnes als ‘Zeugung,’ die Hervorbringung der Welt als ‘Schöpfung.’ Er hält an der cusanischen Grundidee fest, dass das absolute ‘Können’ sich in dem Hervorgehen der aequalitas aus der unitas manifestieren müsse – aber die Stelle der aequalitas wird bei Bruno nicht durch den Sohn, sondern durch das unendliche Universum besetzt.” On the trinitary issue in Bruno see also Fantechi 2007; Scapparone 2008. 36  See De l’infinito in Bruno 2006, 357, 117 and 177; On the Infinite in Bruno 1968, 372, 273 and 300. The fact that the air internal to animals is called “spirto” shows the influence of Stoicism. The denomination “ether” for this fluid, inasmuch as it is pure and fills the space where the stars dwell 34

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p­ lanetary systems or, in Bruno’s terminology, synodi ex mundis).37 And ether (as well as eterea regione, etereo corpo, etereo seno) is the term Bruno usually employs for space inasmuch as it really offers itself to observation, whereas vuoto or vacuo refers to the space when conceived as the pure, absolute (a priori, we could say in Kantian terms) dimensional receptacle, not merely formal, but really existing as a necessary condition for matter. Indeed, ether (or pure air) can be rightly termed space, since it possesses the properties of space: the ability to be traversed38 and absence of resistance to the motion of heavenly bodies (the ether “is without tenacity or resistance, more rare and subtle than the air we breathe”).39 Nonetheless, it is wrong, pace Edward Grant, to affirm that “because the ether seems able to perform all the functions of void, the latter appears as superfluous.”40 Just as matter and form (soul), though coinciding in the one and single substance, can and must be conceived separately as the two principles of substance, void is also a principle conceptually prior, which deserves to be regarded and understood independently of the universe to which it offers a place or location, despite the fact that void space never exists and appears separately. Some weeks before the publication of De l’infinito, Bruno had affirmed in De la causa that intellect, form or universal soul and matter are aspects or expressions of God. What can we say about space? Is it also an attribute or aspect of God? Or is and through which they move, manifests a remnant of the ancient wisdom preceding Aristotle, since the true meaning of this term is “percurribile:” “in quanto poi che è puro e non si fa parte di composto, ma luogo e continente per cui quello si muove e discorre, si noma propriamente ‘etere,’ che dal corso [Greek verb θεῖν] prende denominazione,” ibid., 357. Cf. also De immenso in Bruno 1879, IV, chap. 14, 78–79, where a second etymology [ether, from Greek aithein, to burn] is also adduced: “Aether vero est idem quod coelum, inane, spacium absolutum [...] qui omnia corpora circumplectitur infinitus. Quia maiori ex parte ardet. [...] Aether enim nullius qualitatis, virtutis, vel operationis, vel passionis esse potest subiectum; et sic coelum dicimus vere inalterabile impassibile ingenerabile incorruptibile immobile; quia in eo debent moveri, et currere astra. Hoc totum de spacio et vacui dicimus: hoc est coelum et regia deorum (id est astrorum) ab initio philosophantibus et vulgo cognita.” As pure air, this fluid is identified with the biblical firmamentum and with the image or symbol of Atlas in ancient pagan wisdom. See Acrotismus Camoeracensis in Bruno 1879, 165 (art. lxv): “Ipse [pure air] est figuratum firmamentum per vectorem Atlantem, omnia sine labore sustinentem;” cf. the Italian translation: Acrotismo in Bruno 2009, 125. For the first etymology of ether see Plato, Cratylus, 410b 6–7; Aristotle, De caelo, in Aristotle 1939, 270b 22–23. For the second etymology see [Arist.] De mundo, 392a, 5–6. 37  On this concept see Granada 2010, 2013. In De immenso, I, 3, in Bruno 1879, 213, Bruno presents the concept of synodus ex mundis as secretly transmitted by the Homeric myth of the banquet of the Olympic Gods (suns) among the black Ethiopians (planets). This is a second point of ancient wisdom transmitted to us in the veiled form of etymology and myth concerning the principles and true structure of the universe. 38  De l’infinito in Bruno 2006, 249: “il spacio è tale, per quale possano discorrere tanti astri;” 355: “l’infinito spacio, cioè il cielo continente e pervagato da quelli [the stars].” De immenso, IV, 14, in Bruno 1879, 79: “spacium dicitur aether quia decurritur” [space is called ether because it is run through]. 39  On the Infinite in Bruno 1968, 362; De l’infinito in Bruno 2006, 333. Cf. On the Infinite in Bruno 1968, 340: “so subtle and liquid a body as the air which resisted naught;” De l’infinito in Bruno 2006, 279: “sì liquido e sottil corpo, che non resiste al tutto.” 40  Grant 1981, 189.

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Edward Grant right when he concludes that “the consequences of Bruno’s description of space and the properties he assigned it lead inevitably to an infinite space that is coeternal with but wholly independent of God [...]. It does seem that the space God occupied was not of His own making”?41 This very significant issue and the problem of the relationship between God and infinite space will be our primary concern in what follows.

8.3  The Relation Between God and Space De l’infinito already presents, in 1584, some ambiguous passages in which the subject is often assumed to be the infinite corporeal universe. They can arguably be referred to infinite space as well, with the implication that space is not ontologically prior to or independent from God but, like matter and form, an expression or aspect of God. In the fifth dialogue, when Albertino asks Bruno to proceed with his mission of enlightenment, he says: “Proceed to make known to us [...] how an infinite space is not impossible, but is necessary; how such an infinite effect beseemeth the infinite cause.”42 This infinite effect, is it the universe or the space containing it? It is difficult to say, and possibly both answers are correct. In this case, if the clause refers to space, then it is explicitly declared an effect or production of God, not something existing per se, independently from God. On the contrary, if it refers to the universe as an effect of the divine cause, the fact that space is not an effect of God does not entail, as Grant suggests, that space is independent from God, but (as will be argued later) rather that space is an aspect or expression of God himself. In addition, in the first dialogue, when the infinity of space is discussed for the first time, Bruno affirms: “Why should not that infinite which is implicit in the utterly simple and individual Prime Origin rather become explicit in his own infinite and boundless image able to contain innumerable worlds, than become explicit within such narrow bounds?”43 Even if we take the universe as the subject rather than space, since the universe is usually named the explicatio and simulacrum of God, it could be argued that properly “capacissimo” is not the universe, but the  Grant 1981, 191.  On the Infinite in Bruno 1968, 377; De l’infinito in Bruno 2006, 369: “Séguita a farne conoscere [...] come non è impossibile ma necessario un infinito spacio; come convegna tal infinito effetto all’infinita causa.” 43  On the Infinite in Bruno 1968, 257; De l’infinito in Bruno 2006, 75: “Che repugna che l’infinito implicato nel simplicissimo et individuo primo principio [i.e. God as the One], non venga esplicato più tosto in questo suo simulacro infinito et interminato, capacissimo di innumerabili mondi, che venga esplicato in sì anguste margini [...]?” And on the next page, the passage “bisogna che di un inaccesso volto divino, sia uno infinito simulacro nel quale come infiniti membri poi si trovino mondi innumerabili quali sono gli altri [mondi],” 77 – the image (simulacro) of the inaccessible deity is not necessarily the space, but more probably the infinite universe in it with its infinite worlds. 41 42

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space as void receptacle, the universe being contained in it and consisting in innumerable worlds.44 Thus, space is (like the universe) the explicatio or unfolding of “the utterly simple and individual Prime Origin,” far removed from the ontological independence attributed to it by Grant. Finally, with the same ambiguity we read in the second dialogue: “even as there is in truth one infinite and utterly simple individual entity, so also there is an immense dimensional infinite within that other, and within which is that other, in the same fashion as he is within the all and the all is within him.”45 The dimensional infinite is the universe, but it is also the infinite dimensional space containing both the universe and God himself inasmuch as the universe is the explicatio, unfolding or expansion of God, that is, the external side of the one infinite substance. A beautiful passage from De immenso explicitly states that infinite space is God’s abode, with clear biblical echoes indicating that we are confronted with a doctrinal point deriving (like the synodi ex mundis, the firmamentum or Atlas, and the ether) from ancient wisdom: Space is called ether because it is run through. There are as many heavens as heavenly bodies, if we understand by heaven the space contiguous to and encompassing every heavenly body, just as the heaven of the Earth is called not only the space where the Earth is placed, but also so much space that surrounds it, as distinct from the space that surrounds the Moon and other worldly bodies around us. The heaven of heaven is the space of one system in which this sun is placed with its planets. The heaven of heavens is the greatest and immense space, which is also called ether because it can be entirely run through and all [stars] burn through it entirely [...]. As a consequence, the seat of the blessed are the heavenly bodies, the seat of the gods is the ether or heaven (I call the heavenly bodies gods in a second sense). The seat of God is, in fact, the universe in its entirety and in every part, the immense heaven, the void space whose plenitude [He] is, the father of the light filling the darkness, ineffable.46  Cf. De l’infinito in Bruno 2006, 77: “per la continenza di questi innumerabili si richiede un spacio infinito;” On the Infinite in Bruno 1968, 257: “to contain the innumerable bodies there is needed an infinite space.” 45  On the Infinite in Bruno 1968, 270 (we have modified the translation); De l’infinito in Bruno 2006, 111: “come veramente è uno individuo infinito simplicissimo, cossì sia uno amplissimo dimensionale infinito il quale sia in quello, e nel quale sia quello, al modo con cui lui è nel tutto, et il tutto è in lui.” 46  De immenso, IV, 14, in Bruno 1879, 79–80: “Spacium dicitur aether quia decurritur. Tot sunt caeli quot astra, si caelum intelligamus contiguum et circumstans configuratum uniuscuiusque spacium, ut caelum Telluris dicitur non solum spacium in quo est, sed et quantum spacii perambit ipsum distinctum a spacio perambiente Lunam, et alia (quae circa sunt) corpora mundana. Caelum caeli est spacium unius synodi sicut in quo hic sol est cum suis planetis. Caelum caelorum et maximum et immensum spacium; quod et aether dicitur, quia totum est percurribile, et quia in toto maxime flagrant omnia. [...] Sedes ergo beatorum sunt astra: sedes deorum est aether seu caelum: astra quippe Deos secunda ratione dico. Sedes vero Dei est universum ubique totum immensum caelum, vacuum spacium cuius est plenitudo; pater lucis comprehendentis tenebras, ineffabilis,” (italics are ours). Regarding the biblical terms (coelum, coelum coeli, coelum coelorum) see Pépin 1953. Bruno, for obvious reasons, prefers the singular coelum coelorum (Nehemias 9:6) to the more frequent coeli coelorum, besides interpreting coelum coeli and coelum coelorum not as incorporeal and intelligible regions and entities, but as more or less extended regions in the unique infinite space and corporeal universe. 44

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Accordingly, the heaven (coelum) is the space of a single star or heavenly body (e.g. the earth) through which it moves; the heaven of heaven (coelum coeli) is the space of a synodus or planetary system; the heaven of heavens (coelum coelorum) is the entire infinite space, also called ether (as the first configuration of matter filling it) and filled also by God as totus in toto (all in all and in every part of the all).47 God thus fills space and the universe that fills space. This parallelism between space as vacuum and space as ether, heaven, and ultimately universe, in the relation to God is easy to understand. It is, indeed, like the parallelism between (void) space and matter. Though they are different, as void receptacle and substantial principle contained in it and immediately filling it, they are strongly related, as shown by the Platonic concept of χώρα in the Timaeus (49a, 51a–b, 52 a–b), in which space and matter mingle or coincide without being identical. Bruno twice mentions in De l’infinito the Platonic confluence of space and matter approvingly: “this world, called by the Platonists matter;”48 “Space and the void, if not identical with matter, have a resemblance thereto, as it would seem is sometimes maintained perhaps not without reason, by Plato and by all those who define position as a certain space.”49 Resemblance is not identity, and for that reason Aristotle was wrong when he criticized Plato in Physics (IV, 2, 209b 11–13) for simply identifying space and matter. As the Acrotismus stated 4 years later, “Plato could reasonably have said that matter is a certain receptacle and that place is a certain receptacle. On that account, there was no place for slander, so that, in accordance with Aristotle’s censorship, the receptacle was for him [Plato] the same as matter and matter the same as receptacle.”50 As Bruno explains, the reason for the confusion is that both matter and space are receptacles, but of a different order: matter being an indifferent receptacle of forms, and space (which is “non formabile,” according to De immenso)51 being an indifferent receptacle, first of matter and secondarily of extended bodies, besides also being “sedes Dei,” that is, God’s abode. However, inasmuch as void or absolute space never presents itself to observation, but always appears filled by matter, we can understand how De l’infinito concedes, in the passage quoted above, that beyond “resemblance,” perhaps they are the same thing (“se pur [spacio] non è la materia  De l’infinito in Bruno 2006, 87: “dico Dio ‘totalmente infinito’ perché tutto lui è in tutto il mondo, et in ciascuna sua parte infinitamente e totalmente;” On the Infinite in Bruno 1968, 261: “I say that God is all-comprehensive infinity because the whole of him pervadeth the whole world and every part thereof comprehensively and to infinity.” 48  On the Infinite in Bruno 1968, 254; De l’infinito in Bruno 2006, 69: “[il mondo] da Platonici è detto materia.” 49  On the Infinite in Bruno 1968, 271; De l’infinito in Bruno 2006, 113: “il luogo, spacio et inane ha similitudine con la materia, se pur non è la materia istessa: come forse non senza caggione tal volta par che voglia Platone, e tutti quelli che definiscono il luogo come certo spacio.” 50  Our translation. Cf. Acrotismus Camoeracensis, in Bruno 1879, art. xxx, 126–127: “Potuit sane Plato dixisse, materiam esse receptaculum quoddam, et locum quoddam receptaculum esse. Non propterea calumniae locus erat, ut, juxta Aristotelis censuram, receptaculum illi [i.e. Plato] idem fuerit quod materia, et materia idem ac receptaculum.” See also Acrotismo in Bruno 2009, 92–93. 51  De immenso, I, 8, in Bruno 1879, 232 (ninth attribute of space): “non formabile: hoc enim materiam oportet esse seu subiectum et omnino alterabile.” Cf. the comment by Amato in Acrotismo, in Bruno 2009, 92, n6. 47

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istessa”). And this assimilation is reinforced when it is added immediately that space has an appetite for matter, like matter has an appetite for forms.52 Now, if matter is, like form (or soul) and intellect (or efficient cause, “padre e progenitore,” “artefice interno”),53 the unfolding or expansion of God, is it plausible to argue, with Grant, that space is existent per se and independent of God, something coeternal with Him, “who appears to have utilized it merely as the container of His infinite universe” and of Himself, inasmuch as space is His place? If this assumption were true, it would follow that space is prior to God Himself and necessary for God in order to act and display all His infinite power. God would be, therefore, not causa prima et unica, but dependent on space. The implications of Grant’s solution are rather incompatible with the foundations of Bruno’s ontology; moreover, Grant’s conclusion is hardly compatible (if not totally incompatible) with the sixth ‘common principle’ of De immenso, I, 11, according to which God’s will (or God’s essence) is ‘above all things:’ “Consequenter Dei voluntas est super omnia.”54 In order to find a solution and confirm the nature of space as a ‘fifth genus of cause’ (in addition to the four classical causes analyzed in De la causa), and like the four others related to God as His unfolding or explicatio, we must search for evidence in the Acrotismus. In particular, we turn to a contemporary work regrettably unattended by Grant, namely the Lampas triginta statuarum.

8.4  S  pace and God According to the “Lampas Triginta Statuarum” Written initially in 1587 (the date of the manuscript copy preserved in the Stadtbibliothek Augsburg), but subject to profound revision in the following years, as witnessed by the copy written in 1591 by Bruno’s disciple Hieronymus Besler (preserved in Moscow, in the codex Norov), the Lampas aims to offer a new presentation of Bruno’s ontology. The revision, as shown by the modifications introduced in the later copy, mainly replaces the Neoplatonic character of many initial statements (derived from the sources on which Bruno had relied) with an exposition more in line with the ontology formulated in the Italian dialogue De la causa.55 Perhaps the most salient aspect of this work is the choice of an exposition method that translates the ontological concepts into symbolic images, in imitation (Bruno says) of the method employed by ‘ancient wisdom,’ in order not to veil knowledge, but to grant easier access to it.56 Thus, even if the six primary ontological principles  This point has been rightly emphasized by Fantechi 2006, 582.  De la Causa, dialogue iii, in Bruno 2016, 113–117. 54  De immenso, I, 11, in Bruno 1879, 243. Cf. principles IV and V. 55  On this see the note by Nicoletta Tirinnanzi in Bruno 2000a, xcviii ff. See also Tirinnanzi 2013a, b. Unfortunately, Tirinnanzi pays no attention to the issue of ‘void’ (chaos in Lampas) and limits her examination to the concept of matter (nox). 56  Lampas in Bruno 2000b, 938–940: “Ordo erit procedendi a notioribus nobis sensibilibus et phantasiabilibus ad  intelligibilia et contemplabilia universalia, quae sunt causae et rationes omnium 52 53

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Table 8.1  Superior and inferior triads Superior triad (male)

Inferior triad (female)

Derivation: Father —› Son Pater Intellectus Mens Apollo Plenitudo Fons idearum Chaos Orcus Void Privation Space Desire

Spiritus Lux Nox Matter

(which will be our only concern) admit no visual representation through a figure or statue, because they are essentially infigurable and lack form, they are described in imaginative terms transmitting their indeterminacy and indifference prior to determination through form. These six primordial principles appear in two triads, respectively called ‘inferior’ and ‘superior’ (inferna and superna). These adjectives, though they evoke the cosmological and ontological hierarchy of being and the ensuing superiority of intellect over matter, have no hierarchical import, and are in accordance with the equivalence of the opposite ontological principles established in De la causa. The first, ‘inferior’ triad is that of Chaos, Orcus and Nox, respectively representing the void or space,57 the appetite of void (or passive potency, privation) and matter.58 The second, “superna” triad is that of Pater (Mens, Plenitudo), Intellectus (Apollo universalis, Fons idearum) and Spiritus (Lux).59 In each triad the succession of the second and third with respect to the preceding member is described as one of son and father. Thus, Orcus or Abyss (the appetite in void space) is described as the son of Chaos,60 and Night (or matter) as the daughter of Orcus61; in the other triad, Intellect is the son of father mens, whereas spiritus is described as amor, clearly summoning a derivation from the Christian Trinity, but with obvious cosmological meaning (see Table 8.1)62. particularium: et ideo ab iisdem – tamquam a causis et principiis – facillimo negotio media desumere licebit. [...] [I]taque usum atque formam antiquae philosophiae et priscorum theologorum revocabimus, qui nimirum arcana naturae eiusmodi typis et similitudinibus non tantum velare consueverunt, quantum declarare, explicare, in seriem digerere, et faciliori memoriae retentioni accommodare” (italics are ours). 57  For Chaos as a denomination of void space, Bruno refers to Hesiod (Theogonia, vv. 116–117). The reference is also present in the contemporary Acrotismus; see Acrotismus Camoeracensis, in Bruno 1879, 124 and the Italian translation: Acrotismo in Bruno 2009, 90 (art. 28). Most probably, Bruno owes the reference to Aristotle, whose description of Hesiod’s chaos in Physics, IV, 1, 208b 29–33, he accepts as true against the Stagirite. Thus, Hesiodic chaos is another point of true philosophy present in ancient wisdom. 58  Lampas in Bruno 2000b, 942. 59  Lampas in Bruno 2000b, 1008, 1024 and 1044. 60  Lampas in Bruno 2000b, 958: “Sequitur, tanquam filius patrem, Chaos ipsa Abyssus seu Orcus.” 61  Lampas in Bruno 2000b, 972: “Orci filiam primogenitam Noctem esse intelligimus.” 62  Lampas in Bruno 2000b, 1026: “Hic licet contemplari in patre essentiarum essentiam, in filio omnem pulchritudinem et generandi appetitum, in fulgore ipsum spiritum pervadentem omnia et vivificantem.”

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The sequence from the first to the third step in each triad is not a causal process in time. Every instance is coeternal to the others; e.g., chaos or void is ontologically (or perhaps better, conceptually) prior to matter, but void is initially, or from the beginning, eternally filled with matter, due to the fact that the medium (Orcus as passive potency, privation or infinite desire) instantaneously gives place to infinite matter. In the same way, even if the second and third steps are described as father and son, they are not causal effects of the preceding steps, since they are explicitly said to have no cause. Thus, nox or matter “bears some resemblance to God, inasmuch as it is a cause without cause;”63 likewise, chaos or void space “is not from a cause or caused, but wholly without cause.”64 In my opinion, this means that all the aspects in each triad cannot be interpreted according to a causal process, but as aspects or conceptual moments in a single essence.65 With regard to the relation between both triads, every step in the inferior triad is connected with the equivalent in the superior one, that is: matter or nox is related to spiritus (the universal soul), orcus or privation to intellect (fons idearum, appetitus generandi), and chaos or void space to the father or mens innominabilis. The relation within each pair is presented as that of a married couple. This appears more clearly in the relation between universal soul and matter, whose union (or coitus) produces the series of natural beings constituting the universe.66 It is easy to see that this presentation in the Lampas of the ontological principles and causes of the infinite universe is an expansion of the one previously presented in De la causa: if nox and lux correspond to matter and universal soul as the infinite coextensive material and formal principles or causes of the universe, intellect as “fons idearum,” “activissima efficacia” and “appetitus generandi” in the Lampas corresponds to the intellect as the efficient cause in the Italian dialogue, satisfying as infinite active potency the infinite passive potency, aptitude, privation and desire in Orcus as the son of Chaos. From their union proceeds or results infinite matter informed with the infinite diversity of natural beings in the universe. We are left, then, with the pair Chaos (Void space) and Father (Mens innominabilis, Plenitudo) respectively related as female and male. If we take into account the previously quoted (roughly contemporary) passage from De immenso IV, 14, we find a confirmation of this relation as one of infinite contraries (like matter and form). The passage concludes: “The seat of God is, in fact, the universe in its entirety and in every part, the immense heaven, the void

63  Lampas in Bruno 2000b, 994: “similitudinem quippe habet cum Deo ex hoc quod causa incausata;” 984: “ipsa [nox] causam non habet.” 64  Lampas in Bruno 2000b, 952: “non est a causa seu causatum, sed incausabile prorsus.” 65  For the application of the category of relation to the primordial principles, as well as to the connection between God and the universe, inasmuch as they are reciprocally dependent or mutually implicated, see Del Prete 2016. Del Prete, however, limits her study to the superior triad and to the Trinitary issue, paying no attention to the question of void space and its relation to God. 66  Lampas in Bruno 2000b, 988: “[Matter] est natura seu naturae species, condistincta ab alia natura – quae est lux –, e quorum coitu naturalia generantur;” 994: “in quibus esse distinguitur ab essentia, in his Noctem intueri licet matrem, et lucem patrem.”

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space whose plenitude [He] is, the father of the light filling the darkness, ineffable.”67 Void space (chaos) is the abode of God (of the first element in the superior triad, precisely called Plenitudo, Pater, lux infinita, innominabilis).68 We are, then, confronted with the opposition of two infinite contraries as the ultimate principle and cause of the universe: Father (also called God), and Chaos or Void space. But the first presentation of the Father in Lampas clearly indicates that the three members of each triad are in reality one entity or essence (a tri-unity, so to speak). In the Father “three run together, so that anywhere and everywhere He may be sun, ray and illumination, without any distinction in Him, but unity and identity of all three.”69 The Sun is, of course, the Father, but radius and fulgur (with whom he is identified) are also images or denominations of the intellect and the spirit. Obviously, Bruno has in mind here the Christian Trinity, as is confirmed later in the presentation of intellect: The ancient theologians understand by this center the paternal mind which, when it contemplates itself, produces a certain circle and engenders the first intellect, which they call son. With this conception accomplished, and pleasing itself through the image of its essence, it sends out a brightness, which they call love, that departs from the father when he contemplates himself in the son. Here can be contemplated in the father the essence of essences, in the son all beauty and desire of generation, in the brightness the very same spirit pervading all things and vivifying them.70

There is no need to argue that this Trinity of Father, Son and Spirit has a cosmo-­ ontological dimension, reflecting or consisting of the infinite universe. Generatio ad intra and creation of the universe (creatio ad extra) are one and the same necessary and infinite thing or process. But the same can be said for the opposite triad: void space, privation and matter (or filled space) are also a tri-unity, the same thing or process, related to the other and complementing it, just as the production of the infinite universe is the explication or realization of God, a God containing in Himself (as Nicholas of Cusa, Bruno’s mentor in this matter, had stated), as unity of the contradictories, potency and act or matter and form.

 See n46 above: “Sedes vero Dei est universum ubique totum immensum caelum, vacuum spacium cuius est plenitudo; pater lucis comprehendentis tenebras, ineffabilis.” 68  Lampas in Bruno 2000b, 1008: “De patre, seu mente, seu plenitudine. [...] Typus tamen ipsius est lux infinita.” 69  “Tria concurrunt, ut undique et ubique sit sol, radius et fulgur, ut in eo nulla distinctio sit, sed omnium horum trium unitas et identitas,” ibid. 70  Lampas in Bruno 2000b, 1026: “Antiqui theologi per centrum illud paternam mentem intelligunt, quae – dum se ipsam contemplatur – circulum quendam producit [recall that the circle is defined and produced by its radius], et primum generat intellectum, quem filium appellant; qua conceptione perfecta, in imagine essentiae suae sibi complacens fulgorem emittit, quem amorem appellant, qui a patre seipsum in filio contemplante proficiscitur. Hic licet contemplari in patre essentiarum essentiam, in filio omnem pulchritudinem et generandi appetitum, in fulgore ipsum spiritum pervadentem omnia et vivificantem” (italics are ours). Cf. also Fantechi 2007, 392–396, and 405–406. Unfortunately, Fantechi’s analysis focuses uniquely on the ‘superior’ triad or trinity, leaving aside the ‘inferior’ one of space-matter, structurally and substantially connected with the other. 67

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We therefore arrive at the relation of void space (chaos) to God, the same problem which became such a source of perplexity for Edward Grant, who suggested the solution, wrong in our opinion, that space is not God’s own making, but an eternal principle independent of Him, a principle necessary for God to locate Himself and His infinite universe. Two passages in De la causa can provide a solution to the problem, both terminologically and conceptually. In the third dialogue of this first presentation of Bruno’s mature ontology, when Dicson (Bruno’s disciple) comments on the absoluteness of God and His incomprehensibility by the human intellect, he describes God as being at the same time “sublime light and so profound an abyss.”71 And Bruno, through his mouthpiece Teofilo, confirms that God is, indeed, the coincidence of the contradictories light and darkness (that is, mens and space-­ matter) with a biblical quotation as further testimony of the presence of this doctrinal point in ancient wisdom: The coincidence of this act with the absolute potency has been very plainly described by the divine spirit, when it says, “Yea, the darkness hideth not from thee, but the night shineth as the day: the darkness and the light are both alike to thee.”72

Accordingly, both light and matter (as filled space) belong equally to God or they both coincide in the simple essence of God, who is filled space as well as, or not less than, mind filling it with forms. Later, in the fifth, concluding dialogue, Teofilo comments on the non-unified dualism between the two principles, intellect and matter, according to Aristotelians and Platonists: The philosophical method of the Peripatetics and of many Platonists is to have the multitude of things as middle term, preceded by the pure act at one extremity, and the pure potency [i.e. matter] at the other; similar to other philosophers who affirm metaphorically that the darkness and the light come together in the constitution of innumerable degrees of forms, images, figures and colours.73

And immediately, this parallelism and non-unified correspondence (in which God is the purest act or light, and space-matter the opposite ontological point, the worthless pure potency (or darkness) alien to divinity) is cancelled by summoning the ‘enemies’ of the duality of principles, that is, Bruno’s own concept of God as coincidence of contradictories:

 Cause in Bruno 1998, 68; De la causa in Bruno 2016, 213: “altissima luce e sì profundissimo abisso.” 72  Cause in Bruno 1998, 68; De la causa in Bruno 2016, 213: “La coincidenzia di questo atto con l’assoluta potenza è stata molto apertamente descritta dal spirto divino dove dice: ‘Tenebrae non obscurabuntur a te. Nox sicut dies illuminabitur. Sicut tenebra eius, ita et lumen eius’.” The quote is from Psalms 139:12. 73  Cause in Bruno 1998, 93; De la causa in Bruno 2016, 291: “Con il suo modo di filosofare gli Peripatetici e molti Platonici alla moltitudine de le cose, come al mezzo, fanno procedere il purissimo atto da uno estremo, e la purissima potenza da l’altro. Come vogliono altri per certa metafora convenir le tenebre e la luce alla costituzione di innumerabili gradi di forme, effigie, figure e colori.” 71

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8.5  Conclusion We may conclude, then, with a correction of Edward Grant’s theory. If space is not God’s own making, this does not entail that it is wholly independent of Him.75 Void or Space is God Himself, in the same way that He is the mind-intellect-spirit filling it. This is the true meaning of the expression in De immenso, “void space whose plenitude [God] is” (“vacuum spacium cuius est plenitudo”). God is the space no less than its plenitude, the chaos-abyss-darkness no less than the mind-intellect-­ spirit, because both of these trinities are equivalent as well as one and the same essence. God and the infinite universe are one. According to Bruno, ‘poor Aristotle’s’ error basically lies  in the fact that he remained ‘snared’ by the wrong assumption ‘that contraries cannot concur in the same subject:’ Poor Aristotle was tending to this [the coincidence of contraries in the One] in his thought when he posited privation (to which a certain disposition is joined) as the progenitor, parent and mother of form, but he could not get to it. He failed to attain it because, stopping at the genus of opposition, he remained snared by it in such a way that, […] he did not reach or even perceive the goal. He strayed completely away from it by claiming that contraries cannot actually concur in the same substratum.76

 Cause in Bruno 1998, 93; De la causa in Bruno 2016, 291: “Appresso i quali, che considerano dui principii e dui principi, soccorreno altri nemici et impazienti di poliarchia, e fanno concorrere que’ doi in uno, che medesimamente è abisso e tenebra, chiarezza e luce, oscurità profonda et impenetrabile, luce superna et inaccessibile” (italics are ours). The reference to two ‘princes’ (of light and darkness respectively) clearly alludes to Gnosticism, beyond Platonism and Aristotelianism. The rejection of polyarchy is clearly inspired by Homer’s Iliad, II, 204 (“The rule of many [πολυκοιρανίη] is not good; let there be one ruler”) as quoted by Aristotle in Metaphysics, XII, 1076a 4. This is a further reference by Aristotle to ancient wisdom, which he is unable to follow, contrary to Bruno. As W.D. Ross comments, “Aristotle is not a thoroughgoing monist. He is a monist in the sense that he believes in one supreme ruling principle, God or the primum movens. But God is not for him all-inclusive. The sensible world is thought of as having a matter not made by God,” in Aristotle 1924, II, 405. As Aristotle states in the Physics (II, 7, 198a 22–26), the efficient, formal and final cause “many times come to one” or coincide; cf. infra, n76. 75  Grant 1981, 191. 76  Cause in Bruno 1998, 100; De la causa in Bruno 2016, 315: “A questo [the coincidence of contraries in the One] tendeva con il pensiero il povero Aristotele ponendo la privazione (a cui è congionta certa disposizione) come progenitrice, parente e madre della forma: ma non vi poté aggiungere, non ha possuto arrivarvi; perché fermando il piè nel geno de l’opposizione, rimase inceppato di maniera, che non […] giunse né fissò gli occhi al scopo: dal quale errò a tutta passata, dicendo i contrarii non posser attualmente convenire in soggetto medesimo.” 74

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Aristotle (as well as Plato) transmitted this error to the metaphysical tradition that followed him. This tradition conceived matter as entirely separate from the other three coinciding causes, as we find clearly stated by Maimonides in his Guide of the Perplexed: “One of the opinions of the philosophers, an opinion with which I do not disagree, is that God [...] is the efficient cause, that He is the form, and that He is the end [...] in order to comprise these three causes – that is, the fact that God is the efficient cause of the world, its form, and its end.”77 We can therefore understand why matter was perceived (to speak in the same imagery as Maimonides in his Guide) to be “a strong veil preventing the apprehension of that which is separate from matter as it truly is [...] namely, that we are separated by a veil from God and that He is hidden from us by a heavy cloud, or by darkness.”78 If Spinoza was able to dispel the cloud of matter preventing the knowledge of God precisely by substituting for the false concept of matter the true one of matter-extension as God’s attribute parallel to thought,79 the same, or something very similar, had been done 77  Guide, I, 69, in Maimonides 1963, 167. Cf. the Latin translation: Dux, I, 68, in Maimonides 1520, xxvii verso: “De credibilitate vero ipsorum [philosophorum] et opinione cui ego non contradico, est: quia credunt quod creator est causa eficiens & forma [&] finis: & ideo vocaverunt ipsum causam ut coniungantur in ipso tres causae: & sit ipse factor mundi & forma & finis.” 78  Guide, III, 9, in Maimonides 1963, 436–437. Cf. Dux, III, 10, in Maimonides 1520, fol. lxxv recto: “Materia paries magnus est ante nos: unde non apprehendimus intelligentiam separatam secundum quod est. [...] Propter hoc igitur cum noster intellectus nititur apprehendere Creatorem vel aliquam de intelligentiis separatis, invenit parietem illud magnum dividentem inter ipsum et illa intelligibilia. [...] Ipse vero absconditus est a nobis in nube et caligine.” 79  Ethica, II, 7, scholium, in Spinoza 1925, 46: “substantia cogitans, & substantia extensa una, eademque est substantia, quae jam sub hoc, jam sub illo attributo comprehenditur. Sic etiam modus extensionis, & idea illius modi una, eademque est res, sed duobus modis expressa; quod quidam Hebraeorum quasi per nebulam vidisse videntur, qui scilicet statuunt, Deum, Dei intellectum, resque ab ipso intellectas unum, & idem esse,” (italics are ours). That Spinoza refers to Maimonides is clear from Guide, I, 68, in Maimonides 1963, 163: “You already know that the following dictum of the philosophers with reference to God [...] is generally admitted: the dictum being that He is the intellect as well as the intellectually cognizing subject and the intellectually cognized object, and that those three notions form in Him [...] one single notion in which there is no multiplicity” [Dux, I, 67, in Maimonides 1520, xxvii recto: “Iam scis verbum manifestum quod philosophi dixerunt de Creatore, quod ipse est intellectus & intelligens & intellectum: & quod ista tria sunt unum in Creatore: & non est ibi multitudo”]. The ultimate philosophical source is, obviously, Aristotle, Metaphysics, XII, 9, 1074b 33–35 (“Therefore it must be itself that thought thinks (since it is the most excellent of things), and its thinking is a thinking on thinking,” Aristotle 1985, vol. 2) through the interpretation of Themistius in his Paraphrasis of Metaphysics Book Lambda. See Pines 1996, Harvey 1981; Fraenkel 2006. Interestingly, near the end of eighteenth century Germany, Salomon Maimon (1751–1800) would use, in Give’at ha-Moreh (his second commentary on the Guide of the Perplexed), Friedrich Heinrich Jacobi’s partial German translation of Bruno’s De la causa for arguing, without mentioning Spinoza, that Maimonides should have conceived God as material cause too, and accordingly as extended. See Maimon 1999, 98–100 and 261–268, especially at 261: “comparé à toutes les autres causes, Dieu est la cause ultime. Car si nous posons que Dieu qu’il soit exalté, est la forme et la fin sans qu’il soit la cause matérielle, il nous faudra envisager l’existence d’une matière éternelle, c’est-à-dire non causée. Or ceci contredirait au concept de Dieu, qu’il soit exalté, lui qui est la cause universelle de tous les existants. [...] Dieu, qu’il soit exalté, est, de tous les points de vue, la cause ultime. Eu égard à la complexité de la question, j’ai jugé bon de reproduire ici les propos du philosophe italien Jordan Bruno de Nola tirés de son livre sur la cause.”

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previously by Bruno when he dispelled that cloud or veil through his unitary concept of God as coincidence of potency with act, and of void, privation and space with mind, intellect and soul; and when he conceived infinite space as being God no less than mind is God, that is, as being one of the two opposites coinciding in God’s unity. In his splendid and provoking Much Ado About Nothing, Edward Grant summarized the transformations in the ideas on space in the early modern period, saying that “from the introduction of the Greek concept of a separate, infinite, three-­ dimensional void space in the sixteenth century to Spinoza’s Ethics in 1677, approximately 150 years, space had become indistinguishable from God Himself. Spinoza took the final step and conflated God, extension, matter, and space as one infinite, indivisible substance.” Finally, Grant added: “One could go no further and few, if any, would go as far.”80 I would dare to suggest that Bruno had already and voluntarily gone as far.

References Alessandrelli, Michele. 2014. Aspects and Problems of Chrysippus’ Conception of Space. In Space in Hellenistic Philosophy, ed. Graziano Ranocchia, Christoph Helmig, and Christoph Horn, 53–67. Berlin: De Gruyter. Algra, Keimpe. 1995. Concepts of Space in Greek Thought. Leiden: Brill. Amato, Barbara. 2006. Spazio. In Enciclopedia Bruniana e Campanelliana, ed. Eugenio Canone and Germana Ernst, vol. I, 151–165. Pisa/Rome: Istituti Editoriali e Poligrafici Internazionali. Aristotle. 1924. Aristotle’s Metaphysics, a Revised Text with Introduction and Commentary, ed. and trans. William D. Ross. Oxford: Clarendon Press. ———. 1939. On the Heavens  (Loeb Classical Library 338), trans. William K.C.  Guthrie. Cambridge, MA: Harvard University Press. ———. 1985. The complete works of Aristotle, ed. Jonathan Barnes, vol. 2. Princeton: Princeton University Press. Blumenberg, Hans. 1976. Aspekte der Epochenschwelle: Cusaner und Nolaner. Frankfurt: Suhrkamp. Bruno, Giordano. 1879. Opera latine conscripta, vol. I, 1–2, ed. Francesco Fiorentino. Naples/ Florence: Morano/Le Monnier. ———. 1968. On the Infinite Universe and Worlds. In Dorothea Waley Singer. Giordano Bruno: His Life and Thought, with Annotated Translation of His Work On the Infinite Universe and Worlds. New York: Greenwood Press. ———. 1998. Cause, Principle and Unity, ed. and trans. Robert De Lucca. Cambridge: Cambridge University Press. ———. 2000a. Opere magiche, ed. Simonetta Bassi, Elisabetta Scapparone, and Nicoletta Tirinnanzi. Milan: Adelphi. ———. 2000b. Lampas triginta statuarum. In Bruno 2000a. ———. 2006. De l’infinito. In Opere complete/Oeuvres complètes, vol. IV: De l’infinito, universo e mondi, ed. Giovanni Aquilecchia, 2nd ed. Paris: Les Belles Lettres. ———. 2009. Acrotismo Camoeracense: Le spiegazioni degli articoli di fisica contro i peripatetici, ed. Barbara Amato. Pisa/Rome: Fabrizio Serra Editore. ———. 2016. De la causa. In Opere Complete/Oeuvres Complètes, vol. III: De la causa, principio et uno, ed. Giovanni Aquilecchia, 2nd ed. Paris: Les Belles Lettres. 80

 Grant 1981, 229.

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Cornford, Francis Macdonald. 1935. Plato’s Cosmology: The Timaeus  of Plato. London: Routledge. Courtenay, William J. 1990. Capacity and Volition: A History of the Distinction of Absolute and Ordained Power. Bergamo: Pier Luigi Lubrina. Del Prete, Antonella. 2003. L’ “attiva potenza dell’efficiente” et l’univers infini: Giordano Bruno à propos de l’oisiveté de Dieu. In Mondes, formes et société selon Giordano Bruno, ed. Tristan Dagron and Hélène Védrine, 113–131. Paris: Vrin. ———. 2016. La relation entre Dieu et l’univers chez Giordano Bruno. In Giordano Bruno: Une philosophie des liens et de la relation, ed. Antonella Del Prete and Thomas Bern, 19–34. Brussels: Éditions de l’Université de Bruxelles. Duhem, Pierre. 1913–1958. Le système du monde. Paris: Hermann. Fantechi, Elisa. 2006. Tra Aristotele e Lucrezio: La concezione dello spazio nella teoria cosmologica di Giordano Bruno. Rinascimento, s. II, 46: 557–583. ———. 2007. La posizione sulla Trinità e la riflessione metafisica di Bruno. In Favole, metafore, storie: Seminario su Giordano Bruno, ed. Olivia Catanorchi and Diego Pirillo, 387–406. Pisa: Edizioni della Normale. ———. 2014a. Spacio. In Giordano Bruno: Parole, concetti, immagini, ed. Michele Ciliberto, 1833–1836. Pisa: Istituto Nazionale di Studi sul Rinascimento-Edizioni della Normale. ———. 2014b. Vacuo. In Giordano Bruno: Parole, concetti, immagini, ed. Michele Ciliberto, 2013–2016. Pisa: Istituto Nazionale di Studi sul Rinascimento-Edizioni della Normale. Fraenkel, Carlos. 2006. Maimonides’ God and Spinoza’s Deus sive natura. Journal of the History of Philosophy 44: 169–215. Granada, Miguel Ángel. 1994. Il rifiuto della distinzione fra potentia absoluta e potentia ordinata di Dio e l’affermazione dell’universo infinito in Giordano Bruno. Rivista di Storia della Filosofia 49: 495–532. ———. 2002. “Blasphemia vero est facere Deum alium a Deo:” La polemica di Bruno con l’aristotelismo a proposito della potenza di Dio. In Letture bruniane I.II del Lessico Intellettuale Europeo 1996–1997, ed. Eugenio Canone, 151–188. Pisa/Rome: Istituti Editoriali e Poligrafici Internazionali. ———. 2007. New Visions of the Cosmos. In The Cambridge Companion to Renaissance Philosophy, ed. James Hankins, 270–286. Cambridge: Cambridge University Press. ———. 2010. Synodus ex mundis. In Enciclopedia Bruniana & Campanelliana, ed. Eugenio Canone and Germana Ernst, vol. II, 142–154. Pisa/Rome: Fabrizio Serra Editore. ———. 2013. De immenso, i, 1-3 and the Concept of Planetary Systems in the Infinite Universe: A Commentary. In Turning Traditions Upside Down: Rethinking Giordano Bruno’s Enlightenment, ed. Henning Hufnagel and Anne Eusterschulte, 91–105. Budapest/New York: Central European University Press. Grant, Edward. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Harvey, Warren Zev. 1981. A Portrait of Spinoza as a Maimonidean. Journal of the History of Philosophy 19: 151–172. Henry, John. 1979. Francesco Patrizi da Cherso’s Concept of Space and its Later Influence. Annals of Science 36: 549–575. Konstan, David. 1972. Epicurus on “Up” and “Down” (Letter to Herodotus § 60). Phronesis 17: 269–278. Koyré, Alexandre. 1957. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins University Press. Lovejoy, Arthur Oncken. 1936. The Great Chain of Being: A Study in the History of an Idea. Cambridge, MA: Harvard University Press. Maimon, Salomon. 1999. Commentaires de Maïmonide, ed. and trans. Maurice-Ruben Hayoun. Paris: Cerf. Maimonides, Moses. 1520. Dux seu Director dubitantium aut perplexorum, ed. Augustinus Iustinianus. Paris: Jodocus Badius.

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———. 1963. The Guide of the Perplexed, trans. Shlomo Pines. Chicago: Chicago University Press. Pépin, Jean. 1953. Recherches sur le sens et les origines de l’expression caelum caeli dans le livre XII des Confessions de Saint Augustin. Archivium Latinitatis Medii Aevi 23: 185–274. Philoponus, John. 1991. Corollaries on Place and Void,  trans. David Furley, with Simplicius, Against Philoponus on the Eternity of the World, trans. Christian Wildberg. In Ancient Commentators on Aristotle, ed. Richard Sorabji. London: Bloomsbury Academic. Pines, Shlomo. 1996. Some Distinctive Metaphysical Conceptions in Themistius’ Commentary on Book Lambda and their Place in the History of Philosophy. In The Collected Works of Shlomo Pines, vol III: Studies in the History of Arabic Philosophy, ed. Sarah Stroumsa, 177–204. Jerusalem: The Magnes Press. Scapparone, Elisabetta. 2008. “Nella simplicità della divina essenza:” Giordano Bruno sugli attributi di Dio. Rinascimento 48: 351–373. Schmitt, Charles Bernard. 1967. Gianfrancesco Pico della Mirandola (1469–1533) and his Critique of Aristotle. The Hague: Martinus Nijhoff. Schuhmann, Karl. 1992. Le concept de l’espace chez Telesio. In Bernardino Telesio e la cultura napoletana, ed. Raffaele Sirri and Maurizio Torrini, 141–167. Naples: Guida. Sedley, David. 1987. Philoponus’ Conception of Space. In  Philoponus and the Rejection of Aristotelian Science, ed. Richard Sorabji, 140–153. Ithaca, NY: Cornell University Press. Spinoza, Baruch. 1925. Ethica. In Opera, ed. Carl Gebhardt, vol. II. Heidelberg: Carl Winter. Tirinnanzi, Nicoletta. 2013a. La composizione della Lampas triginta statuarum. In Nicoletta Tirinnanzi, L’antro del filosofo: Studi su Giordano Bruno, ed. Elisabetta Scapparone, 337–356. Rome: Edizioni di Storia e Letteratura. ———. 2013b. Il nocchiero e la nave. Forme della revisione autoriale nella seconda redazione della Lampas triginta statuarum. In Nicoletta Tirinnanzi, L’antro del filosofo: Studi su Giordano Bruno, ed. Elisabetta Scapparone, 357–376. Rome: Edizioni di Storia e Letteratura. Wolfson, Harry Austryn. 1929. Crescas’ Critique of Aristotle: Problems of Aristotle’s Physics in Jewish and Arabic Philosophy. Cambridge, MA: Harvard University Press.

Chapter 9

Libert Froidmont’s Conception and Imagination of Space in Three Early Works: Peregrinatio cœlestis (1616), De cometa (1618), Meteorologica (1627) Isabelle Pantin

Abstract  Libert Froidmont defended a single conception of space in the three books he published as a professor of philosophy at the University of Leuven before, as a professor of theology, he became involved in a series of open controversies (against heliocentrism and in defence of Jansenius). This conception of space was anti-Aristotelian; it was influenced by Stoicism, by the impact of the work of Tycho Brahe, and that of the new telescopic discoveries. However, the style, aim and focus of the successive expositions of this conception did change, as Froidmont became more and more invested both in his theologian studies, and in his defence of the geocentrist cosmology supported by the Roman Church. The Peregrinatio cœlestis (1616), which belonged to the tradition of humanist joco-seria, was meant to contribute positively to the debate first prompted by the publication of the Sidereus nuncius. The De cometa (1619), a dissertation on the 1618 comet, openly supported the 1616 decree against Copernicus. In the Meteorologicorum libri sex (1627), a traditional Aristotelian paraphrase, the demonstration was mainly supported by references to contemporary exegetes, and showed that the interpretation of Scripture was henceforth the issue that most interested Froidmont.

9.1  Introduction Libert Froidmont defended an almost unchanging conception of space in the three books he published as a professor of philosophy at the University of Leuven, before, as a professor of theology, he became involved in a series of open controversies (against heliocentrism, and in defence of Jansenius). This conception of space, closely related to Froidmont’s cosmological views, was influenced by new trends in I. Pantin (*) Ecole Normale Supérieure – PSL Research University, Paris, France e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_9

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philosophy, as it was, broadly speaking, anti-Aristotelian, but it was also, in many respects, conservative. However, there is a contrast between the stability of the underlying philosophical position Froidmont expressed in his successive works, and their marked evolution in style, aim and focus. In particular, by using fiction, irony and other literary devices Froidmont initially showed that he relied on imagination as a tool for undermining the prejudices that hindered the acceptance of new ideas based on recent observations. By contrast, his later works displayed more and more mistrust in anything not founded on experience, reason and authority, and avoided indirect modes of expression, as well as any recourse to fiction. Froidmont’s first published work, Saturnalitiæ cænæ (1616), which records a playful quodlibetal session held at the University of Leuven in the preceding winter, included a jocular narration of an imaginary voyage among the planets. Its title, Celestial Journey (Peregrinatio cœlestis), somewhat echoed the title of Galileo’s pamphlet, The Starry Messenger (Sidereus nuncius, 1610), and its humorous and fanciful tone did not reveal whether Froidmont meant to join, or to gently mock, Galileo enthusiasts. Three years later, Froidmont published a dissertation on the 1618 comet (De cometa, 1619), in which he advocated, without ambiguity, two different though not unrelated positions: first, he supported the Tychonian theory of comets; and second, he openly supported the 1616 decree against Copernicus. The third exposition of his conception of space was embedded in an academic treatise: a commentary on Aristotle’s Meteorologica (1627). In order to inform this evolution and investigate its causes, I shall first explain the complex background of Froidmont’s early works, then summarise the main features of his conception of cosmological space, and finally analyse how each of these books addressed the same issue.

9.2  A Complex Background Libert Froidmont is a historical figure resisting a broad, rigid categorisation or a positivist oversimplification of his character.1 He reminds us that it was possible, at the beginning of the seventeenth century, to be a ‘new philosopher’ without being a Copernican, and to belong to different intellectual spheres simultaneously, implying different kinds and degrees of allegiance to varied institutions and schools of thought. As a professor of philosophy at the University of Leuven Froidmont was to give his students a general, if not refined, knowledge of the Aristotelian doctrine; he did this, but not without utilising the great malleability of scholastic thought towards the end of the Renaissance for his purposes. His teaching duty did not prevent Froidmont from accepting the legacy of Justus Lipsius, the reviver of Stoicism. Froidmont continued Lipsius’s work by editing and commenting on Seneca’s Quæstiones naturales, although he increasingly distanced  On Froidmont’s life and work, see Monchamp 1892, Ceyssens 1963, Bernes 1988.

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himself from Lipsius’ almost unquestioning acceptance of Stoicism.2 At Leuven he further inherited another humanist tradition, which can be traced back to Erasmus: that of wit and irony, mingled with satirical and fantastical fiction. Froidmont’s 1616 Peregrinatio cœlestis was deeply influenced by the humanist tradition of Menippean satire, which, as Ingrid De Smet has shown, had been developed especially in Leuven, from the works of Juan Luis Vives (1492–1540) to those of Lipsius and Erycius Puteanus.3 The literary genre of Menippean satire can be traced back to Antiquity (in works like Petronius’s Satyricon, Seneca’s Apocolocyntosis and Lucian’s Icaromenippus). In the Renaissance it was revived by Leon Battista Alberti (in Momus) and Erasmus, as a serio-comic genre that combined fanciful fiction and mythological burlesque in a rhapsodic composition intended to ridicule pedantry and dogmatism.4 In Leuven, Petrus Nannius (1496–1557) mixed allegorical dream and Menippean satire, and his Somnia are referred to as models of the genre at the beginning of Froidmont’s Peregrinatio.5 Geert Vanpaemel has recently shed light on another aspect of the impact of university culture on Froidmont’s work: like other professors, Froidmont wished to educate his students, and to teach them versatility, acuity and rhetorical skills for use in public disputations, or in other academic or social contexts. He therefore did not adopt a purely scientific and demonstrative style in his writings, but intermingled philosophical argumentation with poetical digressions, and even entertaining narratives. From this perspective, a topic could be handled satisfactorily even if the discussion did not produce a definite conclusion: in universities, “natural philosophy was mainly considered a mere training of the mind, rather than a useful set of ideas.”6 However, in the case of Froidmont the choice between venturing assertive conclusions in philosophical matters and avoiding them was clearly informed by a critical aspect of his personality: from the start, Froidmont wished to become a theologian, and he would gradually become the first collaborator of the most prominent theologian in Leuven, Cornelius Jansenius. As early as at the time of his philosophy studies at the Falcon College in Leuven (1604–1606) Froidmont intended 2  Froidmont’s comments on Seneca would appear in the third printing of the Lipsian edition (Seneca 1632). A new edition, with additions, was published twenty years later (Seneca 1652). On the way in which Froidmont distanced himself from some aspects of Stoic physics, see Pantin 2008. 3  From 1514 onwards Vives mainly lived in the Netherlands. In 1517, as a tutor to the young Cardinal Guillaume de Croy, he moved to Leuven and obtained permission to teach publicly at the university, which he did until 1523. In December 1522 he presided over the jocular Disputationes quodlibeticæ, with considerable success. Lipsius (Somnium, 1581) and Erycius Puteanus also wrote satirical dreams. See Lipsius 1581, Puteanus 1608, De Smet 1996. 4  On this genre see Relihan 1993, Weinbrot 2005. 5  Nannius succeeded Conrad Goclenius at the Collegium Trilingue in 1539. He wrote two satirical dreams (1542 and 1545). See Sacré 1994. 6  Vanpaemel 2014, 67.

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to become a theologian. He suspended this project, probably for economical reasons, but had already entered the Church. Notably, he established close links with the Premonstratensian order, and lived at Park Abbey near Leuven.7 In 1613, he began to study theology in Leuven while teaching philosophy at the University. From 1616 onwards, he is likely to have become acquainted with Cornelius Jansenius who had returned to Leuven one year before completing his own doctorate, and had been given the charge of the new college of St. Pulcheria, founded to host the Dutch students of theology.8 Jansenius, a former student at the Leuven Falcon College, had studied theology in Paris, where he had met Jean Duvergier de Hauranne in 1609, and in his company he embarked on the enormous task of exploring the Bible and the work of the Church Fathers, especially Augustine, to solve the debate about the foundation and efficiency of Grace, and to refute the Molinist theses. On the title page of his commentary on the Meteorologica, which was published in early 1627, Froidmont bore his title of Licenciate in Theology (S. TH. L.). In the dedication he expressed his gratitude to the bishop of Tournai for having elected him as a canon of Tournai. He obtained his doctorate in 1628, while still Philosophiæ Professor Primarius at the Falcon College of the University of Leuven, and already Jansenius’s first collaborator. In 1627, Jansenius and Froidmont had appealed to their patrons for the provision of a house in which they could pursue their work on Augustine and the Church Fathers. This house was partially acquired in April 1628 thanks to the generosity of Andrea Trevisi, court physician, patron of the University, and adversary to the Jesuits.9 Froidmont lived in this house with Jansenius from September 1628 onwards, until he succeeded Jansenius as Ordinarius Professor of theology at the University in 163010; Jansenius was then appointed Regius Professor Scripturæ sacræ. In the following years (1631–1636) Froidmont also read Holy Scripture at the Park Abbey.11 In 1637 he succeeded Jansenius (who was elected bishop of Ypres) as Regius Professor Scripturæ sacræ. Subsequently, while preparing the edition of Jansenius’ Augustinus (1638–1640), he was elected Rector of the University of Leuven, Dean of St. Peter of Leuven, vice-chancellor of the University, and director of the Leuven branch of the Grand Séminaire of Liège.

 His Saturnalitiæ cænæ (1616) are dedicated to Jean Druys, Abbot of the Park and visitor to the university. 8  Jansenius also taught courses at St. Pulcheria, notably on Hebrew language and Thomistic theology. Jansenius was once more absent from Leuven from early 1623 to April 1627. 9  Orcibal 1989, 158–159. Andrea Trevisi was also the dedicatee of Froidmont’s Anti-Aristarchus (1631). 10  Orcibal 1989, 159 and 163; Wils 1927. Froidmont was legens at the University from April 1630 (nominated in August 1630), and regens from 30 September 1634. 11  Orcibal 1989, 159; Jansen 1929, 194. The stipend was forty or fifty florins. Froidmont and Jansenius approved the reformed status of the Abbey (Augustinian in spirit) in 1631. 7

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The turmoil created by the publication of Jansenius’ Augustinus did not diminish the support of those patrons who had backed Froidmont for so many years12: the University authorities and the government of Brabant. Indeed, Froidmont was a bright and well-accepted member of the Theological Faculty at Leuven; he agreed with its main orientation, both intellectual and political. Although a pillar of the Counter-Reformation, the Leuven Faculty retained some autonomy in its relations with Rome, for instance, in its own form of censorship, and its own theological tendencies. From the sixteenth century onwards it had placed much emphasis on the study of Scripture and of the Church Fathers,13 and developed a specific direction of Augustinianism, which was particularly defended by Michael Baius (1513–1589).14 Another of the Faculty’s own traditions was its constant opposition to the Jesuits. Historians have investigated the social and political implications of this conflict, notably Bruno Boute in his remarkable study of the Leuven Privileges of Nomination to Ecclesiastical Benefices.15

9.3  Froidmont’s Conception of Space in His Early Works I have persisted with outlining this complex background since it is in part responsible for the strong idiosyncratic character of Froidmont’s writings – in spite of the fact that his philosophical ideas, taken by themselves, are not really original for a man living in the Netherlands in the initial decades of the seventeenth century. In the three works that will be analysed below, Froidmont called into question the division of the universe into two regions, one (extending from the Earth to the vicinity of the Moon) elementary and corruptible, and the other (from the Moon to the firmament) holding nothing other than incorruptible quintessence. He did not believe in the existence of an orb of fire between the orb of the highest air and the orb of the Moon, which was still represented in many treatises of the sphere. If it was possible to mention ‘fire’ when speaking of the space above the Earth, the word referred to something different: the hot quality possessed by pure air (or ether),  On his death bed (on 6 May 1638) Jansenius had entrusted his manuscript, ready for the press, to his chaplain Reginald Lamæus, the canon Henricus Calenus, and to Froidmont. Froidmont’s role was critical in seeing the manuscript through to publication. The book was printed in Leuven in 1640, with a royal and imperial privilege, and a dedication to the Cardinal-Infante Ferdinand, Governor of the Spanish Netherlands. Throughout the remainder of his life (until his death on 27 October 1653) Froidmont fought in vain for the abolition of the ban imposed on the book by Urban VIII (bull In eminenti, March 1642) and Innocent X (bull Cum occasione, June 1653). 13  Plantin published the main achievements of the theologians of Leuven in print in Antwerp, notably the Biblia Polyglotta (1568–1572) and a new edition of Augustine, supervised by Johannes Molanus (1576–1577). 14  Pius V (bull Ex omnibus afflictionibus, 1567) and Gregorius XIII (Provisionis nostrae, 1579) condemned several Baius’ theses, but this did not prevent the latter from being given the most important responsibilities at the university. 15  Boute 2010. 12

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notably due to (or compatible with) the presence in it of inflammable stuff. In Froidmont’s view an uninterrupted space extended from the top of the mountains (above the region of the clouds) to the firmament: it could be called ‘pure air’ beneath the Moon, and ‘ether’ above it, but these linguistic differences ought not to mask the unified nature and continuity of the entire area. This space was fluid, and exhalations could ascend and circulate through all of it. These exhalations emanated from the Earth, but also, most probably, from all the planets, and even the fixed stars. When a large quantity of them assembled, comets could be produced, not only below the Moon, but also far above. As the heavens contained no ‘solid’ spheres, circles or wheels, the planets had nothing to support them and carry them along; they also had their own motion in the form of the diurnal rotation, driven by a kind of general westward current, or, in the case of their proper movements, thanks to an inner power. In any case, each planet, and more generally each celestial body, was likely to possess its own centre of gravity. Most of these theses had been proposed, or re-proposed, in the sixteenth century, by Copernicus (the multiple centres of gravity and movement in the cosmos),16 Jacob Ziegler and Jean Pena (the continuity of space, demonstrated by optical arguments),17 Tycho Brahe, Christoph Rothmann, and earlier philosophers (the fluidity of the heavens).18 Others (those that concerned the causes and processes of the motion of the stars, and the similarity between the planets and the Earth) had been reinforced or transformed at the beginning of the seventeenth century, thanks to Kepler’s physical astronomy and the Galilean telescopic discoveries (the lunar mountains, the phases of Venus, and the sunspots, linked to the idea of the rotation of the Sun on itself). However, if these ideas were not new, and if some of them gained a larger audience after the publication of Galileo’s Sidereus nuncius (Venice, 1610), they were still untraditional and paradoxical, since they contradicted Aristotle, and were still not included in the university textbooks. Even the most advanced astronomers showed some resistance. Christoph Clavius, the head of the Jesuit mathematical school, opposed cosmological novelties until his death (6 February 1612), and when some of his disciples and successors  – like Christoph Grienberger (1561–1636), Giuseppe Biancani (1566–1624), and Christoph Scheiner (1573–1650)  – tried to introduce these novelties in the astronomical doctrine taught at the Colleges of the Society, their efforts where often suppressed due to the conservative climate that prevailed under the leadership of Muzio Vitelleschi (1615–1645). Although the Jesuits rallied to the geo-heliocentrical system of Tycho Brahe soon after the 1616 condemnation of Copernicanism, they were more reluctant to accept the fluidity of the heavens, the existence of supra-lunar comets and the automotricity of planets; in their view, these concepts radically undermined the Aristotelian cosmology, and the  Copernicus 1543, I, 9. The plurality of the centres of gravity and of movement was already asserted in the first and second postulates of Copernicus’s Commentariolus, written between 1510 and 1514. See Copernicus 2015, I, 232–240. 17  See Lerner 1997, 11–15; Barker 1985. 18  See Lerner 1997, 3–66; Granada 2002, 2006. 16

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complete destruction of Aristotelian cosmology would have dangerous theological consequences.19 The defence of this anti-Aristotelian conception of space formed the central topic of the three books published by Froidmont between 1616 and 1627. Any ­differences between them – each book discusses the elements of this conception in more or less detail – resulted from their different themes, purposes and styles, and these, in turn, from their respective literary genres, intended audiences, and the arguments they proposed.

9.4  Imagining Space: Peregrinatio cœlestis (1616) The Peregrinatio cœlestis, published as part of the Saturnalitiæ cænæ (1616), belonged to the tradition of humanist joco-seria, with the title’s allusion to the Saturnalia referring to the carnivalesque tone of the work.20 Froidmond here appears to have published the text of his interventions as chairman to the precedent session of quodlibetal questions (22 paradoxical and even facetious questions) in order to insert among them the Peregrinatio, a fanciful narration of an interplanetary voyage which showcased his rhetorical skills, but also contributed to the debate that had started with the publication of the Sidereus nuncius. The Peregrinatio is an entirely imaginary narrative and presents a response to Kepler’s Dissertatio cum nuncio sidereo (Prague, 1610), in which Kepler, encouraged by Galileo’s telescopic discoveries, urged so-inclined philosophers in every respect to contradict the practices of the more traditional, quarrelsome, over-serious and stiff-necked professors. Whereas most debaters get all heated up, I regard humour as a more pleasant tone in discussions […]. I seem by nature cut out to lighten the hard work and difficulty of a subject by mental relaxation, conveyed by the style.21

He also alerted them to the fact that celestial navigations are, once more, possible, as they had been for the travellers of Lucian’s True Story: as soon as somebody demonstrates the art of flying, settlers from our species of man will not be lacking […]. Given ships or sails adapted to the breezes of heaven, there will be those who will not shrink from even that vast expanse.22

The association of Kepler with imagination is clearly positive in the first and main part of the Peregrinatio, even given that in a Menippean satire irony may reverse  See Lerner 1995; Pantin 2013. Ugo Baldini has shed light on the inner tensions in the Society concerning these subjects, by analysing documents relating to preliminary censure (Baldini 1992). 20  On the relationship between Roman Saturnalia and Christian Carnival see Grafton et al. 2010, 116. 21  “To the reader,” Kepler 1965, 5. 22  Kepler 1965, 39. 19

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meaning. Notably, in the last part of the book, the Copernicans and their eccentric fantasies – rather than the traditional philosophers’ short-sightedness – become the principal target of the satire: the first step in a development that would lead, 15 years later, to the condemnation of Copernicans as inveterate lunatics. In his controversy with Philip Landsberg, Froidmont reproached the Copernicans for “prefer[ring] the little flame of a foolish imagination” to the light of truth.23 Nevertheless, in the Peregrinatio, imagination – the motor of fantastic comical fiction – is not only a potent weapon against the narrow-minded Magistri nostri (the traditional professors), in a genuine Erasmian manner; it also helps to broaden the philosophical mind, and free it from prejudices. In his preface Froidmont blames those who, instead of believing that which is in front of their eyes, refuse to give credit to anything “that would not have been anticipated by short-sighted old fogeys coming from a mouldy Antiquity.”24 Thus, he metaphorically invites the stupid philosopher (matula philosophi) to take a scythe and cut the brambles and weeds that infest the road, and were long fertilised by common opinion.25 In this satirical dream, the narrator, riding pillion on Pegasus, converses with the Genius, who has abducted him, on the celestial landscapes they are traversing. This narrator plays the role of the dutiful philosophy professor, who clings to the ideas he is accustomed to teaching in school, while the Genius shows these ideas not to correspond to the real cosmos he is now exploring. The discussion is fully developed for the first part of the travel, from the Earth to the Moon. The Genius explains in great detail why the orb of elementary fire cannot exist,26 why what pervades the space between the Earth and the stars can be called “air, or ether if you prefer,”27 and why there can be no solid orbs in the heavens.28 He advances as a proof the comets that sometimes (albeit rarely) wander among the planets, and even above them, and that are made from the hot and viscous exhalations which ascend freely in the heavens, without being hurt by the solid matter of any orb.29 The Genius also proposes a new hypothesis: the above-mentioned exhalations, which are materia mortalis, may have agglomerated around what would become the nova stella in Cassiopeia, and made it visible.30 The idea that the move Froidmont 1631, 108, quoted and translated in Vanden Broecke 2015, 86: “fatuellae imaginationis luculam tam manifestae veritatis luci anteponunt.” 24  Froidmont 1616, a3r: “et nihil credere, nisi lippientibus aliquot e mucida Antiquitate senecionibus prævisum, affirmamus.” Unless otherwise indicated, all translations are mine. 25  Froidmont 1616, a3r: “Sentium, scio, spinarumque aliqua cæde opus, quas diu aluit opinio communis: sed adhibe manum.” 26  Froidmont 1616, 68: “Ignis ille tuus nusquam est; neque si adsit pilum tibi fortasse an unum crispabit.” 27  Froidmont 1616, 73. 28  Froidmont 1616, 74–76. 29  Froidmont 1616, 76–77: “Idem illud, aut fallor, impressissime adferebant sidera comantia, quæ etsi rarenter, inter Planetas tamen, vel supra quandoque, arbitrantibus etiam vobis, nata. Materia ergo, habitus pinguis et flammæ diu nutriens, adeo inoffensa cæli cujusquam solido ascendit.” 30  Froidmont 1616, 76–77: “Ab hac eadem caussa sidus illud insignitum Anno 1572 in imagine Cassiopœæ novitium. Cælica enim et stellans in fornice Firmamenti pars est, quam ampliavit ad speciem circumvoluta materia mortalis, cum sola fallat.” 23

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ment of the heavens could dissipate the soft and malleable matter of the exhalations is absurd: do not rivers transport tenuous bodies with their current without damaging them? Do not fragile birds fly easily even against the winds?31 Then, the Genius makes clear that the mountainous aspect of the Moon, which is a regular cælestis Terra, eliminates beyond all doubt the hypothesis of epicycles and deferent circles.32 And he sneers at the efforts of the narrator to preserve the old theory.33 Then the travellers continue on their upward journey. They encounter battalions of small, previously unknown planets, and as a precaution seek shelter under the roof of the firmament. The narrator notes the usefulness of this wall enclosing the cosmos. Certainly, it must be solid, “lest the light elements should ascend without obstacle and spread through imaginary spaces, unless perhaps the fear of the void above should sufficiently retain them.”34 However, neither character explains what could be these “imaginary spaces” beyond the borders of the world. Does the narrator actually allude to the Stoic concept of a finite world surrounded by infinite void?35 Or does he use the term ‘imaginary’ to discredit this concept? In any case, the voyage across the upper celestial region is not recounted with precision. The narrator confesses that he has lost almost all memory of the marvels he has seen during his travels. He remembers only that all the planets, except the Sun, were porous and permeated with light, like clouds, though light could not traverse them; and that they reflected this light differently, depending on how much they were mixed with opacity.36

The partial lapse of memory suffered by the narrator is all the more unfortunate in that the topics subsequently introduced are of the highest interest; they include, among other things, the theory that the planets (the Sun excepted) are likely to be populated (pp. 82–83); the probability of Venus’ rotating around the Sun which, in turn, rotates around himself (pp. 84–85); the proposition that the stars and planets are moved by a virtue imparted to them by the first mobile, i.e. the firmament; and the explanation that there is no other movement in heaven than the westward revolution (pp.  88–91, 94–99). Additional puzzling problems are introduced when the Copernican hypothesis is examined, such as the question of the location of hell. This second part of the Peregrinatio is both more original and more ambiguous than  Froidmont 1616, 78.  Froidmont 1616, 80. A marginal note calls attention to this issue: “Asperitas manifesta Lunæ non belle patitur Epicyclo circumvinciri.” 33  Froidmont 1616, 80–81. 34  Froidmont 1616, 81: “Et tale profecto esse debuit hoc Universi tectorium; ne Elementa levia sursum obice nullo in Spacia Imaginaria effunderentur: nisi periculum deorsum Vacui, fortasse tamen valide satis retineret.” 35  On this concept, see Algra 1995, 261–239; Sorabji 1988, 125–141, and Sect. 3.2.2 of Bakker’s Chapter 3 in this volume. 36  Froidmont 1616, 82: “Sed quantulum tamen adhuc memini: palantes omnes stellas, excipuo sole, fungosas, bibulasque (impervias tamen) lucis, ut nubes, vidi; quam reflectunt varie, et pro mixtura opacitatis.” 31 32

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the first part. Here the Genius is not as talkative, didactic or assertive as in the first part, and the irony aimed at the Copernicans is biting.37 Nevertheless, the use of references and quotations in this second part is interesting. Kepler’s works are the ones most frequently quoted and alluded to here, especially his Dissertatio cum nuncio sidereo and the preface of his Dioptrics.38 The neo-Stoic tendencies of Froidmont’s conception of space are also perceptible – at least as far as the fluidity of the heavens is concerned, while, as mentioned before, the question of the extra-cosmic void is avoided. Seneca’s Natural questions are quoted several times (though not always in a positive manner), Pena’s optical demonstration of the fluidity of the heavens is pressed into service (probably via Kepler’s preface to the Dioptrics), and the character of the Genius may have been inspired in part by Lipsius’s Physiologia stoicorum, which devotes three dissertations to the topic of the genies who, according to the Stoic, are ministers of the divine providence.39 One reference to an unusual source is also worth noting: when calling into question the Aristotelian definition of air as an element (since it does not have natural qualities) Froidmont commends the Chinese philosophers for not having included air among their five elements.40 Froidmont here probably relies on the De Christiana expeditione apud Sinas, which had been published in early 1616 by the Belgian Jesuit Nicolas Trigault.41 With regard to the Jesuits it is further worth noting that no Jesuit is quoted in the Peregrinatio, not even François d’Aiguillon, whose Optica (Antwerp: Plantin, 1613) had proposed (in spite of the telescopic discoveries) a defence of the Aristotelian conception of celestial space and bodies42; or Christoph Scheiner, who still rejected the analogy between the Earth and the Moon in his Disquisitiones mathematicæ (1614), but admitted the presence of irregularities on the Moon’s surface.43 Froidmont held the view, shared by both aforementioned Jesuits, that the

 See Pantin 2001. This paper opposes the idea, often expressed elsewhere, that Froidmont was sympathetic towards Copernican ideas before the Decree of 1616. See Monchamp 1892, 49–52; Favaro 1893, 738–743; Redondi 1988, 83–85 and 102–103; Van Nouhys 1998, 244–245 and 295–297. 38  Kepler 1611. 39  Lipsius 1604, L. I, diss. 18–20. 40  Froidmont 1616, 73: “applaudamque hac parte saltem Philosophiæ Chinensi, quæ igne, aqua, terra, metallo, ligno Elementa circumscribit, expuncto aere.” A marginal note places further emphasis on this point: “Quinque Elementa Chinensium Philos.” 41  Trigault 1616, 350: “elementa quinque numerari, nec de ea. re apud eos dubitare fas est, aut disceptare. elementa vero sic numerant: metallum, lignum, ignis, aqua, terra, &, quod intolerabilius est, alterum ex altero nasci affirmant. Sed neque aërem, quia non vident, agnoscunt. ubi enim nos aërem, ibi vacuum esse volunt.” The permission from the Provincial Superior of Lyons is dated 10 April 1616. Froidmont’s Saturnalitiæ cænæ were published towards the end of 1616. 42  See, notably, Aiguillon 1613, 419–423: “Disputatio quo pacto luna a Sole lumen accipiat, susceptumque ad nos transmittat.” Aiguillon was the rector of the Jesuit College of Antwerp. 43  See Pantin 2005; Pantin 2013. 37

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planets were like clouds, permeable by light,44 but his conception of the cosmos opposed theirs in his denial of an essential difference between the infra-lunar and the supra-lunar worlds, and he obviously chose not to include their works in his discussion. Froidmont did not attack the Jesuits directly, but only through covert allusions, e.g. when the Genius mocks the explanation of lunar phenomena with the assumption that the Moon, with its mountains, is enclosed in a crystal globe or ­epicycle – an idea which circulated in the Society around 1613.45 The anti-Jesuit trend is thus perceptible in Froidmont’s Peregrinatio, even if not explicitly expressed. Finally, three references to the Bible and the writings of the Church Fathers are worth mentioning, which are introduced in a semi-jocular context. The assumption of Enoch (Genesis 5:22–24) and Elias (Kings II 2:11) is situated within a humorous discussion on the inhabitants of the planets. Even greater emphasis is placed on this by a marginal note: “Elias and Enoch live on a planet, unless it displeases our masters.”46 There is further a reference to the Flood in Genesis 7 in the narrator’s observation that the valleys on the Moon’s surface might hold oceans (he is not certain), and that these bodies of water might have caused the “cataracts poured down by God when he wanted to punish men’s sins.”47 He then mentions that, according to the Copernicans, each planet has its own centre of gravity. In this case (but the narrator does not venture to endorse this opinion himself), it will not be the case that this water falls automatically and spontaneously towards the centre of our planet (the Earth, I mean), more than these oceans do towards the Moon. Accordingly, the man who—according to Heraclides—fell from the Moon, would be a manifest prodigy, if not a mere fable.48

Thirdly, Froidmont ironically praises the possibility of transporting hell from the centre of the Earth to the centre of the Sun – an opportunity for Copernicans to roast the damned and the demons more thoroughly. This would be quite convenient “if Sacred Scripture had not buried them in the centre of the Earth.”49 However,

 See above, note 37.  Froidmont 1616, 80–81. See Pantin 2013. 46  Froidmont 1616, 83: “Elias et Enoch Planetam aliquem incolunt, nisi displicet Magistris nostris.” 47  Froidmont 1616, 84. 48  Froidmont 1616, 84: “Non erit igitur, ut aqua illa automatôs et spontali lapsu magis ad Planetæ nostri (Telluris dico) centrum ruat, quam hæc maria ad Lunam. ut prodigiosus palam fuisset, nisi fabulosus, homo ille quem Luna excidisse tradidit Heraclides.” 49  Froidmont 1616, 86: “nisi sacra Scriptura tamen eos in corde Terræ defodiat.” This may be a reference to Apoc. 12:9: “Et projectus est draco ille magnus, serpens antiquus, qui vocatur diabolus, et Satanas, qui seducit universum orbem: et projectus est in terram, et angeli ejus cum illo missi sunt.” 44 45

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Froidmont adds, according to Augustine and Gregory the matter is so unclear that it would be irresponsible to settle it without the aid of the Holy Spirit.50

9.5  D  e cometa (1619): An Anti-Aristotelian and Anti-­ Copernican Tract The De cometa (1619) forms part of a collection of three Dissertationes on the 1618 comet, published by two professors at Leuven, professor of medicine Thomas Fienus and Froidmont. Froidmont must have been the one to initiate the publication, since he wrote the dedication to the royal physician Francisco Paz, as well as a short letter to Fienus asking him to report on his observations of the recent comet, and to pass his judgment on this phenomenon. Fienus’s response (pp. 9–78), is followed by a second letter by Froidmont, divided into chapters to form a small treatise (pp. 79–140). The book concludes with a short demonstration of the immobility of the Earth, addressed by Fienus to two young Englishmen, Tobie Matthew and George Gays, to continue a conversation begun three days previously during a banquet that Matthew and Gays had hosted.51 The work emphasises, on the one hand, Fienus and Froidmont’s reasoned adherence to the idea that celestial comets exist, which had been demonstrated by Tycho, and even to Tycho’s geo-heliocentric system, or at least its Capellian variant,52 as well as their willingness to celebrate the collapse of Aristotelian cosmology; and on the other hand, their full rejection of Copernicanism. With regard to the first point, the treatise conforms to the existing model of scientific tracts on comets. After congratulating Fienus for having “jugulated their common father Aristotle, stimulated by this beard,”53 Froidmont provides a methodical survey of the literature on the question, ending with his own observations. His focus is on demonstrating the supra-lunar location of the comet, so that the cosmo-

 Froidmont 1616, 86: “quod certe tam clare non facit, quin Augustino, Gregorioque nebula, imo tota nubes reliqua manserit. Ille 20. de Civit. c. 16. In qua parte Mundi Infernus sit, scire neminem arbitror, nisi cui divinus spiritus revelavit.” This reference was traditional. See Petrus Lombardus, In IV Sententiarum, Dis. 44, qu. 3, Art. 2: “Ad tertiam quæstionem dicendum, quod sicut Augustinus dicit, et habetur in littera, in qua parte mundi infernus sit, scire neminem arbitror, nisi cui divinus spiritus revelavit; unde et Gregorius in 4 dialog., super hac quæstione interrogatus respondet: hac de re temere definire non audeo.” 51  Froidmont 1619, 152–153: “Hæc scripsi Generosi D.D. in gratiam D.D.V.V. occasione confabulationis desuper in convivio vestro nudius quartus habitæ; quae ut æqui bonique consulatis, rogo.” Tobie Matthew, a friend of Bacon and Benedetto Castelli, is likely to have informed Fienus of the 1616 edict against heliocentrism pronounced by the Roman Inquisition. 52  According to the ‘Capellian system’ Mercury and Venus moved around the Sun (and the Sun and the superior planets around the Earth). This attenuated form of geo-heliocentricism, described in Martianus Capella’s De nuptiis, was popular in the Netherlands; see Vermij 2002, 32–42. 53  Froidmont 1619, 79: “Ut patrem nostrum jugulares te barba illa stimulavit.” 50

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logical background is only vaguely sketched, and more complete explanations deferred to the last part of the dissertation. Then, in the middle of chapter VII (“Distance and magnitude of the comet”), immediately following a laudatory mention of Kepler (“the prince of Copernicans in Germany”), whose observations on the 1607 comet are eagerly anticipated, Froidmont digresses with a dramatic note. “But about Copernicans, what is it that you have just made me understand?”54 He evokes the decree of 1616 and forcefully expresses his astonishment about the fact that so momentous a decision was only known to a narrow circle, when it would have been crucial to publish it throughout Europe, “especially in universities where there are scholars much exposed to such opinion.”55 He speculates about the underlying motives, and notes the link between the Pope’s concern that Scripture should be read “rigorosissimo sensu” and the spiritual magisterium he exercises on Christendom: If the Pope has decreed that the Earth stays still and the heaven moves, and if he has judged that it matters for the spiritual government of Christendom, I think that [he took this decision because] he had regard for Holy Scripture, notably Joshua 10 and Ecclesiastes 1 […]. Nothing is more evident if you take Scripture in its strictest meaning.56

He then alludes to the principle of accommodation in a negative manner, as the sole and ultimate recourse of the Copernicans: “Let them surrender, unless perhaps they should try this: that sometimes the Bible is accommodating to the common conceptions of men.”57 The conclusion to the treatise on the comets, in which Froidmont presents his theories on the matter of the celestial comets and the planetary system in which they circulate, follows this vehement digression on the 1616 prohibition of heliocentrism. Froidmont points out specific uncertainties, such as the time and origin of the generation of the comets: “their birth is sudden and random (although I do not exclude [the possibility] that the stars might have some influence on the process), and straight afterwards they begin to grow older, as many things do here below.”58 Their principal efficient cause is the Sun, “which, with its rays, inflates their head and extends it into a tail.”59 The most difficult aspect is their matter: according to the  Froidmont 1619, 122: “Sed de Copernicanis quid ex te nuper intellexi VIR CLARISSIME?”  Froidmont 1619, 123: “Maxime per Academias, ubi viri docti, quibus talis opinionis forte periculum.” 56  Froidmont 1619, 123–124: “Si tamen Pontifex terram stare, cœlum circumagi decrevit; et hoc ad spiritualem Reip. Christianæ gubernationem pertinere putarit, credo Scripturam sacram adspexisse, Josue praesertim 10. & Ecclesiast. 1 […]. Quo nihil evidentius, si Scripturam in rigorosissimo sensu accipis.” 57  Froidmont 1619, 124: “Dent manus [Copernicani], aut forte hoc. Scripturam communibus quandoque hominum conceptionibus obsecundare.” On the exegetical principle of accommodation see Laplanche 1991; Granada 1996; McMullin 1998. 58  Froidmont 1619, 130: “Nihil ergo (iterum dicam) de Cometarum generationis tempore certi, nihil comprehensi. Nascuntur subito, fortuitoque (nec tamen nego stellas huc aliquid adferre) ac deinde statim consenescunt, ut multa in his inferioribus.” 59  Froidmont 1619, 130–131: “nam de caussa efficiente, dictum ante, potissimum esse Solem, qui radio Cometæ caput inflat et extendit in caudam.” 54 55

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Copernicans, all the planets, like the Earth, exude exhalations as they rotate around themselves (the Moon excepted). And these exhalations, in turn, naturally rotate around the Sun.60 This, Froidmont adds, “you can even maintain without approving the entire Copernican system of the world.”61 Then Froidmont states that he considers the geo-heliocentric system plausible. Consequently, there is no reason why the planets should not emit exhalations, which, in turn, may rotate around the Sun and produce comets. The fact that we cannot observe any loss of substance in the planets is not a valid objection (p.  132). Of course, the old traditionalist masters may find  Froidmont unreasonable, and therefore he must deal with the objections and explore alternative hypotheses – for instance, the theory that nodes could be formed in the ether and produce comets before being dissolved by the rays of the Sun.62 Froidmont also repeats the hypothesis, already examined by Tycho, that the nova of 1572 might have been generated by a detached part of the Milky Way. In this case the Milky Way, instead of being a part of the firmament, would be a sort of ring, formed by myriads of stars and suspended between Saturn and the firmament.63 Froidmont concludes briefly that the comet is a “star that wanders among the planets, it is made from ethereal substance, and describes a great circle of the sphere, like the planets, by virtue of their proper form – or, if you like, you can attach to them an intelligence.”64 This conception of space is not contradictory to that developed in the Peregrinatio, although it is founded on observations and rational arguments instead of fiction. The rejection of traditional cosmology is as marked here as it was in Froidmont’s earlier work, even if the satirical vein is confined to rare rhetorical bursts. This rejection is all the more remarkable in that it is associated with a dramatic and solemn acceptance of the ban of Copernicanism, out of obedience to the papal decree, and an acknowledgement of its exegetical justification. At the end of his dissertation, Froidmont states that he will go no further, but return to his theological studies after this philosophical interlude.65 The order of his priorities is thus clearly defined.

 Froidmont 1619, 131: “Itaque sicut Copernicus terram circa suum centrum, nubesque et exhalationes, et quicquid cum terra et aqua cognationem habet, motu circulari et eo naturali volvi sciscit, ita forte omnes Planetas (excepta tamen Luna) cum exhalationibus in circumfusum ætherem ex corporibus eorum elicitis, rotari naturaliter circa Solem, ut suum centrum velit.” 61  Froidmont 1619, 131: “Imo hoc asserere potes, licet Copernicanam mundi ordinationem non totam probes.” 62  Froidmont 1619, 133. 63  Froidmont 1619, 133–134. 64  Froidmont 1619, 136: “Breviter ergo Cometa peregrinum in Regione Planetarum sidus est, cohæsum de substantia ætheris, et circulum in Sphæra, majorem, ut Planetæ a propria forma (vel alliga intelligentiam, si vis) describens.” 65  Froidmont 1619, 136: “Non ibo jam longius (videbo quid alias facturus:) et redeo ad alia studia quae hoc labore dies aliquot intercalavi.” 60

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9.6  R  espectfully Dissenting from Aristotle: Meteorologica (1627) Froidmont uses the same conception of space, and the same idea of the exhalations exuded by celestial bodies (the Sun excepted),66 in his 1627 Meteorology.67 This work forms part of the academic tradition of Aristotelian paraphrases: while not a straightforward commentary, nor a compendium, it evidently takes Aristotle’s treatise, which is frequently referred to, as a major basis for its discussions. Yet Froidmont’s Meteorology showed at least one important original trait: it was signed by a licenciate in theology (as mentioned in the title), who considered all knowledge of the natural world subordinate to theology. As we have seen above, Geert Vanpaemel considers the Meteorology primarily a work written (in its content, style and argumentation) for a specific audience, with Froidmont adopting the role of a typical professor: “the impersonation of erudition and universal knowledge, based on a broad familiarity with books and doctrines, and in full awareness of the social status of knowledge claims.”68 In Vanpaemel’s view, the display of such competences was Froidmont’s aim, not the production of definite doctrines and conclusions. However, as far as the conception of cosmological space is concerned, Froidmont is quite clear and unambiguous. At the beginning of the work he criticises Tycho for having maintained a dividing line between the elementary and the celestial world, and his belief that the exhalations, which circulate among the planets “have a celestial nature, different from what is here below.” According to Froidmont, since it is certain that at least some terrestrial exhalations ascend above the Moon, Tycho’s theory would imply that it is possible for these exhalations to move around in a quintessential space. This theory would “mix mortal things with divine and incorruptible ones, which is not appropriate.”69 The Meteorology differs significantly in tone, style, and the choice of arguments from Froidmont’s earlier works. Notably, Aristotle is dealt with respectfully. Whenever possible Froidmont adapts Aristotle’s doctrine to his own conceptions; and when it is not, he either points out that Aristotle remained doubtful on the issue

 Froidmont states that he disagrees on this point with Camillo Gloriosi and Willebrord Snellius (see Gloriosi 1624; Snellius 1619): he thinks that the Sun, the lamp of the universe, must be “exempted from the law of exhalations,” not to suffer losses, as it must be “more immortal” than the other celestial bodies (Froidmont 1627, 119: “quia magis immortalis hæc publica Mundi lampas esse debuit, ne ea. extincta, esset sine lumine”). 67  In the Meteorologicorum libri Froidmont occasionally refers to the De cometa. See, notably, Froidmont 1627, 118–119. 68  Vanpaemel 2014, 58. 69  Froidmont 1627, 3: “Tycho tamen id quod Planetas interfluit, auram quamdam naturæ cælestis, et diversæ ab his inferioribus, credit: sed nondum mihi persuasit […]. Halitus etiam terreni, effusissime rarefacti, supra Lunam scandent quandoque, […] miscebunturque mortalia divinis et incorruptibilibus: quod non decet.” 66

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in question,70 or removes him from the basis of the argument. Thus, Froidmonts suggests that Aristotle, in contrast to the scholastics, was not firmly opposed to the conception of a vast aerial or ethereal space extended from the superior region of the air to the Moon, and even further: So that you do not think that [in matter of exhalations] the air immediately above the clouds is meant, [Aristotle] adds that this exhalation carries away with itself the air close to it: that is, the air that we thus far usually call the supreme region of air. This [air] is what Aristotle properly called air; the other, which is above, and stretches as far as the Moon, or, to speak more truly, to the vault of the firmament, he has called fire, because a great quantity of burning exhalations are mixed in it.71

This paradoxical presentation of the way in which Aristotle distributed the elements in the cosmos is based on his passage on the two kinds of terrestrial exhalations, moist and dry, the latter similar to smoke, and rising above the former, in the region just “below the circular motion [of the heavens],” where “the warm and dry element, which we call fire” is located, above the region of the air. The so-called fire, which is “spread round the terrestrial sphere,” is “like a kind of fuel [hupekkauma],” as the slightest motion will cause it to “burst into flame,” so “whenever the circular motion stirs this stuff up in any way, it catches fire at the point at which it is most inflammable,” and that explains the generation of igneous meteors.72 Almost all Aristotle commentators position this region of fire under the Moon. But Froidmont likely knew the interpretation that, according to Simplicius, John Philoponus (the early Christian opponent to the doctrine of quintessence) had given to ‘hupekkauma,’ translated by Froidmont as ‘fuel of fire,’ “fomes incensionis.” In the standard Neoplatonist reading of Aristotle’s cosmology the ‘hupekkauma’ comprehended both the pure air above the mountains and the elementary fire below the Moon, and it followed the diurnal motion. But Philoponus, quoted and refuted by Simplicius, went much further: to confirm his claim that the entire cosmos was corruptible, he asserted that heaven itself could be some kind of fire, moving in a circle.73 This probable link with Philoponus is significant: Froidmont’s main goal for his discussion of exhalations in his Meteorology appears to be the demonstration of the corruptibility of the heavens.74 And to strengthen this position, Froidmont’s major  According to Froidmont, Aristotle (in De caelo, II, 5) confesses that it is extremely difficult to make any certain pronouncements about the heavens. Thus, if it had been possible to convince the Philosopher “by better reasons” that the heavens are corruptible, he would have agreed (Froidmont 1627, 119). 71  Froidmont 1627, 4: “Ac ne putares intelligi de aëre proxime supra nubes, addit, exhalationem istam rapere secum aërem sibi continuum: id est, illum quem hactenus supremam aëris regionem appellare solemus. Hic ergo est, quem Aristoteles proprie aërem; alterum vero qui superest, et ad Lunam usque, aut verius ad ipsum Firmamenti fornicem, pertingit, propter exhalationum ferventium copiam et mixturam, ignem vocavit.” 72  Aristotle, Meteorology, I, 4, 341b; W.E. Webster’s translation, Aristotle 1931. 73  Simplicius, De cælo I, cap. 2, 34:5. See Simplicius 2011, 28–29. See also Sorabji 2010 (chs. 6 and 7 on space); Wildberg 1988. 74  On Froidmont’s opposition to the partisans of the incorruptibility of the heavens, see also Froidmont 1627, 118. He is more indulgent towards those who simply propose that comets and 70

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references are to biblical passages, through the Church Fathers’ commentaries,75 and to contemporary theologians, all of them Jesuits. Thus, Froidmont quotes Luis de Molina, who in his commentary on Genesis affirms that the heavens (with the probable exception of the Empyrean), must be made of a matter similar to that of the sublunar world, as it was formed from the primeval water.76 The quotation is from the fifth disputation of Molina’s De opera sex dierum, which resolves the objections advanced against Molina’s thesis: “in the beginning, God has created only the Empyrean, the Earth and Waters, then from Water all the other simple bodies were fabricated, including all the celestial moving orbs.”77 The De opera sex dierum forms an appendix to Molina’s commentary on the first part of Thomas Aquinas’s Summa theologica (1592), and was more widely circulated in its second edition (1593), which was reprinted in 1594 and 1622. This second edition also contains extracts from Molina’s Concordia liberi arbitrii cum gratiæ donis (1588), the work that Froidmont and Jansenius examined for their refutation of Molina’s theory of efficacious grace in the Augustinus. Froidmont also quotes two Jesuit theologians favourably who had been radically opposed to the exegetical principle of accommodation, when used in support of Copernicanism.78 He quotes Nicolaus Serarius’s injunction always to read Scripture literally, without being misled by ill-founded Aristotelian prejudices.79 Then he refers approvingly to Cornelius a Lapide’s commentary on the first chapter of Genesis. Like Molina and Serarius, Cornelius asserted that, according to Scriptures, the heavens and the sublunar world had been made from “the abyss of waters,” and were therefore equally corruptible.80

novae might be permanent celestial bodies, like Fienus, who “has given this thesis a new and remarkable verisimilitude, though in a playful style, without being obdurate” (Froidmont 1627, 107: “novam iis et egregiam  – licet ludenti nec pertinaciter inhærenti calamo  – probabilitatis speciem fecit”). 75  He refers to Bede, St Jerome, Cyril and Clement of Alexandria, who affirm that heaven was made from the water that filled the world at the beginning (Froidmont 1627, 119). 76  Froidmont 1627, 119: “Ex Scriptura Sacra aperte colligi arbitramur materiam cælorum (si Empyrium excipias: de quo contrarium probabiliter defendi posset) convenire in specie cum materia rerum sublunarium;” quotation from Molina 1592, 1963. 77  Molina 1592, 1960: “Deum a principio solum creasse Empyreum, terram et aquas, ex aquisque fuisse fabricata cætera simplicia corpora, etiam cœlestes omnes orbes mobiles.” 78  See Kelter 2015. 79  Froidmont 1627, 119–120: “nec esse cur Scripturam non tam proprie accipiamus, nisi anticipatam tantum Aristotelicarum quarumdam, quae facile solvi possunt, rationum opinionem;” quotation from Serarius’s commentary on the second epistle of Peter, ch. 3, qu. 2 (Serarius 1612, part II, 52). Nicolaus Serarius (1555–1609) had occupied the chairs of theology and Sacred Scripture at Würzburg and Mainz. In his Josue, ab utero ad ipsum usque tumulum he went so far as accusing Copernicus of heresy (Serarius 1610, 1004–1006). 80  Froidmont 1627, 120. Reference to Lapide 1616, 12. Cornelius van den Steyn (1567–1637) had been professor of Holy Scripture and of Hebrew at Leuven before teaching the same subjects in the Collegio romano, from 1616 onwards. He wrote commentaries on the Canon and the Deuterocanon, the Book of Job and the Psalms excepted.

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Froidmont’s mitigation of his criticism of Aristotle in the 1627 Meteorology, and his respectful acknowledgment of the excellence of Jesuit exegetical work, are better explained by referring to the historical context. Froidmont was a close c­ ollaborator of Jansenius at the time. He knew of the importance of maintaining, as far as possible, a peaceful climate, to facilitate the composition of the Augustinus, and its reception afterwards. It is likely, therefore, that he was keen to emphasise points of agreement between himself and the Jesuits, such as the rejection of Copernicanism and the necessity of a literal reading of the Bible.

9.7  Conclusion As we have seen, during his entire career as professor of philosophy, Froidmont proposed a single (or nearly the same) conception of the cosmos. However the character, and even the target of his different expositions did change. Initially, Froidmont played the part of the witty and brilliant opponent to scholastic philosophy, in the wake of the revived interest in Stoic cosmology and the recent telescopic discoveries. But over time Froidmont’s interests revealed themselves more and more clearly to be theological in nature. This evolution could help us to shed more light on the complex relationship between Froidmont’s philosophical work and his engagement with Augustinianism, and later Jansenism, as a professor at the University of Leuven.

References Aiguillon, Francois d’. 1613. Opticorum libri sex. Antwerp: Heirs of Johannes Moretus. Algra, Keimpe. 1995. Concepts of Space in Greek Thought. Leiden: Brill. Aristotle. 1931. Meteorologica, trans. Erwin Wentworth Webster. In The Works of Aristotle, ed. William David Ross, vol. III. Oxford: Clarendon Press. Baldini, Ugo. 1992. Legem Impone Subactis: Studi su filosofia e scienza dei gesuiti in Italia (1540– 1632). Rome: Bulzoni. Barker, Peter. 1985. Jean Pena (1528–1558) and Stoic Physics in the Sixteenth Century. The Southern Journal of Philosophy 23 (Suppl): 93–107. Bernes, Anne-Catherine, ed. 1988. Libert Froidmont et les résistances aux révolutions scientifiques. Haccourt: Association des Vieilles Familles de Haccourt. Boute, Bruno. 2010. Academic Interest and Catholic Confessionalisation. The Louvain Privileges of Nomination to Ecclesiastical Benefices. Leiden: Brill. Ceyssens, Lucien. 1963. Le Janséniste Libert Froidmont (1587–1653). Bulletin de la Société d’Art et d’Histoire du Diocèse de Liège 43: 1–46. Copernicus, Nicolaus. 1543. De revolutionibus orbium coelestium. Nuremberg: Johannes Petreius. ———. 2015. De revolutionibus orbium coelestium, ed. and trans. Michel-Pierre Lerner, Alain Segonds and Jean-Pierre Verdet, 3 vols. Paris: Les Belles Lettres.

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De Smet, Ingrid. 1996. Menippean Satire and the Republic of Letters, 1581–1655. Geneva: Droz. Favaro, Antonio. 1893. Gli oppositori di Galileo. II Liberto Froidmont. Atti del Reale Istituto Veneto di scienze, lettere ed arti VIIa ser. 4: 731–745. Froidmont, Libert. 1616. Liberti Froidmont pæd. falconis in Academia Lovaniensi philos. professoris saturnalitiæ cænæ, variatæ somnio, sive peregrinatione cælesti. Leuven: Philippus Dormalius. ———. 1619. De Cometa anni 1618 dissertationes Thomæ Fieni [...] et Liberti Fromondi [...]: in quibus tum istius motus, tum aliorum omnium essentia, effectus et præsagiendi facultas declarantur. Eiusdem Thomæ Fieni epistolica quæstio. An verum sit, coelum moveri et terram quiescere. Antwerp: Gulielmus a Tongris. ———. 1627. Liberti Fromondi S. Th. L. collegii falconis in academia Lovaniensi philosophiæ professoris primarii meteorologicorum libri sex. Antwerp: Balthasar Moretus. ———. 1631. Liberti Fromondi in academia Lovaniensi S. Th. doct. et prof. ord. ant-Aristarchus sive orbis terræ immobilis: Liber unicus. Antwerp: Balthasar Moretus. Galilei, Galileo. 1610. Sidereus nuncius. Venice: Tommaso Baglioni. Gloriosi, Camillo. 1624. De cometis dissertatio astronomico-physica. Venice: typographia Varisciana. Grafton, Anthony, Glenn Warren Most, and Salvadore Settis. 2010. The Classical Tradition. Cambridge, MA: Harvard University Press. Granada, Miguel Ángel. 1996. Il problema astronomico-cosmologico e le sacre scritture dopo Copernico: C. Rothmann e la teoria dell’ accommodazione. Rivista di storia della filosofia 51: 789–828. ———. 2002. Sfere solide e cielo fluido: Momenti del dibattito cosmologico nella seconda metà del Cinquecento. Milan: Guerini. ———. 2006. Did Tycho Eliminate the Celestial Spheres Before 1586? Journal for the History of Astronomy 37: 125–145. Jansen, Josephus Evermodus. 1929. L’Abbaye norbertine de Parc-le-Duc. Malines: H. Dessain. Jansenius, Cornelius. 1640. Augustinus. Vol. 2. Louvain: Zeger. Kelter, Irving Alan. 2015. The Refusal to Accommodate. Jesuit Exegetes and the Copernican System. In The Church and Galileo, ed. Ernan McMullin, 38–53. Notre Dame: University of Notre Dame Press. Kepler, Johannes. 1610. Dissertatio cum nuncio sidereo nuper ad mortales misso. Prague: Daniel Sedesanus. ———. 1611. Dioptrice. Augsburg: David Frank. ———. 1965. Conversation with Galileo’s Sidereal Messenger, trans. Edward Rosen. New York: Johnson Reprints. Lapide, Cornelius a. 1616. Commentaria in pentateuchum Mosis. Antwerp: Heirs of Martin Nutius and J. Meursius. Laplanche, François. 1991. Herméneutique biblique et cosmologie mosaïque. In Les Eglises face aux sciences, ed. Olivier Fatio, 29–51. Geneva: Droz. Lerner, Michel-Pierre. 1995. L’entrée de Tycho Brahe chez les Jésuites ou le chant du cygne de Clavius. In Les Jésuites à la Renaissance. Système éducatif et production du savoir, ed. Luce Giard, 145–185. Paris: Presses Universitaires de France. ———. 1997. Le monde des sphères, II: La fin du cosmos classique. Paris: Les Belles Lettres. Lipsius, Justus. 1581. Satyra menippaea. Somnium. Lusus in nostri aevi criticos. Antwerp: Chr. Plantin. ———. 1604. Physiologiae stoicorum libri tres. Antwerp: Johannes Moretus. McMullin, Ernan. 1998. Galileo on Science and Scripture. In The Cambridge Companion to Galileo, ed. Peter Machamer, 271–347. Cambridge: Cambridge University Press. Molina, Luis de. 1588. Concordia liberi arbitrii cum gratiæ donis, divina præscientia, providentia, prædestinatione et reprobatione ad nonullos primæ partis divi Thomae articulos. Lisbon: Antonius Riberius. ———. 1592. Commentaria in primam divi Thomæ partem. Cuenca: Christianus Barnaba.

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———. 1593. Commentaria in primam divi Thomae partem […] Adiectæ sunt huic secundæ editioni eiusdem autoris disputationes, ad hanc primam partem D. Thomæ spectantes, ex libro concordiæ liberi arbitrii cum gratiæ donis, excerptæ. Lyons: Baptiste Buysson. Monchamp, George. 1892. Galilée et la Belgique: Essai historique sur les vicissitudes du système de Copernic en Belgique. Saint-Trond: Moreau-Schouberechts. Orcibal, Jean. 1989. Jansenius d’Ypres (1585–1638). Paris: Etudes Augustiniennes. Pantin, Isabelle. 2001. Libert Froidmont et Galilée: L’impossible dialogue. In Largo campo di filosofare: Eurosymposium Galileo 2001, ed. José Montesinos and Carlos Solis, 615–635. La Orotava: Fundación Canaria Orotava. ———. 2005. Galilée, la lune et les Jésuites. Galilæana: Journal of Galilean Studies 2: 19–42. ———. 2008. Veniet tempus... Sur un aspect de l’influence des Quæstiones naturales de Sénèque à la fin de la Renaissance. Journal de la Renaissance 6: 37–48. ———. 2013. Le débat sur la substance lunaire après le Sidereus Nuncius: Stratégie et visée de la résistance péripatéticienne. In La lune aux XVIIe et XVIIIe siècles, ed. Chantal Grell, 103–120. Turnhout: Brepols. Puteanus, Erycius. 1608. Comus, sive phagesiposia cimmeria. Somnium. Leuven: Gerardus Rivius. Redondi, Pietro. 1988. Libert Froidmont, opposant et allié de Galilée. In Libert Froidmont et les résistances aux révolutions scientifiques Bernes 1988, ed. Anne-Catherine Bernes, 83–104. Haccourt: Association des Vieilles Familles de Haccourt. Relihan, Joel C. 1993. Ancient Menippean Satire. Baltimore: Johns Hopkins University Press. Sacré, Dirk. 1994. Nannius’s Somnia. In La satire humaniste, ed. Rudolf De Smet, 77–93. Leuven: Peeters. Scheiner, Christoph. 1614. Disquisitiones mathematicæ, de controversiis et novitatibus astronomicis. Ingolstadt: Typographus Ederianus. Seneca. 1632. L. Annæi Senecæ philosophi Opera quæ exstant omnia: a Justo Lipsio emendata et scholiis illustratae. Editio tertia […] aucta Liberti Fromondi scholiis ad quaestiones naturales et ludum de morte Cl. Cesaris. Antwerp: Balthasar Moretus. ———. 1652. L. Annæi Senecæ philosophi Opera quæ exstant omnia: a Justo Lipsio emendata […] Editio quarta […] aucta Liberti Fromondi scholiis […] quibus in hac editione accedunt. eiusdem Liberti Fromondi ad Quaestiones naturales excursus novi. Antwerp: Balthasar Moretus. Serarius, Nicolaus. 1610. Josue, ab utero ad ipsum usque tumulum, e Moysis Exodo, Levitico, Numeris, Deuteronomio. Paris: Edme Martin. ———. 1612. Prolegomena Biblica. Et commentaria in omnes Epistolas Canonicas. Mainz: Balthasar Lipp. Simplicius. 2011. On Aristotle on the Heavens 1.2-3, transl. Ian Mueller. London: Bloomsbury Academic. Snellius, Willebrord. 1619. Descriptio cometae, qui anno 1618 mense Novembri primum effulsit. Leiden: Elzevir. Sorabji, Richard. 1988. Matter, Space and Motion: Theories in Antiquity and their Sequel. Ithaca: Cornell University Press. ———. 2010. Philoponus and the Rejection of Aristotelian Science. 2nd ed. London: Institute of classical studies. Trigault, Nicolas. 1616. De Christiana expeditione apud Sinas suscepta ab Societate Jesu, ex P. Matthæi Riccii ejusdem Societatis Commentariis, Libri V […] auctore P. Nicolao Trigautio Belga. Lyons: Jean Jullieron for Horace Cardon. Van Nouhys, Tabitha. 1998. The Age of Two-Faced Janus: The Comets of 1577 and 1618 and the Decline of the Aristotelian World View in the Netherlands. Leiden: Brill.

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Vanden Broecke, Steven. 2015. Copernicanism as a Religious Challenge After 1616. Self-­ Discipline and the Imagination in Libertus Fromondus’ Anti-Copernican Writings. Lias 42 (1): 67–88. Vanpaemel, Geert. 2014. Comets, Earthquakes and Gunpowder: School Philosophy in Libertus Fromondus’ Meteorologicorum libri sex (1627). Lias 41 (1): 53–68. Vermij, Rienk. 2002. The Calvinist Copernicans. The Reception of the New Astronomy in the Dutch Republic, 1575–1750. Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen. Weinbrot, Howard D. 2005. Menippean Satire Reconsidered: From Antiquity to the Eighteenth Century. Baltimore: Johns Hopkins University Press. Wildberg, Christian. 1988. John Philoponus’ Criticism of Aristotle’s Theory of Æther. Berlin: De Gruyter. Wils, Joseph. 1927. Les professeurs de l’ancienne faculté de théologie de Louvain (1432–1797). Ephemerides Theologicae Lovanienses 4: 338–358.

Chapter 10

Questioning Fludd, Kepler and Galileo: Mersenne’s Harmonious Universe Natacha Fabbri

Abstract  This chapter examines Marin Mersenne’s main objections to Robert Fludd’s, Johannes Kepler’s and Galileo Galilei’s views of the cosmos in order to delineate his own idea of space, as well as several significant changes in his interpretation of the universe. I will discuss how Mersenne sought to single out a model of space and the universe that could perfectly agree with the Mosaic cosmos: he selected different explanatory models and contrasted them with each other to find out which one provided the most reliable explanation of natural phenomena, and was therefore the best ally in his war against atheism and heresy. Mersenne’s definition of a harmonious universe arose from the questions he addressed to his interlocutors, and from his thorough examination of their writings. This essay focuses on Mersenne’s arguments against Fludd’s qualitative and panspermic cosmos; on the theological and metaphysical underpinnings that urged him to abandon Kepler’s geometrical cosmos and harmonic archetypes; and on his refutation of Galileo’s universe, which relied on the intertwining of Scholastic arguments and the seventeenth-century debate about the vacuum and mechanics. Mersenne’s final conclusions, setting forth both metaphysical and physical reasons, marked the sunset of the traditional idea of the harmonic cosmos: across his works the musica mundana begins to fade, and the movements of the bodies within the plenum of the cosmos no longer reveal divine and geometrical archetypes.

I would like to thank the editors for their useful comments on an earlier draft of this paper. All translations are the author’s except where otherwise noted. N. Fabbri (*) Galileo Museum, Institute and Museum for the History of Science, Florence, Italy e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_10

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10.1  Introduction Marin Mersenne has largely been acknowledged as the most representative of the seventeenth-century philosophers who devoted his life to studying the harmonie universelle. It is therefore particularly significant that Mersenne’s idea of space and cosmos grew to be incompatible with both the idea of musica mundana and the Neo-Platonic or Pythagorean readings of the harmony of the universe. This chapter has two principal aims, which are intertwined with each other. Firstly, I will show how Mersenne very rarely directly put forward his own theories or philosophical reflections. Instead, he preferred questioning his numerous interlocutors and correspondents by addressing to them queries relating to his main concerns and interests, chiding or praising their interpretations, examining their writings in great depth, and contrasting different theories with each other in order to find the most reliable explanation for natural phenomena. Mersenne’s view also  emerges from stylistic choices that were strongly indebted to the medieval quaestiones; nevertheless, the sources he employed and considered in his ‘questions’ were not by ancient and medieval ‘authorities,’ but rather by his contemporaries, whose theories and conclusions  informed Mersenne’s respondeo. Of Mersenne’s many direct and indirect interlocutors this article considers particularly Robert Fludd, Johannes Kepler and Galileo Galilei, and his reading of their works, not merely because they provided three very influential accounts of harmonic cosmos, but also because they embodied three diverging ways of interpreting the order of the universe. By examining Mersenne’s main objections to these thinkers’ views of the cosmos it may be possible to discern his own idea of space, as well as to map several significant changes in his interpretation of the universe and, more specifically, a harmonious universe. Fludd exemplified the hermetic philosopher and Rosicrucian alchemist who threatened Catholic orthodoxy, and against whom Mersenne declaimed in his first writings. Kepler was initially a significant source for Mersenne, as he provided a wide range of arguments against both Fludd’s qualitative cosmos and Giordano Bruno’s infinitism, and also effective analogies to face anti-Trinitarian issues. The merging of metaphysical and physical concerns also characterizes Mersenne’s analysis of Galileo’s heliocentric universe and the debate concerning his theory of void and atoms, which were refuted in light of both the statements of contemporary philosophers – in primis Descartes – and Mersenne’s tireless checking of Galileo’s claims. Secondly, I will examine the significant changes Mersenne’s idea of universe underwent over time. His survey on space and the cosmos fit perfectly the idea of the scientia ancilla theologiae, according to which research in natural philosophy was to be adapted to theological matter, and mathematics was a tool for answering apologetic needs – just as it had been done in several of Mersenne’s sources, for instance Augustine’s De quantitate animae and De musica, Joachim of Fiore’s Trinitarian theology, and Grosseteste’s survey on optics.1 This article will trace how

 See Fabbri 2008, 47–57. Vincent Carraud (1994, 145, 147) claimed that, in Mersenne’s thought, “occupying oneself with physics and mathematics corresponds to occupying oneself with natural theology.”

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Mersenne moved away from the Aristotelian-Ptolemaic synthesis, followed Kepler against Fludd, and later abandoned Kepler in favor of a stance that was closer to the debates arising from Descartes’ and Galileo’s philosophy. Nonetheless, from 1623 onwards and up to his last work, Mersenne’s space, enclosed in the Empyrean sphere, was still crossed by swift angels – according to the Thomistic model – and needed to agree with God’s revelations in the Holy Scriptures.2 Mersenne’s work always resorted to a somewhat reversed accomodatio principle, in view of which he attempted to single out, or to work out, an interpretative model of the universe and space that ‘adapted’ to the traditional reading of biblical passages.3 Although Mersenne’s studies in the arena of the middle sciences (astronomy, mechanics, acoustics, optics, ballistics, etc.) were never carried out separate from his theological concerns, his interest in physical issues mostly arose from contemporary debates. The subject of acoustics, mainly unison, clarifies this stance: Mersenne analyzed this musical consonance in the manuscript text Livre de la nature des sons by examining different phenomena of vibration, but only in the Harmonie universelle did he unveil the great utilité of unison for Catholic apologetics, regarding it more useful than mathematicae purae (pure mathematics) in talking per analogiam (by analogy) about the essence of Trinity. For a more comprehensive view of the development Mersenne’s concept of cosmos underwent, and of the different ways in which he intertwined metaphysical and physical issues, I will examine and compare the different images of the universe and the diverse approaches that surfaced in his writings, and in particular, in the largely unknown manuscript Livre de la nature des sons (dating back to circa 1626)4 and the 1648 Liber novus praelusorius. Along the same lines, I shall also focus on the Traité de l’harmonie universelle (published in 1627), the Préludes de l’harmonie universelle (1634), as well as the Harmonie universelle (published in 1636–1637) and its marginalia. I will start with Mersenne’s vehement rebuttal of Fludd’s theories and his fluctuating judgment on Kepler’s cosmos. My examination of Mersenne’s criticism of Galileo addresses three issues that rely on the combination of physics and metaphysics, specifically, his attitude towards those who upheld the idea of a heliocentric universe; his survey on the vacuum; and finally, his distrust of those who interpreted nature with geometrical models. For this purpose I will need to examine some of Mersenne’s statements concerning the epistemological status of mixed mathematics, since they elucidate the philosophical underpinnings of the questions he addressed to his contemporaries.

 Mersenne c. 1648c, 442–456; idem c. 1623c, 336–337. On the similarities between the Commentaire and the Brouillon, see Buccolini 2000, 101–107. 3  That approach was so widespread that even Lodovico delle Colombe – one of Galileo’s most bitter opponents – blamed those theologians who required philosophical subjects to be “accommodated” to Scriptural passages. See Delle Colombe 1608, 92r. 4  Mersenne c. 1626. See Fabbri 2007, 287–308. 2

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10.2  E  xamining Sounds and Cosmos in the Twenties: The Project of the Harmonie universelle Mersenne’s research on acoustics and the manuscript Livre de la nature des sons provide strong evidence for the fact that Robert Lenoble’s theory of a straight and clear shift from metaphysical and theological concerns to mechanism has been stressed unduly to date. Mersenne was, actually, ever more interested in natural philosophy  – mainly due to the debates that arose around Descartes, Galileo, Gassendi, and Roberval, among others; nevertheless, he went beyond a passive summary of his contemporaries’ theories, and also considered these topics from a theological perspective. As his survey on the science of sound attests – and in particular the Livre –, his mechanistic approach did not suddenly emerge at the beginning of the Thirties, and the 1634 treatises were not the first writings adopting such a philosophical approach. Nor did this approach result from his laying aside theological matters: the coexistence of mechanism and theological issues continues through to his final works.5 The draft of the Livre manuscript and the Traité de l’harmonie universelle (published in 1627 under the pseudonym of François de Sermes, and referred to in the Livre)6 are roughly contemporaneous: in Mersenne’s original project – which is outlined in the index (Sommaire) of the Traité – they were intended to be part of a more extensive work. The Traité is composed of two books, although the Sommaire announces 16 books, and the third was to tackle the very topic the Livre addresses. Indeed, the incipit of the unpublished Livre identifies the text as the “third book”: “I will deduce everything belonging to sounds in this 3. Book, as they are the subject and the fundament of music, which I will do in the following theorems.”7 In 1626– 1627 Mersenne, therefore, planned to write a sizeable treatise on universal harmony. The Traité continues the survey Mersenne carried out in La vérité des sciences and L’impiété des déistes: he tackles and refutes cabalistic, astrological and hermetical interpretations of the harmonic cosmos, focusing on Kepler’s astronomical and metaphysical model. At the time, two different approaches to harmony and music coexisted: the Livre addressed it on the basis of natural philosophy, whereas the Traité de l’harmonie universelle presented a strong metaphysical reading. Both recurred in Mersenne’s interpretation of the harmonic structure of the cosmos, and played a role in his rebuttal of Fludd’s and Kepler’s ideas of the cosmos and harmonic space. Before analyzing the Livre’s statements on the cosmos, it is worthwhile to consider its structure, to clarify its similarities and differences with that of the Harmonie 5  Buccolini (2000, 110) has shown that “science is at the service of exegesis” still at the end of the Forties. Conversely, Lenoble 1971 had tried to trace Mersenne’s gradual passage from theological concerns to a mechanistic approach. 6  See note 92. 7  Mersenne c. 1626, f. 1r: “Or ie déduirai tout ce qui appartient aux sons dans ce 3. Livre, car ils sont le sujet, et le fondement de la musique, ce que ie ferai aux theoresmes qui suivent.”

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Table 10.1  A comparison of the theories of sound in the Livre de la nature des sons and in the Harmonie universelle Livre de la nature des sons Le son ne se produit pas, ou du moins ne se communique pas selon toute son etendue, et toute sa puissance en un moment (théoreme II) Le son ne s’étand pas si loing, comme fait la lumiere, ni ne depend pas tant des corps par lesquels il a ésté produit, comme depend la lumiere du corps lumineux (th. VI) Le son est en quelque chose plus subtil que la lumiere, et en quelque chose il est moins subtil (th. VII) Le son represente souvent la grandeur, et les autres qualitez des corps par lesquels il a esté produit (th. X)

Harmonie universelle, Livre premier de la nature et des proprietez du sons Le son ne se communique pas dans un moment, comme fait la lumiere, selon toute son estenduë, mais dans un espace de temps (proposition VIII) Le Son ne depend pas tant des corps par lesquels il est produit, comme la lumiere du corps lumineux (prop. IX) It is a part of Expliquer enquoy le son est plus subtil que la lumiere, et s’il se reflechit (prop. X) Le Son represente souvent la grandeur, et les autres qualitez des corps par lesquels il est produit (prop. XI)

universelle – which was published roughly 10 years later – and its complementarity with the Traité de l’harmonie universelle (Table 10.1). Although this outline concentrates on correspondences between the titles of some théoremes of the Livre and some propositions included in the first book of the Harmonie universelle (titled Livre premier de la nature et des proprietez du sons), it should be noted that the content of the Livre also largely mirrors that of the Harmonie universelle – yet with some significant differences –, especially in their analysis of the echo and musical consonances, and of unison. It is not without significance that one of the most striking differences between the Livre and the Traité on one hand, and the Harmonie universelle on the other, is the issue of void, especially of intra-cosmic void: as will be shown later, Mersenne approached this topic by merging contemporary debates and Scholastic arguments. Even the matters addressed in the last book of the Harmonie universelle, namely the book De l’utilité de l’harmonie, had already been mentioned in the Index of the Traité de l’harmonie universelle: once again, this choice testifies Mersenne’s longue durée interest in showing the usefulness of harmony and music in ethics, rhetoric, upbringing, religion, and theology.8 Mersenne reframed his reading of universal harmony many times, alongside the emergence of new philosophical and mathematical theories: the choice to leave the Livre unfinished, to publish only 2 books of the 16 listed in the Index of the Traité, to add a great number of textual marginalia to the Harmonie, as well as to adjoin the Liber novus praelusorius to the second edition of the Harmonicorum libri, can all be seen as continuous attempts to update his work on the basis of the emerging different theories on the nature of matter, and on the structure of the universe, in those years.

8

 Mersenne 2003, Sommaire des seize Livres de la Musique, 23–26.

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10.3  B  elaboring Imaginary and Magical Harmonies: Toward a Universe of Strings Mersenne’s heated debate with Robert Fludd lasted many years: it started in the Quaestiones in Genesim, went on in the Traité de l’harmonie universelle – to which Fludd composed an answer with his Sophiae cum moria certamen (Frankfurt 1629) and Medicina Catholica (Frankfurt 1629) –, carried on in the pages of the Harmonie universelle, and eventually also saw the involvement of Pierre Gassendi, who was asked by Mersenne to refute Fludd’s alchemy – to which Gassendi devoted several pages of his 1630 Exercitatio.9 Fludd then, once more, replied to these attacks with the Clavis philosophiae et alchymiae Fluddanae (1633). Fludd’s Utriusque cosmi proposed an original chaos, which was then ordered by God, an infinite and fertile divinity who was also natura infinita et natura naturans (infinite nature and nature naturing).10 Mersenne refuted Fludd’s immanentism, the idea of a primordial, infinite and shapeless matter, as well as the Manichaeism that lay in the struggle, division and union of the opposing principles of light and darkness, voluntas (volition) and noluntas (nolition) – the latter emerging from the contraction of light –, which gave rise to the hierarchical structure of the universe.11 According to this model, the spheres of the universe were characterized by the permeation of two opposing pyramids of light (form) and darkness (matter), which reached a perfect balance in the Sun, the sphaera aequalitatis. Such a hierarchical order agreed rather well with the structure of a monochord, by means of which Fludd represented the world by analogy,12 hinting at a widespread Renaissance tradition that had reached its peak with Franchino Gaffurius’ and Cornelius Agrippa’s monochord, as well as Francesco Giorgi’s cosmos.13 The universe was equated with a monochord tuned by the divine hand, and alongside it the spheres of the elements, ether (planets) and Empyrean (angelic hierarchies) were arranged.14 The musical intervals mirrored the degrees of the formal principle’s descent into the matter. God – who was the sol invisibilis (invisible Sun) – embraced creation with a process 9  See idem 1636–1637, De l’utilité de l’harmonie, 48–49; Gaultier to Peiresc, 22 May 1631, in Mersenne 1945–1988, vol. III, 162–163. On Mersenne’s and Gassendi’s refutation of Fludd see especially Cafiero 1964a, b; Mehl 2000; Mehl 2001, 243–253, 263–270; Taussig 2009. 10  Fludd 1617–1621, vol. II, tract. I, 21. Mehl (2001, 264–266) has shown how Fludd alternated statements on immanentism with words proving divine transcendence. 11  Fludd 1617–1621, vol. I, tract. I, 25, 29. 12  See ibid., 79: “the machine of the world is almost like a monochord, whose string – whereby it introduces the agreement of parts – is the intermediate matter of the whole world.” 13  See Gaffurio 1496; Agrippa 1993, b. II, 387; Giorgi 1525, vol. VIII, chaps. XIV–XVI, ff. 178v–180v. The second edition of the book appeared in Paris 20 years later. 14  The Roman decree of February 4, 1627 placed the Utriusque cosmi into the Index librorum prohibitorum. Among the many aspects of Fludd’s work worthy of censure, in addition to his ideas about creation and primordial matter, the decree also disapproved of the monochordum mundi that flowed from those impious assumptions: Archive of the Congregation for the Doctrine of the Faith in the Vatican, Index, Protocolli BB, ff. 392r–393v; 408r–409v.

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of light emanation, by giving light to the Sun through the harmony of the formal octave, and spreading its influences on the Earth through the material octave. The proportions arising from these hierarchical essences did not correspond to geometrical proportions, nor to quantitative numbers; they were numeri numerantes (numbering numbers), rational and formal numbers that sprang from the divine essence’s emanation.15 According to Mersenne, Fludd, together with Francesco Patrizi, was a dangerous exponent of the metaphysics of light: by drawing even on Cabbala, he indeed focused on the identity ‘God-unity-light’ and composed everything of parts of light.16 In the Quaestiones in Genesim and, chiefly in the Traité,17 Mersenne analyzed at length the cosmological model of this “heretic,” “magician,” and Rosicrucian alchemist,18 by referring to the criticism voiced by Kepler in the Harmonices mundi libri V (1619) and in the Pro suo opere harmonices mundi apologia (1622). Mersenne focused on and disparaged Fludd’s numeri numerantes and his impious reading of the anima mundi (world’s soul),19 which identified the latter with God. Neither his monochord nor the two pyramids of form and matter took into account the actual measurements of the universe, as they assumed the existence of the same distance between Earth and Sun, and Sun and Empyrean. Instead, they should have at least represented the dimensions provided by Tycho Brahe’s hypothesis, which – Mersenne claimed – Fludd would not dare to refute.20 The most dangerous aspect of Fludd’s theory of the universe, apart from it being the result of an unruly imagination rather than careful analysis, was that it contributed to the spread of atheism, as it provided readers with a misleading idea of God and the Christian faith. The cosmos of this “evil magician” and – ironically – “more than luminous man”21 was as treacherous as Bacon’s idola specus (idols of the cave)22: they were even more detrimental than ignorance, because people could not readily release themselves from wrong theories relying upon imagination: “it is much better not to know this Harmony than to imagine it entirely different from what it is; as fake imaginations exert I do not know what tyranny over our minds, from which they can only free themselves with great difficulty.”23  Fludd 1617–1621, vol. II, tract. II, sec. I, b. I, chap. XVI, 50.  Mersenne 1625, 281. On Patrizi’s metaphysics of light see Deitz 1999. 17  See Mersenne 1623a, 709–710, 716, 1102, 1556–1558, 1561–1562, 1743, 1750; idem 2003, b. II, th. XII-XIV, 387–427. See also idem 1636–1637, De l’utilité, 49. 18  On Mersenne and alchemy see Beaulieu 1993. 19  See Mersenne 2003, b. II, th. XIII, 409–419. Mersenne widely rebutted the idea of anima mundi: see, for instance, idem 1623a, 1452; idem 1623b, 23–24; idem 1624b, 365–385. 20  Concerning Tycho’s hypothesis, Mersenne identified a distance of 1142 semi-diameters of the Earth between the Earth and the Sun and 128,8 similar semi-diameters between the Sun and the firmament. Mersenne 2003, b. II, th. XIII, 411. 21  Mersenne to Gassendi, 5 January 1633, in Mersenne 1945–1988, vol. III, 356. 22  Mersenne (1625, 206–208) examined Francis Bacon’s idola. 23  Mersenne 2003, b. II, th. XIV, 418–419: “il vaut beaucoup mieux ne connoistre point cette Harmonie, que de se l’imaginer tout autrement qu’elle n’est; car les fausses imaginations exercent ie ne sçay quelle tyrannie sur nos esprits, dont ils ne se peuvent dégager qu’avec une tres-grande 15 16

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Although the Livre (f. 16r) claimed not to address the topic of planetary music, Mersenne developed this in a manner complementary to the Traité de l’harmonie universelle and akin to the analysis carried out in the Harmonie universelle. His distance from Fludd’s illustrations – but also from Kepler’s geometrical harmony – can be seen in both the monochord Mersenne described in the Livre, and the one he outlined in the Harmonie universelle. Folio 33r of the Livre contains calculations of how many octaves there were between the center of the Earth and the firmament (Fig. 10.1). The table towards the left of the page displays the number of octaves (from the first to the 20th) in roman characters, whereas the lengths of the string are given in inches, in arabic numerals. The text clarifies that the length of the semi-diameter of the firmament would embrace about 37 octaves – i.e., it would be the 37th progression of the double proportion –, which would correspond to 577.332.000.000 inches. Once Mersenne sketched out this data, he explained that this string could actually generate actual sounds, although man would not be able to hear them because of the physiological limits of his hearing. In the Harmonie universelle Mersenne further developed this analysis and perspective by integrating it with comments taken from astronomical debates. He shifted his attention from the length of a virtual string to the weight of the planets that were hung upon it. Here he needed to decide whether each planet was composed of the same matter as Earth, and whether it might be the center of its own astronomical system. He thus needed to admit the ontological homogeneity of the cosmos and the plurality of the reference systems of revolution – two tenets refused by the Aristotelian-Ptolemaic view, but in effect in both the Copernican and Tychonic systems. He wrote down a table in which the weight of the Earth corresponded to a range between the 41st and the 43rd octave. We might similarly know the harmony of the seven Planets, and of the Earth which are hung on eight identical chords which have the same thickness and length, as long as we know their weight which we can find based on their magnitude, by assuming that each part of the Planets is as heavy as each part of the Earth, as is claimed by some of those who build particular systems with them and who say that if a part were separated from the Planets, it would come back to them as to its center.24

In conjunction with the idea of a finite universe, which would be enclosed in the outmost sphere of the firmament, Mersenne even claimed that “we can continue the same progression as long as we find a number that corresponds to the weight of the thickness of the firmament.”25 As early as in the Questions Théologiques Mersenne had sought to employ sounds in his investigation of the quantitative dimension of the firmament: in the 44th question he wondered “what strength voice needed to be carried and heard up

difficulté.” This judgment followed the words La Mothe Le Vayer had employed in his Discours sceptique sur la musique, which Mersenne published in the Questions harmoniques (1985b, 154). 24  Mersenne 1636–1637, Des mouvemens et du son des chordes, 185–186. 25  Ibid., 187.

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Fig. 10.1 Mersenne, Livre de la nature des sons et de la manière qu’ilz s’épandent par le milieu et qu’ils arrivent à l’oreille et au sens commun. Paris: Bibliothèque de l’Arsenal, MS 2884, f. 33r

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to the Moon, the Sun and the firmament, both naturally and artificially.”26 The voice might be directed into a tube to increase its extension, as “we can compensate in length what it will loose in width” – a statement that was in full agreement with the principle of mechanics set out by Galileo.27 Nevertheless, in raising this question Mersenne ended up resorting to a traditional theological argument: although no voices or sounds were strong enough to reach the sky, angels could make the human sounds audible even in the Empyrean, thus creating a concert performed by the union of the Triumphant and Militant Churches.28 The debate on the actual dimension and setting of the cosmos played a key role in establishing the reliability of the different models of harmony that had been put forward to that date. Mersenne did not acknowledge the superiority of the Copernican system, much less that of the Keplerian model, despite praising the harmonic proportion of their planetary arrangements. In the Traité the search for musical consonances was, indeed, applied to not only the heliocentric system and Kepler’s cosmos, but also the Ptolemaic and Tychonic worlds, with the admission that “we do not know the distances, or the motions of planets, precisely enough.”29 Although he clarified that Kepler’s planetary harmonies were subject to a fair approximation, Mersenne drew a clear distinction between Kepler’s model – worthy of consideration and study – and Robert Fludd’s in the Utriusque cosmi. They epitomized the discrepancy between mathematics and hermetical symbolism30: Kepler’s analysis was based on geometry and used the compass, whereas Fludd’s reading drew on alchemy and employed fire and alembics.31 Nevertheless, even Kepler’s geometrical model of space and the universe would eventually cause Mersenne to be bewildered.

10.4  H  armonic Archetypes and Unfathomable God: Moving Away from Kepler’s Geometrical Cosmos In the Livre and the Harmonie universelle Mersenne did not propose the actual presence of musical consonances or of perfect scales in the skies, but only the possibility of defining which sounds planets might correspond to. By contrast, the Traité was quite different in this regard. Especially regarding the relationship between mathematics, metaphysics and physics, Mersenne’s thought underwent several changes.  Mersenne 1985c, 417.  Ibid., 417–418: “If the strength of the voice does not lose anything from one side that she does not recover from another side (as we say of moving forces, and of Machines, which do not lose anything in length of time that they do not recover in strength [...]), we need to conclude that the voice of a man, and every other sound can be heard from the Earth until the firmament.” 28  Ibid., 421–422. 29  Mersenne 2003, b. II, th. VIII, 361. 30  See idem 1623a, 1556–1557. 31  See idem 2003, b. II, th. V, 338. 26 27

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In the wake of Kepler, Mersenne established a point of union between metaphysics and mathematics in the Traité, thus leaving open the possibility for man to grasp divine harmony and, therefore, the harmonious archetypes of creation  – even though, at this time, he had already pointed out the discrepancy between physics and mathematics, often stressing that geometrical models and natural phenomena only approximate each other, but do not fully match each other.32 In the Harmonie universelle this possibility was denied in a rather definite manner, and the change in his epistemological thought brought about the harsh tones he then directed against Kepler – thus passing on from praising to blaming him.33 The Traité summed up Kepler’s idea of a harmonic cosmos: Mersenne sketched out three outlines that displayed the information provided in the Harmonices mundi libri V, albeit with several clerical mistakes.34 Moreover, in the Traité the archetypal divine music was adopted as reference point for all kinds of music: The Divine Music, on which our own depends, is in the divine intellect. […] The created music lies in the Divine one, and can be divided into as many parts as the species in the world; it is nothing else than the order and the harmonic proportion that is between the parts of the world and each individual in particular. […] The World music is the harmonic order and proportion, that is pleasant to the intellect, which is in the fabric of the heavens and of the elements, and their properties and motions.35

In this text, Mersenne claimed a perfect co-essentiality between God and mathematical propositions, which were said to be as eternal as God’s essence.36 Indeed, the interior divine music consisted of the harmonic proportions that were originally contained in the essence of God, intellectually in his intellect, in an exemplary manner in his ideas and practically in his will.37 This bears traces of the Keplerian model: the musica mundana (music of the world), which depended on the divine music, was pleasant to the human mind and seemed to be able to provide a gateway to accessing the divine intellect and essence.38 Mersenne narrowed the definition of the interior divine music to the concept of cosmic harmony, with the specific aim of showing how the movements, intervals and magnitudes of planets were comparable to musical consonances. However, he always refers to ‘comparisons,’ never a perfect match or identity. In the Traité, those statements that were more indebted to  See Boutroux 1922, 286; de Buzon 1994; Fabbri 2003, 151–156.  Mersenne’s rebuttal of Kepler throughout the Harmonie universelle has been examined in Field 2003, 29–44. 34  See Mersenne 2003, b. II, th. VIII, 356–358. 35  Ibid., b. I, th. XIII, 80; th. XIV, 83; th. XV, 86. 36  See Mersenne 1624a, 446–454. Jean-Luc Marion proposed a reading of Mersenne’s first three writings (Quaestiones in Genesim, Impiété and Vérité) in light of the theory of the univocity between God’s ideas and essence on one hand, and mathematical truths on the other – and this theory recurs in the Traité as well: Marion 1991, 161–178. See also idem 1994. 37  See Mersenne 2003, b. I, th. XIII, 82. See also idem 1623a, 332, 436; idem 1624a, 411; idem 1624b, 311–312. 38  Nevertheless, neither did Mersenne embrace the Platonic doctrine of innatism and reminiscence in the Traité, nor did he undertake a stronger rebuttal of Kepler’s reading of it in the Harmonie universelle. See Mersenne 1636–1637, Des consonances, 86. 32 33

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Kepler’s thought indeed coexisted with an incomplete mathematization of nature, which relied on a difference between mathematics and physics which increased in the course of his subsequent writings. The identity of the essence of God and the archetypal world containing the divine ideas was still mentioned in the Harmonie universelle, but Mersenne at the same time firmly denied the possibility that the human mind could rise to the archetypical world by means of mathematics. This was mainly due to the increasing divergence between mathematics, physics and the realm of possibilities from which God chose freely: “the intelligible world, or archetype, as in the divine ideas, is not different from the divine essence; but the big challenge is to know how he made it visible, and how he made it subject to time and place.”39 Mersenne ruled out any analogy that could have agreed with immanentism, in the form in which it appeared in Kepler’s belief in the Trinitarian image that God would have engraved in the spherical structure of the world and in his interpretation of the planetary animae motrices (moving souls) of the planets.40 The unique analogy between God and the physical world that Mersenne held  – and developed throughout the years – was one between the divine Trinitarian essence and unison.41 Mersenne’s emphasis on the divine transcendence prevented him from continuing to follow Kepler’s model: the perfect congruence between space and geometry, and the co-essence and co-eternity between God and mathematical truths that featured in Kepler’s thought, made the relationship between God and cosmos, Creator and Creation, a controversial and puzzling issue.42 The geometrical image of the divine essence that God would have impressed into the cosmos and every level of creation (which Kepler often referred to in his works and correspondence) was at odds with the statements on the unfathomable will of God, and also with the voluntarism that characterized most of Mersenne’s work. Nor, as is well known, did Mersenne embrace the Cartesian model of creation of mathematical truths, or agree with the consequent distinction between divine essence on one hand, and mathematical propositions and archetypes on the other.43 Nevertheless, he regarded the perfect knowledge of several mathematical propositions as not sufficient for grasping the concept of divine archetypes, which concerned everything that did not contain any contradiction.  Idem 1636–1637, Des instrumens de percussion, 78.  See Kepler 1938, Praefatio antiqua, 23; chap. II, 45–46. Idem 1953, b. I, 51. On Kepler’s interpretation of the planetary souls, see, for instance, idem 1940a, b. IV, 264–286. 41  See Bailhache 1994, 22–23; de  Buzon 1994, 126–127; Fabbri 2008, 58–67; Van Wymeersch 2011, 261–274. 42  Within the broad literature on the theological roots of Kepler’s cosmology, see especially Field 1984; eadem 1988; Methuen 2008, chap. 7. 43  By referring to Descartes’ letter of April 15, 1630, Lenoble (1971, 277) stated that Descartes and Mersenne shared the same view with regard to the absolute freedom of God’s will and the rebuttal of Naturalism. Conversely, Jean-Luc Marion (1991, 163–167, 174–176, 178–203) emphasized the difference between Mersenne’s and Descartes’ readings, by viewing Kepler as the implicit interlocutor in the 1630 letters from Descartes to Mersenne, as well as the model Mersenne gestured to in defining the mathematical truths. 39 40

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The unfathomableness of the decreta Dei (decisions of God), which ensued from the voluntarist theology, had significant repercussions on Mersenne’s rebuttal of three cosmological models – Bruno’s, Kepler’s and Galileo’s – which he interpreted as reliant on necessitarism or, at least, on a serious attempt to limit God’s free will. Mersenne’s emphasis on the absolute omnipotence and freedom of God embraced both the spatial and the temporal dimensions of the universe. Mersenne’s analysis and refutation of Bruno’s arguments concerning the relationship between God’s infinite power and the necessary creation of an infinite universe – which would be the infinite effect of God’s infinite power – have been largely examined with reference to the infinity of space.44 Even when Mersenne seemed to be open to the possibility of such an infinite universe, he continued to refer to voluntarism: God could have created – not should have created, as Bruno had claimed – an infinite universe, if he had wanted to do so. As for Jordan, although he uses bad fundaments, it is, however, rather probable that the world is infinite, if it can be so. For why do you want an infinite cause not to have an infinite effect? On other occasions, I had other demonstrations against this, but the solution is effortless.45

The greatly praised simplicity of Copernicanism was also not looked upon as a parameter according to which its superiority over other astronomical hypotheses could be established, inasmuch as God, who was absolutely free in his ad extra (external) activity, might have created a more or less complex universe.46 But we have neither science nor revelation concerning the way in which God regulated the movements of the Universe; since, although He makes nothing in vain and there is nothing superfluous in His works, there can be significant reasons for which He arranged for the firmament to turn and for the Earth to rest. This is the reason why it seems to me that it is more appropriate to suspend our judgment than to be carried away by conjectures.47

Mersenne’s voluntarism also had consequences for the difficult issue of the eternity and immutability of the world. “Why could not God cease conserving the Universe?”48 God might interrupt the existence of the universe at any given time and he would be able to change the course of nature. As Mersenne stressed in many of his writings, God could have chosen to order the celestial world differently from the regularity observed in the sublunary world, or in a way that differed from the simplicity on which Copernicus and Galileo built  In L’impiété des déistes Mersenne paraphrased and refuted meticulously Bruno’s De l’infinito and De immenso. See Del Prete 1998, 139–161; Buccolini 1999; Del Prete 2000; Granada 2000; Margolin 2004. For Bruno’s infinitism see also Granada’s Chapter 8 in this volume. 45  Mersenne to Rey, 1 April 1632, in Mersenne 1945–1988, vol. III, 275: “Quant à Jordan, encore qu’il se serve de mauvais fondemens, neantmoins il est assés probable que le monde est infini, s’il le peut estre. Car pourquoy voulés-vous qu’une cause infinie n’ait pas un effet infini? J’ay autresfois eu d’autres demonstrations contre ceci, mais la solution en est aisée.” See also Mersenne 2003, b. II, th. I, 334. 46  See idem 1623a, 844. 47  Idem 1985b, Epistre, 108–109. See also idem 1623a, 914; idem 1985c, 216. Idem 1985a, 37. 48  Idem 1624a, 324–325. 44

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their cosmos, and from Kepler’s geometrical space. If some propositions of arithmetic and geometry were recognized by the human mind as being apodictically true, such a degree of certainty could hardly be found in physics – nor, therefore, in astronomy. This led Mersenne to tirelessly conduct research: such certainty was considered necessary to claim the truthfulness of an astronomical or mechanical theory.49 Mersenne’s forsaking of the Keplerian model of cosmos – which was chiefly the aftermath of his disapproval of Kepler’s metaphysical underpinnings – involved the issue of the planetary concert as well. Mersenne questioned the existence of a musica mundana, both in the form of an audible sound produced by planets, as well as in the form of a rational concert caused by exact musical proportions that the human mind might be capable of discovering by comparing the orbital speeds of the planets, as well as their distances from the center of the cosmos (both in the heliocentric and in the geocentric system).

10.5  The End of the Planetary Concert Leaving behind the refutation of deism, alchemy and hermetism – which had characterized his early works up to the 1634 Questions, and to which his rebuttals of Fludd, Patrizi, and Bruno are to be counted –, Mersenne focused on the geometrization of nature often advocated by his contemporaries. His idea of the universe at the time can be summed up as a finite Tychonic cosmos, in which planets revolved through a generic plenum of subtle air, and their movements were ordered according to a harmonic setting – even though he did not specify a model for this order. Spurred on by contemporary debates, he put all his effort in discussing – and, in the end, rejecting – both Kepler’s and Galileo’s models of cosmos and space. This stance mostly arose from Mersenne’s definition of the epistemological status of the mathematicae mixtae, and among them astronomy. As has been pointed out since Popkin first published his sharp analysis, Mersenne never presented a true explanation of the universe, only the most probable one50: the interplay between his ‘mitigated skepticism’ and theological assumptions prevented him from gaining exhaustive knowledge of the physical world.51 Mersenne selected from different explanatory models, and from time to time he chose one as both the closest to the true constitution of nature, and his best ally in his war against atheism and heresy.  In this regard, one of Descartes’ answers to Mersenne is enlightening: “Requiring from me a geometrical demonstration in a matter that depends on physics is wanting from me impossible things” (Descartes to Mersenne, 17/27 May 1638, in Mersenne 1945–1988, vol. VII, 231). 50  On Mersenne’s ‘methodological skepticism,’ see Popkin 1957; idem 1979, 130 sq. See also Dear 1988, 25–47. Mersenne’s epistemological skepticism is instead advocated by Joly 1999, vol. II, 257–276. 51  Of the scholarly literature on the relation between voluntarist theology and modern science, see esp. Harrison 2002; idem 2005; Henry 2009. 49

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In order to place Mersenne’s survey on space and his attitude about contemporary theories into context, it is useful to follow a brief diversion into the epistemological status of the mathematicae mixtae. As a passage of the Questions théologiques epitomizes: As we cannot know the true reasons, or the science of what happens in nature, since there are always some circumstance, or instance that make us doubt whether the causes we figure out are true, and whether there are any at all, or whether there might be other ones, I do not see how we have to call for any other thing from the most savants than their observations, and the comments they will have made about the different effects or phenomena of nature.52

Nevertheless, within the mathematicae mixtae Mersenne had a predilection for optics and acoustics, as he valued them for carrying a higher level of certainty due to their strong geometrical roots. He clarified that human reason was, indeed, also gifted with an intellectual light – the ‘natural light’ given by God – that relied on the soul’s incorruptibility and immortality. The soul, which was just as eternal as mathematical truths, was also able to formulate arithmetical and geometrical propositions. This epistemological model had the advantage of managing the inaccuracy of sensible experience and of ensuring that a very high level of reliability could be attained, at least in those mathematicae mixtae that were more closely related to geometry, such as optics and acoustics. It is most certain that the mind has a being that is distinct from body and matter, and that depends only on the one who has the being of himself, whose image we bring on […]. From there it comes that it [i.e. the mind] makes propositions that are eternally true, for example […] that all the lines drawn from the center of a circle to its circumference are equal […], and an infinite number of similar propositions that the mind of man knows, or can know perfectly. This cannot happen unless it holds them formally, or eminently, and unless it has the same incorruptibility that it knows in them […][;] suffice it here to assume that the mind of the musician which considers sounds is incorruptible and immortal.53

Human knowledge of mathematical truths no longer flowed from the grasping of divine ideas, as Mersenne was more inclined to suggest in the Traité de l’harmonie universelle. It is God who gave man an incorruptible and immortal mind, enabling him to have perfect knowledge of the things endowed with the same perfection and eternity as he himself. Although Mersenne often denied the possibility of reaching apodictic conclusions in mixed sciences, he nevertheless admitted that the method and the experiences carried out in those sciences help man perfect natural light: [the intellect] makes up for the failings of the external senses, as well as of the internal ones, and it does so through a spiritual and universal light that it has of its own nature since the

 Mersenne 1985c, 224: “Puisque nous ne pouvons sçavoir les vrayes raisons, ou la science de ce qui arrive dans la nature, parce qu’il y a tousjours quelques circonstances, ou instances qui nous font douter si les causes que nous nous imaginons sont veritables, et s’il n’y en a point, ou s’il n’y en peut avoir d’autres, je ne voy pas que l’on doive requerir autre chose des plus sçavans que leurs observations, et les remarques qu’ils auront faites des differens effets, ou phenomenes de la nature.” 53  Mersenne 1636–1637, Livre premier de la Voix, 80 (my emphasis). 52

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The natural light is spiritual, in that it belongs exclusively to the mind and depends directly on God; it is universal, as it belongs to all of mankind; and it is perpetual, as it has been present since the beginning of the creation of man. The mind does not hold innate principles: the natural light – upon which the main difference between men and animals relies – needs to resort to the recta ratio (right reason), whose acts are possible in men that are of sound mind in their adulthood, by leaving behind the sensory illusions, as well as by carrying out research and having experiences.55 However, the natural light achieves the highest perfection only after entering into the glory of Christ, when the supernatural light enables it to know the divine essence. This position provides a good explanation for Mersenne’s need to repeat experiments, and to compare his results with the information provided by his contemporaries. Furthermore, his claims about the impossibility of considering physics as exact a science as pure mathematics, as well as his rejection of transposing geometrical patterns and apodictic demonstrations to the field of natural phenomena, rule out the possibility that the mathematicae mixtae can reach any exhaustive knowledge. These assumptions led Mersenne to suspend judgment – as in the case of astronomical issues – or to an endless checking of other philosophers’ experiments – as happened with the research carried out mostly in the mixed sciences, such as optics, acoustics, ballistics and mechanics. In the case of cosmic harmony, Mersenne could not verify quantitative variables and planetary patterns, and therefore he could not provide rigorous demonstrations or formulate the relevant apodictic conclusions, based just on an alleged likeness between the planets and other physical bodies. This epistemological position, in addition to the theological voluntarism that underlay Mersenne’s works, played a crucial role in marking the fall of the traditional idea of harmonic cosmos. Notwithstanding the fascinating theory of Kepler’s harmonic cosmos, his geometry of space – which drew on the Neo-Platonic philosophy and, especially, on Proclus’ reading of Euclid’s Elements  – turned out to be unsatisfactory. This was not the case for metaphysical reasons only. Kepler’s model still assumed the subordination of the musica instrumentalis to the musica mundana, yet it was no longer based on the numeri numerantes: the music played by man employed the proportions according to which God had created the world, and which corresponded to the rationes that resulted from the inscription of a diameter, triangle, square, hexagon, octagon, and pentagon within a circumference.56 54  Idem 1625, 193: “[… l’entendement] supplée aus manquemens des sens exterieurs, et même des interieurs, ce qu’il fait par une lumiere spirituelle, et universelle qu’il à de sa propre nature des le commencement de sa creation […]. Cette lumiere naturelle de l’esprit est perfectionée, et mis en acte par le moyen de la meditation, de l’étude, de l’experience, et des sciences […].” 55  Denying the existence of that lumen would imply that one is agreeing with skepticism and reducing man to the animal-like status: Mersenne indeed blamed skepticism for “reducing us shamefully to the vilest level and to the lowest state of beast” (Mersenne 1625, Dédicace, 8). 56  See Kepler 1940a, books I, II, III.

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Conversely, in the wake of Vincenzo Galilei, Mersenne abandoned the parallelism between these two musicae and relied on research carried out within the empirical dimension. According to Mersenne, the legend of Pythagoras  – who was said to have defined the ratios of the sounds produced by both the planetary concert and the hammers in a smithy by means of experimentation with the monochord, glasses, pipes, etc. – implied, firstly, the perfect overlap of the musicae instrumentalis and mundana, establishing the dependence of the second on the first57; secondly, the dialogue between the a priori and the experimental arena. The traditional interpretation of Pythagoras’ discovery of musical consonances – put forward by Franchino Gaffurio58 and Gioseffo Zarlino, among others – was questioned and refuted thoroughly by Vincenzo Galilei, and thereafter by Mersenne59: they reproduced the experiments ascribed to Pythagoras and pointed out their errors, arguing that the procedure he had adopted was strongly indebted to the a priori process and belonged primarily to numerology (the so-called numeri numerantes). This new reading also entailed the liberation of music (and techne) from its subordinate role of the ‘imitation of nature,’ as well as breaking the parallelism between the numerical proportions that corresponded to the consonances and proportions which shaped the planetary order. In his diatribe against the music theoretician Gioseffo Zarlino, Vincenzo Galilei came to assert the artificiality of every tuning system, including the one that had been largely regarded as natural until then. Mersenne, too, in his Harmonie universelle, overturned Zarlino’s statement by claiming that even the syntonic-diatonic intonation was founded on art rather than nature.60 Although Mersenne did not subscribe entirely to Vincenzo Galilei’s strict position, the line they traced between cosmic harmony and music played by man represented a watershed in the interpretation of the harmonic space of cosmos. Mersenne’s attempts, in the Traité and, partially, in the Quaestiones in Genesim, to define a credible model of cosmic harmony, and to subordinate the musica instrumentalis to the musica mundana, were ultimately ineffective. He rejected this theory also because the numerical proportions of musical consonances in human concerts did not derive from either ‘natural proportions’ or divine rationes. Kepler’s idea of harmony – which the Traité often echoed – called for a co-essence of God, geometrical shapes and musical consonances, whereas in Mersenne’s thought the unison (1:1)  – which he often returned to when discussing the concept of the Trinity – turned out to be no more than a very effective analogy in his attempt to convert his readers to the truthfulness and rationality of Catholicism, as well as to employ music as one of the most powerful weapons in his campaign against anti-Trinitarians.  See Mersenne 2003, b. II, th. VIII, 359–360.  See Gaffurio 1492; Galilei 1581, 134. Vincenzo Galilei’s survey was analyzed by Palisca 2000, 509 sq. 59  Mersenne 2003, b. II, Préface, 295; th. XIII, 413. Idem 1636–1637, Nouvelles observations, 25–26. On Mersenne’s indebtedness to Vincenzo Galilei see the seminal work by Palisca 1998. See also Cohen 1984, 85, 101–102, 183–184. 60  Mersenne 1636–1637, Livre des Instruments, 8–9. 57 58

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The absence of musical consonances in Galileo’s interpretation of the harmonic order of the cosmos61 – which largely drew on the ‘very perfect harmony’ of the Copernican system – might instead have urged Mersenne to analyze bodies, space and the structure of the universe only with the ‘tool’ of acoustics, rather than with patterns based on harmonic proportions and musical archetypes.

10.6  M  ersenne’s Reading of Galileo’s Universe: Contrasting Atoms, Void and Heliocentrism Galileo’s research had aroused Mersenne’s interest since the end of the Twenties: in addition to engaging with Galileo’s studies through his correspondence, in 1634 the Minim published the first edition of the Mecchaniche in French translation; he summed up the first 2 days of the Dialogo in the Questions théologiques – and at the end of the summary, he added the text of the 1633 sentence against Galileo and his abjuration; he also provided a French rendition of the Discorsi  under the title Nouvelles pensées de Galilée.62 As the following sections shall show, Mersenne’s idea of the Mosaic cosmos was, indeed, strained by the issue of the void as well as the alleged existence of an infinite number of atoms. Galileo’s geometrization of nature was, alongside Kepler’s and Descartes’, one of the most recurrent debating points in Mersenne’s thought. It was, indeed, based on a merging of Platonic and Archimedean readings of the universe, which still seemed to rely on an unfounded faith in the cognitive ability of men, who would have perfect knowledge of the mathematical propositions according to which God created and ordered nature. However, Galileo did not run the risk of opening up the knowledge of divine essence and archetypes to human beings, as he neither offered a strong theory about the coessentiality between divine essence and mathematics, nor a doctrine based on innatism. Mersenne did not join Galileo’s Platonism with Kepler’s: Galileo’s model of ‘intensive knowledge’ – according to which the human knowledge of several mathematical propositions equals that of God – did not agree with Kepler’s knowledge of the divine reasons and Trinitary’s essence.63 The well-­ known excerpt on the intendere intensivo (intensive knowledge) – which is delivered at the end of the first day of the Dialogue – was, indeed, not formulated in the 61  See Galileo 1933b, 148. On the geometrical order of the Galilean universe see Galluzzi 1979. On Galileo’s idea of the harmony that pervaded the heliocentric system see Fabbri 2008, 211–228. 62  On Mersenne-‘editor’ of Galileo, see Costabel and Lerner 1973, vol. I, 15–43; Shea 1977, 55–70; Raphael 2008. Mersenne owned a copy of the Saggiatore, too: Buccolini 1998. 63  See Galileo 1933b, 128–129. Conversely, Jean-Luc Marion supposed that Galileo and Kepler shared the same reading with regard to the definition of the ontological status of mathematical truths, and the univocity between divine and human science: Marion 1991, 204–227. On the difference between Galileo’s and Kepler’s mathematization of nature see, rather, Fabbri 2008, 189–196. Galileo’s distance from Kepler’s epistemological model also emerged from the pages of Galileo’s letter to Gallanzoni (July 16, 1611). For an enlightening comparison of these two natural philosophers, see Bucciantini 2003.

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course of an emphatic extolling of human abilities: in those pages Galileo expressed his distrust towards those who believed that men were capable of knowing nature exhaustively, and that any finalistic reading could interpret the book of nature correctly: “Very great seems to me the smallness of those who would like God to have made the universe more proportionate to the small capability of their discourse rather than to His immense, or more exactly infinite, power.”64 Only few mathematical propositions could be saved from the uncertainty that surrounds the world of man, which was eventually comparable to the world of earth-worms and maggots – as Galileo had written in his 1624 letter to Francesco Ingoli.65 According to Galileo, the existing relation between nature and human mind was established in keeping with the temporal order of Creation. God created the universe by choosing freely from the realm of possibilities66; only afterwards did he create the human mind, giving it the ability to discover – even if with great effort – a part of the universe: “But I would reckon sooner that nature made things beforehand, according to her manner, and then fabricated human discourses so that they were able to understand (albeit with great difficulty) something about her secrets.”67 However, it was not possible to state the opposite: man would not be able to narrow the divine model of creation down to what his mind could conceive; man had to be bound to the description of nature as de facto, without inquiring how it could be de jure.68 Indeed, man could not say or know anything about the essence of God, his plans, as well as the essence of natural bodies. The possibilities of human knowledge that Galileo traced were secured by the metaphysical underpinnings underlying his natural philosophy: firstly, God’s immutability – which expressed itself both through nature’s inexorability, and the fact that God neither intervenes with miracles in the regular course of nature nor breaks the laws he gave to it69; secondly, the mathematical structure God imparted to nature, which could finally be grasped by the human mind thanks to geometrical demonstrations and sensible experiences. Of the regularities uncovered in the movement of natural bodies the principle of simplicity that nature seems to follow epitomizes Mersenne’s and Galileo’s divergence. In Galileo’s thought it played a crucial role both in his astronomical model – surfacing in his adhesion to heliocentrism and to the circularity of planetary orbits – and in his survey on how bodies behaved on the Earth. The third day of the Discorsi sheds light on how Galileo’s belief in the principle of simplicity was the  Galileo 1933b, 397. See also ibid., 126–127, 394.  See Galileo 1933a, 530. 66  See idem 1933b, 45. 67  Ibid., 289: “Ma io stimerei più presto, la natura aver fatte prima le cose a suo modo, e poi fabbricati i discorsi umani abili a poter capire (ma però con fatica grande) alcuna cosa de’ suoi segreti” (my emphasis). With “discorsi umani” Galileo also refers to mathematical definitions: see idem 1933d, 74. 68  See idem 1933b, 289. See also ibid., 444–445; idem 1932, 351. On the distinction between de facto proof and de jure legitimacy (geometrical principles) in Galileo’s physics, see Stabile 2002, 225 sq. 69  On Galileo’s ‘inexorable nature’ see Stabile 1994; idem 2003. 64 65

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result of a balance between mathematical demonstrations and sensible knowledge. Galileo claimed that he did not grow confident about the exactness of his law of free fall until after verifying that the law was in agreement with what naturalia experimenta revealed to human senses. Moreover, he had considered nature’s customs (consuetudines) and procedures in other fields as well, remarking that “she habitually employs the first, simplest and easiest means.”70 Therefore, Galileo did not propose simplicity as an a priori principle, but rather as something that was observed and noticed with sensory experience, and that concerned how nature acted de facto. Mersenne shared this belief that nature usually follows the simplest way: “if nature did not follow the shortest way, it would do useless movements and it would work in vain.”71 Nevertheless, he refrained from inferring anything from this about the simplicity of God’s plans and actions. Nature was not ‘inexorable,’ and God could change her course and make her complicated at any time.72 Furthermore, Mersenne clarified, any definition of what was considered simple and easy by the human mind would not be valid if compared to God’s knowledge and power. In the second day of the Dialogo Galileo had praised the simplicity of the heliocentric hypothesis.73 At the end of Mersenne’s résumé of this part of Galileo’s Dialogo in the Questions théologiques, he instead invoked God’s almightiness by claiming that “for God it is not more difficult to make every part of the circumference immobile than the center.”74 In addition to dissociating himself from the use that Galileo made of God’s immutability – which clashed with God’s voluntarism, which Mersenne insistently referred to –, Mersenne’s refusal of heliocentrism went through the rebuttal of the mathematical structure of nature that underlay Galileo’s natural philosophy and led him to advocate the truthfulness of Copernicanism. As Galileo formulated in his more complete version of the correspondence between the mathematical analysis of the continuum and the structure of matter, when abstracting from the imperfections of matter, man could “produce no lesser demonstrations [when talking about matter] than the other rigorous and pure mathematics do.”75 This was another tenet Mersenne could not share: man cannot neglect the accommodations to which mathematical models are necessarily subject when he adds matter to immaterial shapes, forces, movements, etc.76 Such an approximation is not to be accepted: for instance, bodies cannot be assumed to move in the vacuum since the existence of void is false, as Mersenne still pointed out in his 1643 letter to the Accademia dei Lincei.77 Mersenne’s rebuke of Galileo’s mathematization of nature fully expresses itself in  Galileo 1933d, 197; trans. 1974, 153.  Mersenne 1636–1637, Des instrumens à vent, 250. See, for instance, also Mersenne to Rey, 1 September 1631, in Mersenne 1945–1988, vol. III, 188. 72  See also note 47. 73  Galileo 1933b, 148. 74  Mersenne 1985c, 385. 75  Galileo 1933d, 51. See idem 1933b, 234. 76  See idem 1933d, 155; trans. 1974, 113. 77  Mersenne to Lincei, 1 July 1643, in Mersenne 1945–1988, vol. XII, 222. 70 71

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the emphasis he put on Galileo’s inaccuracies in the experiments – and failures – to prove his assumptions: indeed, he often scolded Galileo, contrasting the results that came from his great number of expériences with Galileo’s thought experiments.78 Mersenne intertwined this topic with the analysis of Galileo’s atomism as well, and developed it throughout his private correspondence, in the Harmonie universelle and its marginalia, in the Nouvelles observations added to the Harmonie universelle in 1638, in the Cogitata physico-mathematica of 1644, in the Nouvelles pensées de Galilée of 1639, in the Novarum observationum tomus III of 1647, as well as in the Liber novus praelusorius which had been added to the Harmonicorum libri XII in 1648. Mersenne’s survey on void – which has been largely examined by many scholars – would ultimately characterize all of his final works.79 Along these lines, in 1643 Mersenne wrote a letter to the Lincei in which  – implicitly drawing on Descartes’ opinions on Galileo’s Discorsi which he had expressed 5 years earlier in reply to Mersenne’s request80 – he raised several questions as to what the Discorsi had stated.81 Galileo’s atomism, which stemmed from the idea of transferring the mathematical analysis of the continuum to natural phenomena and to the idea of matter, strongly piqued Mersenne’s interest.82 Galileo replaced the Aristotelian definition of a continuous quantity that can be actually divided only into continuous quantities83 with that of a continuous quantity composed of an infinite number of indivisible and unquantifiable (“non quante”) parts.84 Descartes had questioned, and Mersenne would question later, the interpretation of the Rota Aristotelis paradox Galileo provided in the Discorsi, as well as his definition of a continuum composed of an infinite number of unextended points, among which an infinite number of indivisible vacua (“infiniti vacui non quanti”) were interposed.85 Whereas Descartes stressed the fact that the existence of Galileo’s 78  See, for instance, Mersenne 1636–1637, Du mouvement des corps, 87, 112 (already quoted by Rochot 1973, 11–12). On Mersenne’s attitude, see Lenoble 1971, 357–360, 461–471; Dear 1995, 129–132; Palmerino 2011, 101–125. 79  See Lenoble 1971, 426–437. A comprehensive overview of this topic has been provided by Maury 2003, 179–238. 80  See Descartes to Mersenne, 11 October 1638, in Mersenne 1945–1988, vol. VIII, 96–99. See also the recent analysis carried out by Renée Raphael (2017, 78–97), in which Descartes’ letter, the Nouvelles Pensées, the marginalia Mersenne added to two copies of the Discorsi, and Mersenne’s letter to the Accademia dei Lincei are compared. 81  See Mersenne to Galileo’s friends in Italy, 1 July 1643, in Mersenne 1945–1988, vol. XII, 221–223. 82  See, for instance, Galileo 1933d, 72; trans. 1974, 33: “What is thus said of simple lines is to be understood also of surfaces and of solid bodies, considering those as composed of infinitely many unquantifiable atoms.” 83  See Aristotle, De coelo, 298b; Aristotle, Phys., 231a sq. Galileo denied that definition both in the first day of the Discorsi (Galileo 1933d, 77; trans. 1974, 38–39), and in the Postille alle esercitazioni filosofiche di Antonio Rocci (1933c, 682–683, 745–750). 84  Of the wide-ranging literature on Galileo’s atomism, see Shea 1970; Baldini 1976; Smith 1976; Redondi 1985; Palmerino 2000, 275–319. See especially Galluzzi 2011. 85  On Galileo’s interpretation see Drabkin 1950, 179–198; Palmerino 2001, 381–405; Boulier 2010, 371–385.

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interstitial “little vacua” (namely, the “vacui non quanti”) could not even be figured out, and added that those arguments were merely sophisms, Mersenne wrote that Galileo’s aim was more to astonish than to convince.86 The Galilean analysis of the continuum was based on “little subtleties that are worthless”87: for instance, if no line could be composed of a finite number of points but only of an infinite number, all lines would therefore be equal: they would be neither longer nor shorter than another, as all lines would be composed of an infinite number of points.88 As Lenoble had already pointed out,89 in the end, Mersenne preferred Descartes’ theory of subtle matter to Galileo’s model of space, to Gassendi’s atomism, as well as to Roberval’s empty geometrical imaginary space.90 He did not accept Descartes’ subtle matter unreservedly, but did consider it to be more probable than atomism, given that it was more compatible with his experiments and that, last but not least, it was easier to bring into line with Catholic dogmas.91

10.7  Can Bodies Move in an Intracosmic Void? In the Harmonie universelle, Mersenne attempted to define the space that lies beneath the firmament by interlacing contemporary debates about the vacuum with theological assumptions, as well as by using the ‘tool’ of acoustics. In order to draw a more comprehensive portrait of Mersenne it is necessary to first consider his writings on this topic dating from circa 10 years earlier. In the manuscript text Livre de la nature des sons, Mersenne examined the idea of sounds produced by the movements of planets. He raised the question “How the sky could produce sounds” (“Comment est ce que les cieux pourroient produire des sons”): This however will not make me grant the sound of the Heavens to the Platonists, unless we assume two things, the first, that the Heavens are solid bodies that move; the second, that every movement produces some sound, for then we should confess that the sky resonates; nevertheless, it would not be necessary for the Heavens to be solid, as it would be sufficient that the planets, and the stars, make their movements in the air stretched up beyond the firmament. The solidity of the sky is far from necessary, it would rather impede the sound, assuming that the air is necessary to produce the sound, and that there is not any air in the sky. But I do not want to amuse myself here with these celestial sounds, both because they are of no use to our sounds, and because we shall talk about this in another place.92  See Descartes to Mersenne, 11 October 1638, in Mersenne 1945–1988, vol. VIII, 97.  Mersenne 1973, 30. See Costabel 1964. 88  Mersenne 1973, 22–23. 89  See Lenoble 1971, 430, 436. On Mersenne’s opinion on the atomism of Galileo and Gassendi, see especially ibid., 413–437. 90  See Mersenne to Descartes, 28 April 1638, in Mersenne 1945–1988, vol. VII, 174. 91  See Mersenne 1644, Hydraulica, 166; Tractatus mechanicus, 83–84. Idem 1648b, 2. 92  Idem c. 1626, 16r: “Ce qui ne fera pourtant pas que i’accorde le son des cieux aux Platoniciens, si ce n’est que nous supposions deux choses, la premiere que les cieux sont des corps solides qui 86 87

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The “other place” mentioned here by Mersenne was the Traité de l’Harmonie universelle: besides suggesting new arguments that testified to the impossibility of hearing cosmic harmony, he focused on defining the conditions that enabled planets to produce sounds, thus shifting the attention from the level of perception to the level of production.93 Adhering to Brahe’s fluidity of the Heavens and assuming that the density of air in the sky was uniform, Mersenne concluded that the motion of the planets produced sounds, since even the very slow movements of cannon balls (when compared to those made by planets) were capable of generating sounds.94 If the dimension, movement, speed and material of a body were known, it would be possible to apply acoustic laws to the movement of the planets, and to define the sounds they corresponded to – although it would be very difficult to define which one each of them was, because of the large dimension and the very high speed of these bodies.95 Several years later, the Harmonie universelle attended to this subject again, although it examined it from a different viewpoint. Prior to addressing the issue of strings vibrating in the universe, Mersenne clarified the philosophical background of this kind of analysis, by merging the Scholastic tradition and seventeenth-century discussions. He introduced two hypotheses: we can consider two types of void, namely the universal and the particular, the first of which is nothing other than the privation of all bodies that are in the world; this would happen if God stopped conserving the bodies He created, as nothing other than the space where they are would exist  – the space that we usually call imaginary. We can, however, consider another void, one that is a little less universal than the first, namely the void that the air fills: once the air is removed from the place it has now, through either annihilation or transport, it leaves the concavity of the firmament empty of air.96

In the first hypothesis, Mersenne does not assume that the void and the imaginary space precede, or exist prior to, the creation of bodies; following in Duns Scotus’ footsteps with regard to his discussion on imaginary space and intracosmic void, Mersenne rests the possibility of their existence on voluntarism, and more precisely, on a divine action that could cease to conserve bodies.97

se meuvent; la 2 que tout mouvement produit quelque son, car pour lors il faudroit confesser que les cieux resonneraient; il ne seroit neantmoins pas necessaire que les cieux fussent solides, car ce seroit assez que les planettes, et les estoilles fissent leurs mouvemens dans l’air étendu iusques par dessus le firmament; tant s’en faut que la solidité des cieux fust necessaire, elle empecheroit plustost le son, supposé que l’air soit necessaire pour produire le son, et qu’il n’y ayt point d’air entre les cieux. Mais ie ne veus pas m’amuser icy a ces sons celestes, tant parce qu’ils ne servent de rien à la force de nos sons, que parce que nous parlerons de ceci en un autre lieu.” 93  See idem 2003, b. I, th. XV, 89. 94  As early as in the Quaestiones in Genesim, Mersenne valued the idea of the fluidity of Heaven: Mersenne 1623a, 813, 843. See also idem 2003, b. I, th. XV, 90. 95  See idem 2003, b. I, th. XV, 90–91. 96  Idem 1636–1637, Livre premier de la nature et des proprietez du son, 8. A reading of this passage is also provided in Buccolini 2014, 389–392. 97  See Duns Scotus, Quodl. 11.17, 11.21. About Duns Scotus’ arguments concerning the intracosmic void, see Lewis 2002, 71–74. For an overview on the medieval discussion of the imaginary space and the extra-cosmic void see Grant 1981, 116–147.

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Mersenne’s second hypothesis is about the annihilation of air only, leaving all other bodies intact. It is possible to foreshadow here the idea of the God mechanicus: God, the first mechanicus, would draw the air from the sphere of the universe-­ machine, in a similar way to Mersenne’s and his contemporaries’ attempts with other machines (e.g. Hero’s pneumatic machines described in the Cogitata physico-­ mathematica), or through Torricelli’s and Valeriano Magni’s experiments, or lastly, by putting a little bell inside a bell jar emptied of air, as the Liber novus praelusorius illustrated.98 The image of the Deus mechanicus had first been discussed in the sixteenth-century commentaries to Pseudo-Aristotle’s Mechanical questions  – which Mersenne himself referred to as early as in the Quaestiones in Genesim99 – and had often been employed to emphasize the productive and ordering activity of God, rather than the realm of possibilities and geometrical archetypes.100 Both God’s inscrutability and the human inability to grasp all divine purposes resulted in circumscribing the epistemological pattern to what God created de facto  – in Galileo’s model – or how he could have created the world – in Descartes’ fable. If Mersenne’s theory was still strongly indebted to the Scholastic tradition  – which led him not to rule out the possibility of intracosmic vacuum by drawing on theological arguments, and chiefly on the concept of divine omnipotence –, in order to settle the question of the vacuum he also turned to the experimental dimension and wondered whether sound could be generated in a universal or particular void.101 The question that arose from the first hypothesis is quickly solved: since sound is produced by the movement of a body, it cannot exist in the universal vacuum, which is defined by the absence of bodies. The setting of the second hypothesis is very different: before considering the particular vacuum, it is first necessary to examine the question whether bodies move in an alleged empty space.102 Should the answer to Mersenne’s question be positive – as, in fact, it is – this would mean that

 See Mersenne 1648b, 1–2.  See idem 1623a, 97–98, 111. Idem 1985c, 241. In those commentaries, Alessandro Piccolomini, Bernardino Baldi, Alessandro Giorgi, and also Henri de Monantheuil, had described God as the almighty mechanic. See, for instance, Giorgi 1592, 4r: “the machina mundi itself is arranged according to measure, number and weight – as we read in the Book of Sapience; since Ctesibius (as Vitruvius wanted) was not the inventor of pneumatic machines, nor were Vulcan, or Daedalus of self-propelled machines, as asserted by the ancients, but it was the Master himself of this structure of the world.” See also Monantheuil 1599, 5; ibid., 6–7 (my numbering): “the greatest work of works was made and conserved [...] by another ‘maker of machines’ who surpasses man infinitely as to excellence, wisdom, and power: with the same amount this machine of the world surpasses and is superior to the machine of all men, even of the Archimedeans.” 100  As stated by Hans Blumenberg, the absolute transcendence of God was one of the chief features of the seventeenth-century world machine: “the expression ‘machina mundi’ pertains to a theology which either – as in Lucretius – is directed against the Stoic metaphysics of providence (pronoia) or in which God hides behind his work rather than manifesting himself in it” (Blumenberg 2010, 63–64). 101  Mersenne had been discussing the hypothesis of the existence of vacuum that ensued from divine omnipotence since the Quaestiones in Genesim (1623a, 721–722). 102  See Mersenne 1636–1637, Livre de la nature des sons, 8: “since sound presupposes movement, we firstly have to see whether one or more bodies can move in the vacuum: because if movement is not possible, we have to conclude that sound cannot be made there.” 98 99

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in the vacuum bodies can produce sounds, which, however, do not reach our ears. Although this issue had been discussed at length before, Mersenne makes no reference to the atomists, nor to the Aristotelian philosophers: he turns his attention to the empirical dimension and makes a distinction between sound emission and sensory perception. He introduces the experiences carried out on a lute chord, which would vibrate with the same ‘force’ both in the air and in the vacuum, as its speed does not seem to be delayed. Since this issue is “very problematic” and “its difficulty has not been sorted out yet,” Mersenne is inclined to conclude that the silence that one might assume being created in an empty space does not equate with the absence of sound: the movement of bodies always produces sound, although this cannot always arrive at human ears – as seems to be the case here.103 In this passage, Mersenne does not mention Descartes’ subtle matter at all and suddenly cuts off his analysis as “there is no void in nature.”104 He nevertheless continues testing the existence of sound in an allegedly empty tube, and in the Novarum observationum he actually returns to Descartes’ theory of matter. Mersenne claims to have heard the sound of a bell which had been stimulated and put into a state of emptiness of air: “from which it is noticed that it is possible to conclude that sound is not only the percussion and movement of air, but also of the subtle matter that is in that emptiness of air.”105 Moreover, he spells out that, if absolute vacuum existed, no body would likely be able to move through it. In the Harmonie universelle the universe was said to be full of air and the firmament was compared to a huge vase full of water: Those who are in Heaven can notice the movements of air made here, although they are very weak when they arrive in Heaven. Because, if we are compelled to admit that a part of water that is set in motion in the center of a vessel is the cause of the movement of all the water, why isn’t it possible to conclude the same thing for air, which is a kind of less thick water that is enclosed within the firmament or in the infinity of the universe, just like in a very huge vase, which is a work worthy of God’s power and wisdom?106

In the Nouvelles observations physiques et mathematiques, Mersenne specified that the difference between the air on Earth and the air surrounding the Sun and the stars – he was actually thinking of a Ptolemaic or Tychonic cosmos – could be measured with a thermoscope (if the latter were to be extended to those heights): it would, thus, be possible to quantify the diverse degree of density and heaviness. He then added a reference to those who upheld the existence of the extra-cosmic void:

 Ibid. See also idem 1647, 85–92.  Idem 1636–1637, Livre de la nature des sons, 8. 105  Idem 1647, Praefatio secunda, 4 (my numbering). See also ibid., 197; idem 1644, 166. 106  Idem 1636–1637, Livre de la nature des sons, 10–11: “[...] ceux qui sont dans le Ciel peuvent appercevoir les mouvemens de l’air qui se font icy, quoy qu’ils soyent tres-foibles quand ils arrivent au Ciel: car si l’on est contraint d’avoüer qu’une partie d’eau estant meuë au milieu du vaisseau est cause que toute l’eau se meut, pourquoy ne peut-on pas conclure la mesme chose de l’air, qui est une espece d’eau moins grossiere, laquelle est contenuë dans le firmament, ou dans l’immensité de l’Univers comme dans un tres-grand vase, qui est un ouvrage digne de la Sagesse et de la puissance de Dieu.” 103 104

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We can figure out that if there is nothing besides void beyond the medium region of air – as someone thinks – we can say that the vapors that are lighter than air start weighing more when they arrive on the surface of the void, where they find a really cold temperature, since there is no longer a subject capable of receiving and holding warmth and therefore that is the highest place they can rise to.107

Although some might think that Mersenne was too daring in seeking to “take the Harmony to Heaven, and to speak about sounds or about the movements of stars,” he clarified that he was just trying to perform his duty, namely to be a witness to and admirer of God’s almightiness and wisdom.108 It was in this context that he continued to try and assess the planetary speeds, by drawing on the Platonic myth that Galileo had put forward in the first day of the Dialogo and in the fourth day of the Discorsi.109 Mersenne analyzed the information given in Galileo’s description and attempted to define the ‘sublime sphere’ from which God would have let the planets fall, by combining the orbital period of each planet according to Kepler’s Mysterium Cosmographicum (1621) with the dimension of orbits as stated by Lansberg, and Galileo’s law of free-falling bodies.110 Galileo’s Platonic myth would have enabled Mersenne to define the position and dimension of the firmament, besides being the testing ground for the law of odd numbers. Mersenne’s expectations were not met. The discrepancy between the Platonic myth, observational data and computations provided an additional argument for upholding the hypothetical status of the Galilean universe and, more generally, of Copernicanism.111 In this case, just as in Galileo’s law of odd numbers, Mersenne’s attitude toward Galileo was the result not only of his skepticism, but also of his more general argumentative strategy.112 In 1627 Mersenne had already ­acknowledged

 Idem 1636–1637, Nouvelles observations, 6–7: “Sur quoy l’on peut s’imaginer que s’il n’y a plus rien que du vuide par delà la moyenne region de l’air, comme estiment quelques uns, on peut dire que les vapeurs plus legeres que l’air, commencent à peser davantage lors qu’elles arrivent à la surface du vuide, où elles trouvent un tres grand froid parce qu’il n’y a plus de sujet capable de recevoir, et d’entretenir la chaleur, et consequemment que c’est le lieu le plus haut où elle puissent monter.” 108  Idem 1636–1637, Du mouvement des corps, 103. 109  On the passage of the Timaeus which Galileo might have hinted at  – many scholars have assumed that it was Timaeus 38 C-39 A – and on the role it played in his astronomical system, see Sambursky 1962; Wisan 1986; Barcaro 1984; Acerbi 2000. See Galileo 1933b, 44; idem 1933d, 284. See Florence: Biblioteca Nazionale Centrale, MS Gal. 72, ff. 134, 135, 146. Studies on this manuscript include Meyer 1989; Büttner 2001. 110  Mersenne 1636–1637, Du mouvement des corps, 103–107; idem 1648a, Praefatio, 3–4 (my numbering). 111  See idem 1636–1637, Du mouvement des corps, 107. 112  In the 1634 collection Mersenne presented the odd numbers law as the explanation that better agreed with the phenomena, whereas in the 1647 Novarum observationum he viewed it just as possible as other explanatory models. It is likely that Mersenne’s thought was about the conclusions reached by Descartes, Godefroid Wendelin, Honoré Fabri, Pierre Le Cazre, Ismael Boulliaud and Giovanni Battista Baliani in the meantime. See Dear 1988, 215–218; Galluzzi 1993, 86–119. Mersenne’s change of mind with regard to Galileo’s odd-number law was analyzed in depth by Palmerino 1999, 274–324; eadem 2010. 107

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that “I know that it is much easier to find fault in other people than to do better than them, and that it would be more useful to establish something certain about the Harmony of the World than to refute what others have said about it until now: but the first does not impede the second.”113 As Galileo’s case attested, this approach lasted until his final works.

10.8  Conclusion Mersenne’s meticulous  – at times pedantic  – examination of the most debated seventeenth-­century concepts of space led him to overrule the traditional idea of the harmonic universe. Now, the dance and choir of the planets and the stars held only metaphorical value: he sought to display the order of the cosmos, even though this order did not correspond to musical consonances or scales, and even though it did not perfectly match the astronomical systems discussed to that date. Mersenne’s God was still a musician, but not in the sense of Fludd and Kircher, or even Kepler. Mersenne’s God musician did not entail a panspermic view, according to which God permeated the cosmos with his fiat. Nor did he imply a Musician who built the templum naturae (temple of nature) following harmonic archetypes composed of precise musical ratios (as Kepler stated) or, more generally, adopting harmonic proportions (according to Jean Bodin’s model). God was, first of all, a mechanicus, virtually imagined in the act of hanging planets on a string, or of drawing air from the sphere of the universe – if he wanted to –, without any possibility of accessing his archetypes. Music no longer revealed divine archetypes but was, firstly, one of the two preferred fields and tools employed by Mersenne for the investigation of the nature of space. It was, however, still the cornerstone on the basis of which the ideas of God and universe were outlined, since it gathered the three terms of which the world was composed: measure, number and weight.114 In the 1634 Préludes, Mersenne had already expounded this point by referring to the analysis carried out in the “first book on Music,” which we can assume to be the work he had been undertaking on the Livre manuscript to give it the form of the first book of the Harmonie universelle.115 Notwithstanding the approximation of the mixed sciences, the survey carried out in those fields helps man fulfill his duty, namely, to reach a degree of knowledge that is as complete as possible with creation and God’s wisdom. In this task, Mersenne reckons the science of sound to be more useful than other sciences: indeed, it enables men to obtain a higher knowledge about natural phenomena as “all the impressions that things make on us are not different from a sort of sound,  Mersenne 2003, b. II, th. XIII, 418.  See idem 1636–1637, Livre premier de la nature des sons, 43: “we can represent everything that is in the world, and consequently all sciences, by means of the sounds, because, since everything consists of weight, number and measure, and sounds represent these three properties, they can signify everything one would like.” See also Mersenne 1623a, 1570. 115  See for instance Table 10.1. 113 114

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since they consist of a movement by means of which the bodies transmit their properties to us.”116 “Our knowledge is very imperfect” since – contrary to the one possessed by the angels and the blessed – it also relies on a flawed sensory perception which, for instance, is incapable of noticing very big and very small movements, speeds, and numbers – e.g. in the case of the movement of the planets, falling bodies, bodies on an inclined plane, or projectiles. If man was able to count the number of movements and vibrations of the flame of a candle or of sunlight, he would also know every proportion within the creation, and maybe even all the consonances and dissonances existing in natural phenomena, as well as the precise dimension of the universe. Instead, man needs to content himself with aspiring to – but yet not partaking in – the perfect knowledge of saints.117 Mersenne still considered the universe as a harmonious creation, with ‘harmonious’ not so much relating to musical consonances, but to the orderly and systematic arrangement of an Earth-centered and finite universe. Within the sphere of the firmament, bodies most likely kept moving in a plenum of subtle matter: the sounds – both audible and inaudible – did not generate a concert, but rather provided man with a set of measurements concerning the movements and properties of natural bodies. This information led Mersenne to enter into a process of discovery – albeit always a partial one  – of how nature works, and to question both contemporary theories on matter and astronomical hypothesis on the structure of the cosmos.

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Chapter 11

Imaginary Spaces and Cosmological Issues in Gassendi’s Philosophy Delphine Bellis

Abstract  Pierre Gassendi (1592–1655) is often viewed mostly as an antiquarian because of his interest in reconstructing Epicurean philosophy. Admittedly, Gassendi was one of the main actors in the revival of atomism in the seventeenth century, but he was also a supporter of Copernican cosmology, and he proposed a groundbreaking theory of space: not only did he depart from the Aristotelian notion of place, but he even proposed a new ontological conception of space as neither a substance nor an accident. For Gassendi, space was a homogeneous, infinite, three-dimensional entity which could be filled with bodies but was independent of them and could remain void. This new conception of space was elaborated not only as a revival of Epicureanism, or as a foundation for the new science, but also through a re-­ elaboration of the scholastic notion of imaginary spaces. The aim of this paper is to unravel some of Gassendi’s unacknowledged scholastic sources and explore how Gassendi, a staunch anti-Aristotelian, relied on a reinterpretation of this scholastic notion for his construction of a cosmological system immune to theological criticisms otherwise directed at the Epicurean and Brunian infinitist worldviews. This reinterpretation directly paved the way for a geometrical conception of space.

11.1  Introduction Pierre Gassendi is often viewed mostly as an antiquarian, because of his interest in reconstructing Epicurean philosophy, all the more so as he made no major contribution to the new science of the seventeenth century. However, Gassendi was not only an erudite editor and translator of Epicurus, but also one of the main actors in the Research for this article was made possible by a Veni grant (275-20-042) awarded by NWO (the Netherlands Organisation for Scientific Research). All translations are the author’s except where otherwise noted. D. Bellis (*) Department of Philosophy, Paul Valéry University, Montpellier, France e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_11

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revival of atomism as an alternative theory of matter to Aristotelian hylemorphism. He was a supporter of Copernican and Keplerian cosmology, as well as of Galilean physics.1 Even if Gassendi did not contribute much to the elaboration of the new scientific theories of his time, according to Alexandre Koyré, he did something that was no less important, that is, Gassendi “provided [the new science] with the ontology, or rather with the complement of ontology, it required.”2 Indeed, in his Syntagma philosophicum, Gassendi proposed a theory of space that departed from the Aristotelian notion of place and provided a new ontology of space by stating that space is a homogeneous, infinite, three-dimensional entity, which can be filled with bodies but is independent of them and can remain void.3 He proposed a new ontological conception of space as neither a substance nor an accident because it has no positive nature, but can subsist on its own.4 This new ontology of space was to influence scientists like Newton significantly.5 Yet, this new conception of space emerged as the result of various interests and constraints. Indeed, if Gassendi was initially a supporter of Copernican cosmology, he had to revise his cosmological views significantly after Galileo’s condemnation in 1633. Not only did he gradually distance himself from a strong version of heliocentrism, and eventually, in the Syntagma philosophicum, explicitly adopt Tycho Brahe’s system, but he also revised his cosmological Brunian-inspired worldview and endorsed the idea of a finite world surrounded by infinite void spaces which he was to call, in scholastic terms, ‘imaginary.’ What I will show is that Gassendi’s new conception of space was not only elaborated as a revival of Epicureanism, or in Koyré’s view as an ontological category suited to the new science, but that it was also forged by reappropriating this scholastic category of imaginary spaces. Admittedly, Gassendi was a staunch anti-­ Aristotelian.6 In his anti-Aristotelian work, the Exercitationes paradoxicae adversus Aristoteleos, one finds statements such as: “Once I was on my own and began to examine the whole matter more deeply, I soon became aware how vain a 1  On Gassendi’s support of Copernican and Keplerian cosmology, see Sakamoto 2009; Zittel 2013, 2015. On Gassendi’s interest in Galileo’s physics, see Clark 1963; Tack 1974, 161–188; Palmerino 1998, 2001, 2004a, b. 2  Koyré 1957a, 176: “il lui a apporté l’ontologie ou, plus exactement, le complément d’ontologie, dont elle avait besoin.” 3  For an account of the various conceptions of place and space in antiquity see Algra’s Chapter 2 in this volume. 4  That space is neither substance nor accident is a statement that can already be found in Francesco Patrizi’s Nova de universis philosophia. Patrizi, however, remained trapped in a rather confused ontology in which he claimed space to be “an incorporeal body, and a corporeal non-body,” Patrizi 1591, 65. On Patrizi’s conception of space, see Henry 1979; Muccillo 2010; De Risi 2016; Ribordy’s Chapter 7 in this volume. Gassendi acknowledged his debt to Patrizi in the Syntagma philosophicum: see Gassendi 1658, vol. 1, 246a. Raffaele Aversa even anticipated the position adopted by Gassendi and Patrizi according to which space is neither substance nor accident. But contrary to Gassendi, for Aversa, space did not have extension or magnitude: “Hoc spatium [sc. imaginarium] non est quicquam reale & positivum, neque substantia, neque accidens, neque extensio seu magnitudo,” Aversa 1625, 788a. 5  See Westfall 1962; McGuire 1978. 6  See Brundell 1987.

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discipline [Peripatetic philosophy] was and how useless in the pursuit of happiness”7; and “every day [Aristotelians] pile up inanities and questions on rubbish that could never have occurred to Aristotle.”8 Moreover, while Gassendi explicitly and frequently referred to a host of Ancient texts, he almost never mentioned late scholastic commentaries or textbooks, so much so that interpreters have suggested that he never engaged with this type of sources.9 The aim of this paper will, consequently, be twofold: first, to establish that the new conception of space that Gassendi put forward actually relied on a close reading of the scholastic notion of ‘imaginary spaces’ which became associated with a physical conception of void space; and second, to show that this appropriation of late scholastic sources was not purely instrumental but opened the way to a more geometrical conception of space, a conception which was crucial to the new science of the seventeenth century. Therefore, I deem the connection Gassendi established between his own conception of space and the scholastic imaginary spaces to be far more than a “rhetorical trick.”10 On the contrary, in my view, it epitomizes how a diverse philosophical tradition could offer new conceptual resources to early modern natural philosophy and open the way to renewed conceptions of space which would be inherited by Gassendi’s successors like Newton.

11.2  T  he Immensity of Space Reinterpreted Against the Background of New Cosmologies In order to give an overview of Gassendi’s cosmology and theory of space, and their evolution, I will start by tackling two issues which were initially connected, but then parted ways in Gassendi’s philosophy: the first is his endorsement of heliocentrism and his move towards Tycho Brahe’s theory; the second is his attitude towards the issue of the infinity or plurality of worlds. In the 1620s Gassendi was never ambiguous about his endorsement of heliocentrism, which he associated with an expanded vision of the cosmos. In the preface to the Exercitationes paradoxicae he promised to establish in book IV (which was never published, and probably not even written) the following: “I put to rest the sun and the fixed stars and impute motion to the earth as one of the planets. Then the multiplicity, or rather the immensity, of the world is shown to be probable [...].”11 Gassendi correlated the issue of heliocentrism with that of the extent of the cosmos. Notably, he here seemed to equate the immen Gassendi 1972, 18; 1658, vol. 3, 99.  Gassendi 1972, 23; 1658, vol. 3, 101. 9  See, for example, LoLordo 2007, 35: “None of the great diversity of views within late scholasticism is apparent from Gassendi’s treatment of Aristotelianism, either in the Exercitationes or in his later work. He almost never identifies individual scholastics or discusses their disagreements.” 10  LoLordo 2007, 122. 11  Gassendi 1972, 24–25; 1658, vol. 3, 102. Gassendi would later dissociate the immensity of the world from the too Brunian-sounding issue of its plurality. 7 8

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sity with the multiplicity of world(s). In other words, a theologically acceptable notion like that of immensity (which did not refer to an actually infinite cosmos) seems to cover a more Epicurean cosmological conception. In a letter to Galileo of August 1625, Gassendi expressed his support for the Copernican theory that allowed his mind to wander “through immense spaces, now that the common barriers and systems of the world have been broken.”12 In 1631 he observed the transit of Mercury, which he saw as a confirmation of Kepler’s Rudolphine Tables, and hence an indirect support of the heliocentric hypothesis, as well as an indication of cosmological distances.13 The issue of the dimensions of the cosmos indeed played a pivotal role in the vindication of the heliocentric system: in order to alleviate the difficulties related to the absence of apparent stellar parallax – a parallax that was supposed to occur if the Earth were to move – the dimensions of the cosmos had to be pushed away exceedingly. In a letter to Peiresc dated 26 February 1632, Gassendi did not shy away from stating his Copernican opinions explicitly, declaring that, “following Copernicus’ opinion, I conceive of the Sun as located in the center of the world and there rotating on its own axis in the space of twenty-eight days [...].”14 Further, in a letter of 1 November 1632 to Galileo, in which he thanked the latter for a copy of his Dialogo, Gassendi clearly appeared to be an enthusiastic supporter of Galileo’s cosmology.15 At the time, Gassendi displayed no doubt regarding the realist significance of Copernican cosmology. It is no wonder, then, that Gassendi was affected by Galileo’s condemnation in 1633. This led him to rethink his cosmological conceptions, so that he would end up leaning towards the Tychonic system, at least in some explicit statements found in the posthumous Syntagma philosophicum (1658).16 In the meantime, the way  Gassendi 1658, vol. 6, 4b: “Imprimis ergo, mi Galilee, velim sic tibi persuasum habeas, me tanta cum animi voluptate amplexari Copernicaeam illam tuam in Astronomia Sententiam, vt exinde videar mei probè iuris factus, cùm soluta, & libera mens vagatur per immensa spatia, effractis nempe vulgaris Mundi sistematisque repagulis.” (“First, my dear Galileo, I would like you to be convinced that I receive your Copernican opinion in astronomy with such pleasure in my soul that I seem honestly to be in my right when my mind, detached and free, wanders through immense spaces, now that the common barriers and systems of the world have been broken.”). This might recall Lucretius in De rerum natura, book I, 72–74. 13  Gassendi to Peiresc, 26 February 1632, in Peiresc 1893, 258: “je ne rapporte pas à un petit bonheur d’avoir fait ceste observation de Mercure devant le Soleil; elle est tres importante tant pour estre la premiere qui a esté faite de ceste façon, que pour devoir servir à ceux qui viendront apres nous soit pour determiner la grandeur et l’esloignement, soit pour regler les mouvements de ce planete.” On Gassendi’s activities as an astronomer, see Humbert 1936. On his observation of Mercury’s transit before the Sun, see Gassendi 1632; 1658, vol. 4, 499–510. 14  Peiresc 1893, 259: “suivant l’opinion de Copernicus je conçoy le Soleil logé au centre du monde, et là tournant sur son propre escieu dans l’espace de quelques vint huit jours [...].” Indeed the rotational period of the Sun viewed from the Earth is approximately 28 days. The fact that Gassendi located the Sun at the center of the world suggests that the world or the solar system is finite – what is infinite has no center – but this does not exclude the existence of an infinity of worlds or of an infinite universe. In that case the center of the world, where the Sun is located, would only be relative to the solar system. 15  Gassendi 1658, vol. 6, 54a. 16  See Brundell 1987, 30–47. In the Syntagma philosophicum Gassendi claimed that the Ptolemaic system is the “least probable” of all three cosmological systems. The Copernican one “seems 12

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Gassendi dealt with cosmological issues was far from unambiguous. In De motu (1642) he went to great lengths to show that the arguments based on the motion of bodies and used to reject the Copernican system were not conclusive and, more importantly, he based his explanation of the tides on the double motion of the Earth.17 In his De vita et doctrina Epicuri, an early version of the Syntagma philosophicum, the only cosmological systems he mentioned in 1641–1642 were the Ptolemaic and the Copernican ones.18 In another part of De vita et doctrina Epicuri (1642–1643), he still claimed that the Copernican system was “more probable and evident.”19 But in 1645–1646 he finally introduced the Tychonic system, on a par with the Ptolemaic and the Copernican systems, in his lectures at the Collège Royal, which were later published under the title Institutio astronomica.20 It is worth noting here that his colleague, Jean-Baptiste Morin, who had been appointed Professor of mathematics at the Collège in 1629, had fiercely expressed his disapproval of the Copernican theory and his support of the Tychonic system.21 Interestingly enough, in the Syntagma philosophicum, when Gassendi subscribed to the Tychonic system, his endorsement of cosmological theories had undergone a conspicuous epistemological shift. Whereas at the beginning of his career as an astronomer Gassendi had proposed mainly realist interpretations of astronomical phenomena in relation to his adoption of the Copernican theory, after 1633, and in particular in De vita et doctrina Epicuri (1642–1643) and in the Syntagma philosophicum, he declared that it was no more possible to prove that the Earth was stationary than that it was moved.22 He stated that even if there was a possibility that the heliocentric system was correct, clearer and more elegant.” But on scriptural grounds, the Tychonic system should be preferred because, according to the decree of the Church, the sacred texts attribute real motion to the Sun and real immobility to the Earth, and do not deal only with appearances: Gassendi 1658, vol. 1, 149a. Zittel claims that there is no evidence in Gassendi’s Life of Tycho Brahe (Paris: widow of Mathurin Dupuis, 1654) of his support of the Tychonic system, while Gassendi reported appraisals of the Copernican system from Catholics in his Life of Copernicus: see Zittel 2015, 260–261. In the latter text, Gassendi also briefly rebuked traditional objections against the Earth’s motion: see Gassendi 1658, vol. 5, 502b–503b. Be that as it may, the text from the Syntagma philosophicum I have just referred to displays Gassendi’s explicit support of the Tychonic system. 17  De motu, in Gassendi 1658, vol. 3, 519a. See Palmerino 2004a. 18  Gassendi 1641–1642, f. 442r. On this see Brundell 1987, 42. 19  Gassendi 1642–1643, f. 627r. 20  In the Institutio astronomica the geocentric Ptolemaic system was presented in a schematic way which is “the figure [schema] according to which the disposition of the world’s parts, such as they are commonly conceived and taught, are represented,” Gassendi 1658, vol. 4, 2a. This system corresponds to the “commonly received opinion,” ibid., 2b: “receptam vulgo sententiam.” The Tychonic and Copernican systems, by contrast, were presented as having gained the favor of “noble supporters,” ibid. But Gassendi did not state which system he favored. On the chair of mathematics at the Collège Royal, see Pantin 2006. 21  See Morin 1631. 22  Regarding his early realist interpretations of astronomical phenomena, Gassendi was clearly in alignment with Copernicus and Tycho Brahe. In his Life of Copernicus, Gassendi defended the realist import of Copernicus’ theory against Osiander’s interpretation: see Gassendi 1658, vol. 5, 510b, 514a. On Gassendi’s later positions, see Gassendi 1642–1643, f. 653v; 1658, vol. 1, 630a.

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he accepted the decision of the Church on that matter and considered the Tychonic hypothesis both the most probable and the most apt to “save the phenomena.”23 Nevertheless, this did not deter him from presenting, in the same Syntagma philosophicum, a modified theory of the tides which still presupposed the Earth’s motion. Despite explicit claims to the contrary, Gassendi’s final scientific endeavors were still based on a heliocentric cosmology.24 Interestingly enough, this period between 1633 and 1658 also saw an intensive reworking of the notion of space, and we will observe similar ambiguities in Gassendi’s thoughts on the extent of the cosmos. Gassendi was aware of the theological implications involved in cosmological issues, especially with regard to the issue of the infinity of worlds which was part of Giordano Bruno’s cosmology.25 As early as 1626 Gassendi was engaged in a philological and philosophical project based on the revival of Epicurus’ thought. But the Epicurean cosmological model was also based on the idea of an infinity of worlds in infinite space.26 Consequently, Gassendi had to take a stand on this cosmological view. As we have seen, in the preface to the Exercitationes Gassendi evoked the multiplicity of the worlds. In 1636, in book XII of De vita et doctrina Epicuri, Gassendi insisted on the arguments that give some plausibility to the hypothesis of the infinity of the universe. At that stage, this hypothesis was a consequence of the possibility of the hypothesis of the infinity of bodies.27 While the driving motivation was the specific Epicurean focus adopted in that text, Gassendi distanced himself from this cosmological view mainly for religious reasons, because “the holy faith has rejected” it.28 But the question remains whether Gassendi was ever tempted to subscribe to the theory of an infinite space full of worlds while being a supporter of heliocentrism. The two positions did not go hand in hand, as is manifest in Copernicus’ and Kepler’s cases. The limits of the cosmos could be moved away exponentially, but this cosmological immensity was not necessarily equal to actual infinity, as Bruno  The idea of “saving the phenomena” was expressed in his Institutio astronomica (1647): see Gassendi 1658, vol. 4, 25a. See also his Syntagma philosophicum in Gassendi 1658, vol. 1, 615a, 617b, 630a. On Gassendi’s move from a realist to a hypothetical approach to astronomy, and from a Copernican to a Tychonic cosmology after Galileo’s 1633 condemnation, see Brundell 1987, 30–47. 24  See Palmerino 2004a. 25  For Bruno’s infinitism see also Granada’s Chapter 8 in this volume. 26  See Bakker’s Chapter 3 in this volume. 27  Gassendi 1636, f. 161r–v: “Atque haec duo [sc. the infinity of spaces and infinity of bodies] quidem sunt, quae defendere nihil obstat. Aliud superest, quod planè non liceat, videlicet non modò plureis praeter hunc asserere Mundos; sed concedere etiam per inane illud immensum infinita corpuscula, ex quibus vel creati sint, vel creari adhûc plures Mundi possint. Sane et sacra fides id respuit, et ratio etiam naturalis, qua infrà edocebimur fabulosam penitùs esse, quam Epicurus adstruit constituendi Mundi rationem.” 28  Ibid. 23

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wished.29 Notably the use of the terms ‘immense’ or ‘immensity’ for the cosmos, although adopted by Bruno in the title of one of his works, was also a convenient way to circumvent the debate about the finiteness or infinity of the cosmos, while at the same time hinging on terms that encapsulate the mode of presence of an infinite God in his creation. As we will see, Gassendi would retain this terminology in his later works, but dissociated it from the idea of an infinity of worlds and focused on its theological import instead. Even if it were impossible to demonstrate that no other worlds existed and even if the infinity of worlds could not be excluded on purely logical or physical grounds, Gassendi came to openly acknowledge the uniqueness of our world on scriptural grounds.30 However, he could not completely abandon the “spatia immensa” opened up by Copernicus, Kepler, and Galileo.31 Gassendi owned a copy of Giordano Bruno’s De immenso and explicitly mentioned Bruno in the Syntagma philosophicum.32 Antonella del Prete has convincingly shown that, while in the Syntagma philosophicum Gassendi openly rejected the Epicurean infinity of worlds on theological grounds, as far as more physical topics like the shape of the world or its dimensions were concerned, many of his arguments were still tinged with a Brunian cosmological view.33 Gassendi was thus led to envision that all fixed stars might not be located on the same surface, and that each of them might be a sun surrounded by planets invisible to the eye. Even so, one should add that, as an astronomer and as an empiricist philosopher, Gassendi did not need to postulate a plurality of worlds. His realm of investigation was de facto limited to the fixed stars. What was beyond could be full (of worlds like in Epicurus’ and Bruno’s cosmologies) or void (like in the Stoics’ representation of the world), yet this made no difference to the seventeenth-century science of astronomy.34 The period from 1624 to 1658 thus represented a less-than-straightforward thought process toward a mostly geocentric (hybrid) finite world system, that is to say, a system consisting of a finite, though very extended, world with the Earth at its center in an immense (infinite) void space which Gassendi called ‘imaginary.’

 See Helden 1985.  Gassendi 1658, vol. 1, 141a–144b; 1641–1642, ff. 461r–463v. 31  Let us recall that Copernicus conceived the universe as being immense but finite. As for Galileo, he seems to have leant toward a conception of an infinite universe, but in his letter to Ingoli (1624), he only claimed that it was uncertain (and would most probably remain so for the human sciences) whether the world was finite or infinite. See Galileo 1896, 529; Koyré 1957b, 95–99. 32  See Sturlese 1987, 123; Canone 1993, xxxi, referred to in Del Prete 2000, 57 n1. See Gassendi 1658, vol. 1, 140a where he explicitly refers to Giordano Bruno in a marginal note, evoking the model of an infinite universe composed of worlds which communicate with one another (which is distinguished from the Epicurean model in which worlds are separated by void space). 33  See Del Prete 2000. 34  For the opposition of the Stoic and Epicurean worldviews, see Section 3.2 of Bakker’s Chapter 3 in this volume. 29 30

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11.3  T  he Introduction of Imaginary Spaces in Gassendi’s Cosmology In order to show how Gassendi integrated some arguments of late scholasticism to the development of his notion of infinite void space in the period between the 1630s and 1658, I will first attend to book XIV, entitled “De Inani seu Loco et de Tempore,” of Gassendi’s De vita et doctrina Epicuri which was written around 1636–1637.35 In chapter 4 Gassendi set out his arguments in favor of the existence of extramundane void spaces which “are usually called imaginary.”36 Neither here nor in later texts in which Gassendi appealed to this notion did he identify those who call these spaces ‘imaginary.’37 This notion of imaginary spaces appeared in medieval philosophy, in the wake of the bishop of Paris Étienne Tempier’s 1277 condemnation of some Aristotelian propositions which tended to limit God’s power.38 As a consequence, it was claimed that God, by his absolute power, could create a plurality of worlds separated by void space, or move the existing world from one place to another and leave a void behind. Imaginary spaces existing beyond the limits of the finite world were then supposed to allow for God’s immensity, which could not be limited to his presence in the finite world.39 Beyond the boundaries of the finite world lay infinite spaces which were, however, non-dimensional (because for most medieval authors no distance could be measured in void space, and because God’s presence was not to be conceived as a local presence in three-dimensional space).40 They were initially labelled ‘imaginary’ because they could not be apprehended by  See Pintard 1943, 32–46; Bloch 1971, xxix–xxx, 173. This piece of writing was never published and survives in manuscript form as shelfmark 709 at the Bibliothèque municipale in Tours, France. 36  Gassendi 1637, f. 201v. Chapter 4 is entitled thus: “Vt concipiendum Spatium, in quo Ratio loci consistat.” Gassendi 1637, f. 202r: “Itaque suppono imprimis esse extra mundum spatia illa, seu interualla, quae imaginaria vulgὸ adpellantur.” The early reference to imaginary spaces in book XIV of De vita et doctrina Epicuri overturns Brundell’s statement according to which the introduction of this notion in the Syntagma philosophicum might result from a reaction to Descartes’ Principia philosophiae; see Brundell 1987, 68. 37  Gassendi who usually explicitly mentions all his sources did not do so with regard to imaginary spaces. At best, he mentioned “Aristotle’s supporters” (Gassendi 1637, f. 203v: “Aristotelis Sectarores”), “us,” that is to say the Catholics (Gassendi 1637, f. 206v: “nos”), or “the Doctors of the Church” (Gassendi 1658, vol. 1, 183b: “Sacrorum Doctorum”). There is no explicit reference to late scholastics in his discussions on space, but some passages are conceptually and textually so close to some scholastic texts on the topic that it is almost impossible to deny that Gassendi read some of them. Given, on the one hand, his early philosophical training and his teaching position in philosophy in Aix-en-Provence, and on the other hand, his fierce rejection of Aristotelianism, it should come as no surprise that Gassendi was knowledgeable about late scholastic texts but avoided claiming them among his sources. 38  See Grant 1981, 108–181. 39  Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 519: “In hoc igitur imaginario spatio asserimus actu esse Deum: non vt in aliquo ente reali, sed per suam immensitatem: quam quia tota mundi vniuersitas capere non potest, necesse est etiam extra coelum in infinitis spatiis existere.” 40  See Grant 1981, 123–124, 143. 35

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the senses, but by reason alone. Reminiscent of these discussions, the argument in Gassendi’s De vita et doctrina Epicuri proceeds as follows: it is possible to admit that other worlds, even an infinity of worlds, could be created or that the existing world could be expanded. For that, it is required to imagine spaces that have long existed, and in which the things to be created could be located, and therefore to conceive that our unique finite world was set in an infinite space in which this plurality of worlds could be created.41 God created the world in a determinate part of infinite space, but he could have created it elsewhere.42 This means that Gassendi refused to consider the possibility that the required spaces might be created ‘on demand,’ so to say, i.e. each time a new world was created.43 The assumption is that void space must already exist for a new world to be created. Imaginary spaces beyond the world constitute the condition of possibility for God to exert his power. But one might say that God could create more space if he wanted to create another world or a more extended world.44 Why does space have to be uncreated? Indeed, Gassendi explicitly stated that space existed from eternity and had not been produced by God, which amounted to say “nothing more than those among us who allow imaginary spaces.”45 Nicole Oresme, for example, thought that infinite void 41  Gassendi 1637, f. 202v: “haud-dubiè imaginantur spatia jampridem existentia, in quibus creanda collocari possint [...].” Ibid., ff. 202v–203r. 42  Ibid., f. 202v: “Heinc etiam hunc mundum concipimus fuisse in hac determinata parte infiniti spatij a Deo constitutum; qui in alia quauis parte constitui potuerat, & in quam adhûc posse agi intelligitur, hac ipsa stante inuariabili; cùm siue illi aduenerit, siue ab illa recesserit mundus, ipsa semper eadem constet.” 43  This is the solution adopted, for example, by Albert of Saxony, see his Quaestiones in Aristotelis De Caelo, book I, qu. 11  in Albert of Saxony 2008, 139: “bene tamen concedo quod, quando crearetur lapis extra mundum, crearetur spatium extra mundum [...].” 44  Gassendi would address this objection in the Syntagma philosophicum; Gassendi 1658, vol. 1, 189b–190a: “Respondebunt Deum, siue hunc Mundum ampliet, siue nouum creet, creaturum simul spatium, quod à superaddita huic, aut à tota alterius mole occupetur; seu potiùs quod noua ipsa moles, eiúsve extensio, dimensióque sit; neque enim esse aliud spatium volunt, quàm extensionem corpoream, ipsásve corporis dimensiones. Verumtamen, praeter iam dicta, vt constet nihil esse opus creare nouum spatium, & confirmetur dari extensionem, dimensionésque non corporeas, quae Inani spatio competant; cùm possit Deus pro lubitu aut propè, aut procul ab isto nouum Mundum condere, condat tantâ distantiâ ab hoc dissitum, quantum est, v.c. milliare; quaeso, ista distantia ecquid aliud erit, quàm spatium?” 45  Gassendi 1637, f. 206v (my emphasis): “at spatium sive Intervallum non modo est locato prius, sed ab aeterno etiam est. Postremὸ requiri heic potest, sit-ne Interuallum reale, an-non? [...] Instabis, erit igitur aliquid reale, quod Deus non produxerit? Sed ne inuidiose id vrgeas, adtende vt heic nihil ampliùs dicamus, quàm qui ex nostris Spatia Imaginaria vulgò concedunt. Caeterùm enim et nos quoque, quicquid reale vulgo concipiunt, hoc est omneis substantias, omniaque accidentia Deum verum habere autorem fatemur. Quid quod res saltem videtur esse longè tolerabilior communi doctorum virorum Scholarumque sententia, quae statuit rerum essentias esse & aeternas, & a Deo vt improductas, sic independenteis, cum sint tamen id, quod est in substantiis, accidentibusque praecipuum?” Raffaele Aversa already identified this kind of position as potentially risky from a theological point of view: “Si hoc spatium esset ens reale & positivum, vel esset aeternum, & improductum, ac independens a Deo: & hic esset grauis error in fide, ac etiam contra rationem [...].” It cannot be something produced, either, because then it could be destroyed, but God would be able to create bodies in the place which was occupied by this space, which would lead to an

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space needed to exist beyond the limits of our world, where God could create other bodies or worlds.46 But why do imaginary spaces have to pre-exist the creation of the world(s)? For Buridan, for example, no pre-existing space was required for God to create bodies.47 Aquinas denied the existence of any space or place before the creation of the world.48 And actually, the proposition according to which it was necessary that a void space existed for God to create a world was condemned in 1277 by Bishop Tempier.49 The fact that Gassendi did not consider these alternatives indicates rather clearly that he did not elaborate his conception of infinite extramundane space out of theological concerns. Rather, his approach consisted of finding available theological arguments that could give weight to a conception of space that he was forging on conceptual grounds. In the 1649 Animadversiones, however, Gassendi addressed the objection in a more straightforward way, claiming that the creation of void space for each newly created world would not solve the problem of the intermediate interval between those created worlds, which should also consist in void space, since it could be measured.50 In book XIV of De vita et doctrina Epicuri Gassendi then proceeded with an appeal to an annihilatio mundi, which is a type of thought experiment already used by medieval authors like Henry of Ghent, Peter John Olivi, Richard of Middleton, Duns Scotus, William of Ockham, John Buridan, Thomas Bradwardine, Nicole Oresme, and Albert of Saxony, and by late scholastics like Aversa or Suárez, or by Patrizi.51 The matter comprised in the sublunary sphere could be reduced absurdity. Consequently Aversa, contrary to Gassendi, concluded that imaginary space “non est quid improductum nec productum,” Aversa 1625, 788b. One finds the same kind of statement in Goclenius’ Lexicon philosophicum about imaginary space; Goclenius 1613, 1067b: “Non enim est verum Ens, quia nec creatum est; nec increatum Ens [...].” The Coimbrans also stated that space is uncreated and has always existed, but that it is not a positive being; Conimbricenses 1596, vol. 2, 518: “Item, nec esse vllum aliud reale ac positivum ens, cum nihil tale praeter Deum ab aeterno fuerit; hoc verò spatium semper extiterit, semperque esse debeat.” 46  Questiones super Physicam, IV, 6 in Oresme 2013, 458: “Quarta conclusio quod capiendo vacuum primo modo, in infinitum spatium vacuum est extra mundum. Probatur ex descriptione, quia vacuum primo modo est: ubi non est corpus et potest esse; sed conceditur quod Deus, qui est omnipotens, posset ibi facere unum corpus aut unum mundum absque creatione novi loci, ergo ibi est vacuum primo modo.” Oresme 2013, 459: “Tertio, quicumque ponunt mundum generatum esse, necessario habent ponere vacuum esse, ubi factus est mundus; sed secundum veritatem ponendum est quod mundus factus est, ergo etc.” This agrees with a passage in Aristotle, De caelo, III, 2, 301b31–302a9. 47  See Buridan 1509, book IV, qu. 2, f. 68r, col. 1–2. 48  See Summa theologiae, part 1, question 46, article 1. 49  See Grant 1981, 111. 50  Gassendi 1649, 200: “Nam quòd nonnulli quidem dicunt, si Deus crearet mundos alios, spatia quoque alia, in quibus collocarentur, creaturum esse; inextricabilem profectò difficultatem subeunt, quae illis obiicitur de interiecto spatio inter duos quoslibet mundos; cum id cadere in mensuram valeat, & per maiorem, minoremve distantiam possit explicari.” 51  On the appeal to annihilatio mundi in medieval philosophy, see Suarez-Nani 2017. See Henry of Ghent 2007, 3–10; Olivi 1922, 590; Richard of Middleton 1591, vol. 2, 186, col. 2; Duns Scotus 1895, 441b; Ockham 1980, 45–46; Buridan 1509, book III, qu. 15, f. 57r col. 2-f. 57v col. 1; Bradwardine 1618, 177–178; Oresme 1968, 166; Oresme, Questiones super Physicam, IV, 6 in

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to nothing.52 But the three dimensions of the sublunary sphere would remain and we could imagine this region void of all bodies. This should lead us to think that, independently of bodies, there exist some incorporeal immense dimensions in length, breadth and depth that constitute space. Gassendi justified the logical possibility on which the argument rests with an indirect appeal to God’s power: this is no more impossible than to accept the creation of vacuum in nature by divine force.53 The argument of the annihilation of the world was here restricted to the sublunary sphere, as it was by most medieval authors, who at most extended it to the finite world. In the Animadversiones and in the Syntagma philosophicum Gassendi would extend precisely this reasoning ad infinitum, thus justifying the infinity of extramundane void spaces.54 Admittedly, Gassendi also attempted to connect the infinity of space with that of God, or to derive the former from the latter, as was customary in medieval considerations on imaginary spaces. In chapter 5 of book XIV of De vita et doctrina Epicuri (entitled “Place is such space, and not the internal surface of the surrounding body”),55 Gassendi linked God’s infinity to that of space, but almost in passing.56 Later, in the Syntagma philosophicum, Gassendi elaborated further on the link between the immensity of extramundane void space and the immensity of God: From this, it is proved that God cannot exist, except as infinite and absolutely immense, because if the divine substance had any limits, it would be for that very reason imperfect. For however vast it would be, it would be limited by some boundaries; it could be regarded as nothing by comparison with infinity; there would be an infinite variety of places in which it would not be able to act at all; in which it would not know that something happens or does not happen; it would be restrained as if by some force, so that it could not extend itself beyond, since even if it wanted to, still it could not.57 Oresme 2013, 458; Albert of Saxony 2008, 132, 135, 136; Aversa 1625, 787a. Suárez, Disputationes metaphysicae, disp. XXX, section VII, 34 in Suárez 1861, 106a: “Deinde, quis neget posse Deum conservatis coelis annihilare totam sphaeram rerum generabilium et elementorum, vacuo manente toto spatio medio.” See Patrizi 1591, f. 65r; 1943, 240. For the role of the annihilatio mundi thought experiment in Suárez and Patrizi, see Ribordy’s Chapter 7 in this volume. 52  Gassendi 1637, f. 203r (my emphasis): “Cogitemus quippe vniuersam Aristotelis elementarem regionem, corpora dico terrae, aquae, aëris, & ignis, sic in nihilum redigi, vt concaua illa coeli Lunae superficies nullum prorsùs contineat, an-non semper cogitamus spatium, in quo illa corpora fuerint? & in quo denuò collocari possint? an-non tanta ibi est longitudo, latitudo, ac profunditas, quanta fuerit anteà? Non-ne semper cogitamus eundem circumferentiae diametrum? Nonne centrum concipimus in hujus diametri dimidio? Non-ne semper imaginamur vbi regiones elementorum discriminitae fuerint? Quae foret distantia duorum corporum si in hoc spatio collocarentur? & id genus similia.” 53  Ibid., f. 203r: “Dices fortè suppositionem esse impossibilem: at neque impossibilis est ijs qui posse vacuum vi diuina in rerum naturam induci concedunt [...].” 54  See Gassendi 1649, 615; 1658, vol. 1, 183a. 55  Gassendi 1637, f. 203v: “Tale Spatium, non Interiorem continentis corporis superficiem esse Locum.” 56  Ibid., f. 204r: “Etenim Deus infinitus, cùm dicitur esse in loco, infinitum spatium statim cogitatur [...].” This passage is taken up in Gassendi 1649, 618; 1658, vol. 1, 218a. 57  Gassendi 1658, vol. 1, 304a–b: “Non posse porrò esse Deum, nisi Infinitum, prorsúsque immensum, ex eo probatur, quòd si diuina Substantia limites aliquos haberet, eo ipso imperfecta esset;

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God’s immensity cannot be limited to the finite world; it must extend beyond the world, hence the necessity for infinite space to exist, even before any world is created, i.e. to co-exist with God, and to be co-present with God. But Gassendi’s reasoning is actually very telling, because it does assume that some places could exist independently of God if God were not infinite.58 The ground for space’s infinity is first and foremost conceptual rather than theological for Gassendi. As he will later write in the Syntagma philosophicum, space is infinite “of itself.”59 Moreover, it seems to me that the development of Gassendi’s theory of infinite extramundane void space did not originate from theological considerations, but rather from a refinement of Epicurean cosmology: Gassendi attempted to preserve whatever he could from the infinite Epicurean spaces, namely infinite uncreated spaces deprived of their content of infinite worlds and instead filled with God.60 In the Syntagma philosophicum Gassendi made explicit that God could have created a plurality of worlds but did not actually do so.61 Already in a letter to Louis de Valois, dated 24 October 1642, after having expounded Epicurus’ conception of the infinity of space and bodies, he added: “At this point, although the infinity of spaces can be tolerated, since indeed even those of our confession usually admit that there are infinite spaces beyond the world, which they call imaginary and in which they acknowledge that God can make innumerable worlds, still the infinity of bodies cannot be tolerated in the same way.”62 Gassendi’s train of thought here clearly started from the conceptual acceptability of infinite worlds in void space, from which he removed, for theological reasons, the overabundant worlds. The Epicurean or Brunian void spaces deprived of their infinite worlds were, consequently, christened ‘imaginary spaces.’ Gassendi’s infinite void space acted as an acceptable substitute for the Epicurean or Brunian infinity of worlds, while at the same time emerging as a fundamental category of his ontology and an epistemologically required notion for a natural philosophy based on the acceptance of the vacuum. quoniam quantumvis ingens foret, finibus tamen concluderetur; haberi posset pro nihilo, comparatione infinitatis, infinita foret varietas locorum, in quibus agere nihil posset; in quibus quid vel ageretur, vel non ageretur, nesciret; cohiberetur quasi vi quadam, ne se se vltrà protenderet, cùm etsi vellet, non tamen posset.” 58  In a letter to Sorbière of 30 January 1644, Gassendi even reversed the conceptual order between God and space usually observed by the theologians. Ibid., vol. 6, 179a: “so that by reasoning on that [sc. place or the dimension of length, width, and depth], we conceive God as immense, and by reasoning on this [sc. time] as eternal” (“adeò vt ratione illius concipiamus Deum Immensum, & ratione huius Æternum”). 59  Ibid., vol. 1, 131b: “Spatium non potest limitari reipsâ, quasi vlteriùs spatium non sit; sed designatione, seu positione dumtaxat. Spatium ex se infinitum est, concipitùrque etiam diffusum vltra fineis Mundi.” 60  On the importance of Gassendi’s work on Epicurean philosophy for the genesis of his cosmology and conception of space see Rochot 1944, 145–151. 61  Gassendi 1658, vol. 1, 139–144. 62  Ibid., vol. 6, 158a: “Quo loco cùm infinitudo spatiorum tolerari possit, si quidem & nostri plaerumque admittunt esse vltra Mundum infinita spatia quae Imaginaria appellant, in quibus fatentur Deum posse condere innumeros Mundos: non perinde tamen tolerari potest infinitudo corporum.” See also Gassendi 1649, 200, 234–235.

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It is also telling that Gassendi appealed to the notion of imaginary spaces in an obviously physical context, as is the case in De motu (1642). Here Gassendi dealt with gravity, i.e. with the attraction of the Earth of heavy bodies. For Gassendi, gravity is a magnetic attraction of the Earth working on heavy bodies, and not the power exerted by the center of the world conceived as their natural place. Reminiscent of the Epicurean explanation of magnetism, Gassendi’s account of gravity relied on the Earth spreading corpuscles which attract heavy bodies. But the magnetic attraction decreases with distance. As a consequence, beyond a certain distance  – for example, as Gassendi wrote, beyond the Lunar sphere or outside the world – the Earth can no longer attract a stone. Void spaces beyond the world are homogeneous and isotropic. A stone at rest in those spaces would remain at rest because the Earth would not be able to exert its attractive force on it: “Now picture a stone in those imaginary spaces that stretch beyond this world and in which God could create other worlds. Do you think that out there where it had been made it would fly off straightway toward this earth instead of remaining motionless in the spot where it was first put as if it did not have any up it could flee from or any down to tend toward?”63 In order to make his argument more compelling, Gassendi then appealed to the thought experiment of the annihilation of the world: “If you think it would travel in this direction, imagine that not only the earth, but also the entire world was reduced to nothing, hence that these spaces were empty as they were before God created the world; at that time at least all spaces were alike [similia] since there was no center. You will appreciate that the stone would not approach this way, but would rest fixed in that place.”64 Therefore, Gassendi extracted the notion of imaginary spaces from its initially mainly theological context, and distorted its conceptual content in order to draw some specific conclusions in the realm of natural philosophy, and to fashion a cosmology which would be acceptable on theological grounds. But, as we will now see, this was not all he did: in fact, the adoption of the scholastic notion of imaginary spaces had additional, far-reaching consequences for his ontology of space.

11.4  T  he Ontological Status of Gassendi’s Imaginary Spaces: Toward a Mathematical Conception of Space? Now I would like to examine in more detail some of the consequences of Gassendi’s adoption of the scholastic notion of ‘imaginary spaces’ in his identification of the infinite void space surrounding his finite world. Obviously, Gassendi introduced into his own conceptions of space and the structure of the world a notion which  Gassendi 1972, 136; 1658, vol. 3, 494b.  Gassendi 1972, 136 (trans. modified); 1658, vol. 3, 494b. Imaginary spaces are also the setting for Gassendi’s formulation of the principle of inertia in the Syntagma philosophicum, see ibid., vol. 1, 349b, 354b.

63 64

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looked back upon a long philosophical and theological history dating back to the Middle Ages. But instead of applying this notion to his theories as a somewhat exogenous element which would have only a justificatory or apologetic function (i.e., that of distancing his conception of infinite void spaces from Epicureanism or Brunianism), Gassendi did something more subtle and more interesting from a conceptual point of view, a kind of grafting that opened new conceptual paths. I will first briefly explore some consequences of this grafting for the ontology and what I deem to be a mathematization of space. Identifying the conceptual strategy elaborated by Gassendi to forge his ontology of space is all the more important as it was to be highly influential, especially on Newton’s theory of absolute space and time, at least via Walter Charleton’s Physiologia Epicuro-Gassendo-Charltoniana, which was based on Gassendi’s 1649 Animadversiones.65 As far as the ontological status of space is concerned, the notion of imaginary spaces provided Gassendi with an array of possibilities which proved useful in particular in the final version of his ontology of space in the Syntagma philosophicum.66 Here, Gassendi went as far as to formulate a final radical revision of the traditional Aristotelian ontological categories: space and time are real beings and not entia rationis. Gassendi’s space is even one of the most fundamental types of being, because space and time are neither substance nor accident, but are specific and additional types of beings. In doing so, Gassendi relied on Patrizi’s anti-Aristotelian theory of space, but succeeded where Patrizi had failed, namely in formulating a coherent ontology of space, time, and bodies.67 Contrary to Aristotle, Gassendi did not want to make of space or place a species of quantity insofar as it is usually considered as a corporeal accident. Gassendi thus disconnected the notion of space from that of corporeal quantity to consider it as incorporeal quantity, therefore as a specific type of incorporeal being: On the other hand, because it seems to us that, even if there were no bodies, there would still remain an immovable place and a flowing time, for that reason it seems that place and time do not depend on bodies and are not in fact corporeal accidents. But they are not on that account incorporeal accidents, as if they inhered in some incorporeal substance the way accidents inhere, but they are incorporeal entities of a different kind than those that are usually called substances or accidents.68  See Westfall 1962, 172–173.  On Gassendi’s conception of space in his Syntagma philosophicum see Mamiani 1979, 93–121; Schuhmann 1994; LoLordo 2007, 100–129. 67  Gassendi certainly borrowed from Francesco Patrizi this radical exclusion of space and time from the Aristotelian categories of substance and accident. Gassendi acknowledged his debt to Patrizi in the Syntagma philosophicum, recognizing his perfect agreement with Patrizi’s conception of three-dimensional space; see Gassendi 1658, vol. 1, 246a. But Gassendi managed to remove the ontological confusion between space and body that still pervaded Patrizi’s theory. Concerning time, this amounted to a radical break from Epicurus, who considered time an accident of bodies and void. On Gassendi’s evolution regarding the ontological status of time, especially his departure from the Epicurean conception and the role of Galileo’s mechanics within it, see Bloch 1971, 181–194. 68  Gassendi 1658, vol. 1, 182a: “Nobis porrò, quia videtur, etsi nulla essent corpora, superfore tamen, & Locum constantem, & Tempus decurrens; ideò videntur Locus, & Tempus non pendere 65 66

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Gassendi also insisted on the physical independent reality of space and time: [T]here is no substance, or accident which is not somewhere or in some place, and sometime or in some moment, so that, even if such a substance or such an accident perished, the place would no less continue to subsist or the time to flow. From this it follows that place and time must be considered as true things or as real beings [res verae, Entiave realia]. For, although they are not like what is usually considered as substance or accident, still they actually do exist [revera sint tamen], and they do not depend on the intellect like chimeras, since, whether the intellect thinks or not, the place will remain and the time will continue to flow.69

Space is defined as “the three-dimensional interval consisting of length, and depth into which a body can be received or through which a body can pass,” and more precisely, as “an incorporeal quantity.”70 Here again Gassendi intended to show that space is identical with void by appealing to the thought experiment of the annihilation of the world, in order to establish the existence of space independently of bodies. God could reduce the sublunary sphere to nothing and we would be left with empty space that can be measured by its dimensions: Now, I ask, since the lunar sphere is circular, if we take a point on its concave surface, do we not conceive that there is, in this empty region, between that point and the opposite point, a certain interval or a certain distance? Isn’t this distance a certain length, namely an incorporeal and invisible line, which is the diameter of the region, and in the middle of which there is a point which is the center of the region and of the sphere, and which had previously existed as the center of the Earth itself? Do we not immediately understand how much of the region around this center had been previously occupied by earth, water, air, and fire? Do we not in our minds designate how much of this corresponds to the surface and how much of each of this to the interior? Hence, do the dimensions of length, breadth and depth that we can very well imagine, not still exist there? Certainly, wherever it is possible to conceive an interval or a distance, it is also possible to conceive a dimension, in so far as such an interval or such a distance is of a determinate measure, that is to say, it can be measured. The dimensions that we call incorporeal and spatial are, then, of this kind.71 à corporibus, corporeáque adeò accidentia non esse. Neque verò idcircò sunt accidentia incorporea, quasi incorporeae cuipiam substantiae accidentium more inhaereant, sed incorporea quaedam sunt genere diuersa ab iis, quae Substantiae dici, aut Accidentia solent.” On time as an entity that would continue to flow independently of the existence of bodies, and on time as a continuous entity in which it is not possible to distinguish parts, see Disquisitio metaphysica, Against Meditation III, Doubt IX, art. 2, in Gassendi 1658, vol. 3, 346b–347b. 69  Ibid., vol. 1, 182a: “Id nempe, quia nulla substantia, nullum accidens sit, cui non competat esse alicubi, seu quopiam in loco; & esse aliquando, seu aliquo tempore; atque ita quidem, vt, tametsi talis substantia, taléve accidens pereat; non ideò minùs constare Locus, aut fluere Tempus perseueret. Ex hoc verò fit vt Locus, & Tempus haberi res verae, Entiáve realia debeant; quòd licet tale quidpiam non sint, quale vulgò habetur aut Substantia, aut Accidens; reverâ sint tamen, neque ab Intellectu, vt Chimaerae dependeant, cùm seu cogitet Intellectus, seu non cogitet, & Locus permaneat, & Tempus procurrat.” 70  Ibid., vol. 1, 182a: “Interuallum triplici dimensione, longitudinis, & profunditatis constans, in quo corpus recipi, aut per quod transire corpus possibile sit”; “incorpoream Quantitatem.” “Latitudinis” is a correction found in the 1727 edition of Gassendi’s Opera omnia; see Gassendi 1727, vol. 1, p. [li]. 71  Gassendi 1658, vol. 1, 183a: “Quaeso autem in hac Inani regione, cùm orbiculare Lunae Caelum sit, nonnè accepto vno in concaua illius superficie puncto, concipimus esse ab illo in punctum

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Notably, Gilles Personne de Roberval seems to have sustained exactly the same type of reasoning as Gassendi, and appears to have drawn from it a conclusion that Gassendi did not explicitly draw here, namely that space is the foundation of the truth of geometry. This is reported in a letter from Mersenne to Descartes: “If we suppose that God had created nothing, [Roberval] claims that there would still be the same real solid space as exists now and he founds the eternal truth of geometry on that space which is such as would be the space in which the bodies enclosed in the firmament are, if God annihilated all those bodies.”72 This is related to the question whether space is something created or uncreated, just as mathematical truths might be considered either as eternal and uncreated, or created. For Descartes, just as mathematical truths were created truths and there could not be any uncreated entity apart from God, an uncreated space that would exist prior to God’s creation was impossible as well.73 Notably, just as Gassendi rejected the creation of mathematical truths, he considered space to be uncreated, which suggests that space might belong to the same class of objects as mathematical truths. On the one hand, space and time are real beings, and, on the other hand, Gassendi claimed that space and time were not produced by God and were independent of him.74 As a consequence, he was forced to steer between two abysses: from a physioppositum certam intercapedinem, seu distantiam? Nonne haec distantia longitudo est quaedam, incorporea puta, ac inuisibilis linea, quae regionis diameter sit, & in cuius medio sit punctum, quod sit regionis, ac Caeli centrum, quódque priùs centrum ipsius Terrae exstiterit? Nonnè subinde intelligimus quantum regionis circa hoc centrum occupatum priùs fuerit à Terra, ab Aqua, ab Aëre, ab Igne? Nonne designamus mente quantum cuiusque superficiei, quantum profunditati vniuscuiusque respondent? Nonnè proinde ibi supersunt, quas apprimè imaginemur, dimensiones longitudinis, latitudinis, & profunditatis. Profectò, vbicumque concipere licet intercapedinem, aut distantiam aliquam, ibi & dimensionem concipere licet; quatenùs talis intercapedo, aut distantia determinatae mensurae est, siue cadere in mensuram potest. Huiusmodi ergo dimensiones sunt, quas & incorporeas dicimus, & spatialeis.” 72  Mersenne to Descartes, 28 April 1638, in Descartes 1996, vol. 2, 117: “supposé que Dieu n’eût rien créé, [Roberval] prétend qu’il y aurait encore le même espace solide réel, qui est maintenant, et fonde la vérité éternelle de la Géométrie sur cet espace, tel que serait l’espace où sont tous les corps enfermés dans le Firmament, si Dieu anéantissait tous ces corps.” 73  See Descartes to Mersenne, 27 May 1638, in Descartes 1996, vol. 2, 138; 1991, 102–103: “You ask whether there would be real space, as there is now, if God had created nothing. At first this question seems to be beyond the capacity of the human mind, like infinity, so that it would be unreasonable to discuss it; but in fact I think that it is merely beyond the capacity of our imagination, like the questions of the existence of God and of the human soul. I believe that our intellect can reach the truth of the matter, which is, in my opinion, that not only would there not be any space, but even those truths which are called eternal – as that ‘the whole is greater than its part’ – would not be truths if God had not so established, as I think I wrote you once before [...].” 74  Syntagma philosophicum in Gassendi 1658, vol. 1, 183b–184a: “Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, Chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur. Non vertunt autem incommodo dici ea Spatia improducta, independentiáque à Deo, quoniam positiuum nihil sunt, hoc est, neque Substantia, neque Accidens; qua vtraque voce comprehenditur quicquid rerum est à Deo productum” (“Indeed, [the Doctors of the Church] allow these spaces to be called imaginary, not because they would depend merely on the imagination, like the chimera, but because we imagine their dimensions like corporeal dimensions which fall under the senses. But they are not deterred

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cal point of view, space and time must have an independent reality and cannot be mere fictions of the mind; but because they are uncreated entities they cannot be assigned a plenary ontological status at the risk of being in competition with God.75 But Gassendi could find in the scholastic notion of spatium imaginarium the kind of ontological entity which suited his goal. Leaving aside Suárez, who claimed that imaginary spaces were entia rationis (which Gassendi potentially knowingly rejected), we can turn to Fonseca’s and the Coimbrans’ conception of imaginary spaces as an intermediary between pure nothingness and divine reality.76 Indeed for those scholastics, imaginary spaces were not purely fictitious, and were not entia rationis, but they were not real, positive beings either77; they were positioned in between these extremes, so to say. Imaginary spaces are not nothing or fictions of the mind, precisely because ‘imaginary’ is not a synonym for fictitious here, but denotes a mental relationship with corporeal reality. Space is not imaginary in the sense that it would depend only on the imagination, just like chimeras. As the Coimbrans write: because of the inconvenience there would be to say that these spaces are neither produced by God nor dependent on him, since they are nothing positive, that is to say they are neither substance nor accident, two words which include any thing that was produced by God”). Gassendi did not make explicit what kind of independence space has with regard to God. One way to downplay the heterodox flavor of such a statement would be to consider that Gassendi envisaged this independence as independence from God’s will, which would not exclude some kind of dependence regarding God’s intellect. But Gassendi never formulated a clarification of this kind. 75  Gianni Paganini identified this tension in Gassendi’s conception of space in the Syntagma philosophicum. In the 1649 Animadversiones, although Gassendi claimed that space and time are things (res), are something real (aliquid reale), and do not simply depend on the imagination like a chimera, he did not present them as entia realia that would be even more fundamental than substance and accidents; Gassendi 1649, 614, 616. See Paganini 2005, 2008. However, as early as 1649, Gassendi did claim that space “is not only prior to what is located, but also to everything since the dawn of time,” Gassendi 1649, 622: “non modo est locato prius, sed omni etiam ab aevo est.” 76  Suárez, Disputationes metaphysicae, disp. LI, section I, 24, in Suárez 1861, 979a–b: “Itaque, quatenus hoc spatium apprehenditur per modum entis positivi distincti a corporibus, mihi videtur esse ens rationis, non tamen gratis fictum opere intellectus, sicut entia impossibilia, sed sumpto fundamento ex ipsis corporibus, quatenus sua extensione apta sunt constituere spatia realia, non solum quae nunc sunt, sed in infinitum extra coelum […]. Ubi etiam annotavimus, cum corpus dicitur esse in spatio imaginario, illud, esse in, sumendum esse intransitive, quia non significat esse in alio, sed esse ibi ubi, secluso corpore, nos concipimus spatium vacuum, et ideo hoc, esse ibi, revera est modus realis corporis, etiamsi ipsum spatium ut vacuum vel imaginarium nihil sit.” For Suárez, there is no middle ground between real being and being of reason. If something is not a real being, it can only be a being of reason: “si ens reale non est, quale ens esse potest, nisi rationis, cum inter haec non sit medium,” disp. LI, section I, 24, in Suárez 1861, 979a. In themselves, imaginary spaces are nothing; disp. LI, section I, 12, in ibid., 975b: “Sed nihilominus sufficienter videtur posse convinci illud spatium, prout condistinctum a corpore continente et contento, revera esse nihil, quia neque est substantia, neque accidens, neque aliquid creatum aut temporale, sed aeternum.” On late scholastic Jesuit conceptions of imaginary spaces, see Leijenhorst 1996. 77  Conimbricenses 1596, vol. 2, col. 518: “Spatium hoc non esse ens rationis[.]” Oresme refused to assimilate space to a chimera: “non est sicut chimera aut hircocervus,” Questiones super Physicam, IV, 6, in Oresme 2013, 461. Conimbricenses 1596, vol. 2, col. 518: “Item, nec esse vllum aliud reale ac positivum ens, cum nihil tale praeter Deum ab aeterno fuerit [...].”

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This space is not a being of reason, for bodies are received by it in reality inside the world, without any aid of the intellect, and could be so received outside the world (if they were created there by God). Therefore, their dimensions are commonly called ‘imaginary,’ not because they are fictitious or depend solely on a notion of the mind or do not exist outside the intellect, but because we imagine that they correspond in space to the real and positive dimensions of bodies by a certain proportion.78

Although Gassendi never explicitly referred to the Coimbrans, he had adopted exactly the same position in De vita et doctrina Epicuri and in the Animadversiones: space is imaginary insofar as its dimensions are imagined in the way we imagine bodily dimensions.79 In the Syntagma philosophicum Gassendi explained: [I]t is certain that, by these words ‘space’ and ‘spatial dimensions,’ we do not conceive anything but those spaces that are commonly called imaginary and which the greatest part of the Church Doctors admit as existing beyond the world. Indeed, they allow these spaces to be called imaginary, not because they would depend merely on the imagination, like a chimera, but because we imagine their dimensions like the corporeal dimensions which fall under the senses.80  Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 518–519: “Spatium hoc non esse ens rationis, cum ab eo reipsa absque opera intellectus intra mundum corpora recipiantur, & extra mundum recipi queant, si illic a Deo creentur. Quare eius dimensiones non idcirco imaginariae dici consueuerunt, quod fictitiae sint, aut a sola mentis notione pendeant, nec extra intellectum dentur; sed quia imaginamur illas in spatio, proportione quadam respondentes realibus ac positiuis corporum dimensionibus.” That those spaces are called ‘imaginary’ not because they are fictitious, but because they are imagined, was also stated by Aversa: “Et ideo vocatur imaginarium, quia ita imaginatione nostra apprehenditur. At non per hoc est penitus fictitium, sed verè datur,” Aversa 1625, 788a. This can also be found in Fonseca, see Fonseca 1589, 605: “Non est igitur spatium, quod & corporibus occupatur, & extra caelum infinite in omnem partem distentum est, quantitas ulla vera & realis, sed imaginaria. Non, quia ipsum spatium ex imaginatione pendeat, quasi nullum sit vsquam nisi cum nos illud omnino fingimus; sed quia spatium, quod re vera suo modo est, semperque fuit, ac erit, non est vera quantitas, sed ficta quantitas.” 79  Contrary to what Paganini claims, this apprehension of space by the imagination is not something that appears only in the Animadversiones: see Paganini 2008, 189. Gassendi 1637, ff. 202v–203r: “Et dicito has dimensiones aliquid non realeis, sed imaginarias; reuerâ tamen, ac nemine cogitante sunt, quantumuis ipsas ex corporearum comparatione imagineris.” See also Gassendi 1649, 199: “Primùm, nihil esse videtur, quod obstet asserere spatia vltra hunc mundum infinita. Quippe Doctorum etiam nostrorum quam-plurimi illa defendunt, Imaginaria appellitantes, quod in iis longitudinis, latitudinis, altitudinis dimensiones, illis, quae in corporibus sunt, consimileis imaginemur”; ibid., 616: “Etenim constat nomine Spatij, Dimensionumque Spatialium, nihil intelligere nos aliud, quàm quae Spatia vulgò Imaginaria nominant, qualiáque Sacrorum Doctorum maxima pars dari admittit vltra Mundum: Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur.” This passage is reproduced in the Syntagma philosophicum (see fn. 80). This undermines Paganini’s interpretation of the Animadversiones as downplaying the reality of space in comparison both with book XIV of De vita et doctrina Epicuri and the Syntagma philosophicum; see Paganini 2005, 298, 332. 80  Gassendi 1658, vol. 1, 183b: “Etenim constat nomine Spatij, dimensionúmque Spatialium, nihil intelligere nos aliud, quàm quae Spatia vulgò Imaginaria nominant, qualiáque Sacrorum Doctorum maxima pars dari admittit vltra Mundum. Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, Chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur.” Ibid., 189b: “Hoc sanè, vt iam aliquoties insinuauimus, nihil aliud est, quàm quae pars maxima Doctorum vocat, admittitque spatia Imaginaria, quippe Imaginaria dicunt, reputantque, non quòd non reuerâ seclusaque imaginatione 78

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This explains that we can have some knowledge of space, even if space is not perfectly sensible. We can conceive the dimensions of space by analogy with the dimensions of bodies.81 Admittedly, Gassendi’s notion of space is distinguished from the traditional notion of imaginary spaces which, on theological elaborations, were conceived as non-dimensional for the medieval and most late scholastics, because they were the place for God and the angels.82 But Gassendi relied on the scholastic theory of imaginary spaces to sustain the reality of an extramundane void space that is, contrary to the scholastic imaginary spaces, three-dimensional, but is deprived of any positive nature. On a scholastic account, imaginary spaces were not an actual container, but only a possible or virtual place for bodies. Imaginary space, for Suárez and the Coimbrans, was non-dimensional and corresponded to God’s immensity as long as it remained void, but could be filled with body and acquire dimensionality, thus becoming real space.83 This explains why, according to the Coimbrans, one could conceive geometrical objects, rather than real bodies, to be in those imaginary spaces: “One must therefore understand […] that, beyond the sky, there is an infinitely extended space; which is not something real, but imaginary, in which it is allowed to conceive points, lines, and surfaces enduring in this same imaginary interval [...].”84 non sint, sed quòd eas, quae in ipsis dimensiones spatiales sunt, instar corporearum, quae in corporibus familiare est obseruare, imaginemur.” 81  The apprehension of space by the imagination as it is here stated by Gassendi might seem to contradict one of his later claims, namely that we have no sensation or imagination of the infinite. Gassendi indeed appealed to infinite spaces and times as that which goes beyond the limits of the imagination and is seized only by the intellect. He was thus able to justify the existence of a human intellect having some kind of autonomy in relation to the imagination because it relates to some specific objects. Ibid., vol. 2, 452b: “quid verò, quod etiam dari spatia imaginaria vltra Mundum disserimus, quae ratio omni fine carere, infinitave esse ostendat; & constat nihilominùs nullam in nobis speciem, imaginemve infiniti esse; ac nostram proinde Imaginationem longè esse, vt tantam illorum spatiorum, quanta est magnitudinem, extensionem, vastitatem capiat? Imaginatio quidem nostra aliquovsque vltra Mundi amplitudinem exporrigitur; at breui tamen terminatur, soláque ratio superest, quae superesse spatia absque vllo termino concludat. Sic et cùm profitemur Deum Mundos per illa spatia infinitos posse producere, Imaginatio quidem nostra adnititur aliquovsque hanc multitudinem prosequi: at quàm breui quaeso, resistit, soláque Intellectus vis est, quae superesse vltra omnem imaginabilem numerum innumerabilem multitudinem arguat.” This seeming contradiction can be solved if one considers that space as a whole escapes the imagination due to the fact that its infinity cannot be apprehended by the imagination. But its dimensions can be imagined, i.e. some specific (namely geometrical) determinations can be apprehended by the imagination. 82  Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 518: “Hoc spatium non esse veram quantitatem, trina dimensione praeditam; alioqui non possent recipi in eo corpora, cùm plures eiusmodi dimensiones in eodem situ naturae viribus simul esse nequeant.” Grant 1981, 164: “To identify imaginary, infinite space with God’s immensity and also to assign dimensionality to that space would have implied that God Himself was an actually extended, corporeal being […] [and] such a move would have been completely unacceptable in medieval and early modern scholasticism.” 83  See Grant 1981, 156, 162–163. 84  Conimbricenses 1596, book IV, chap. V, qu. 1, art. 2, vol. 2, col. 31: “Sciendum igitur est […] dari extra coelum spatium quoddam infinite patens; quod non est aliquid reale, sed imaginarium,

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Among the late scholastics, Gassendi’s theory of space appears closer to that of Toletus. Indeed, for Toletus, imaginary spaces could be understood in two different ways. Either they were something we imagine outside our world, and they were fictitious. Or they were abstractions of bodies, similar to mathematical objects, and then one could consider their dimensions.85 What Gassendi did is, I think, to unite in his own concept of extramundane imaginary space that which Toletus considered separately as two different concepts of space. For Toletus, according to the second way of conceiving space, space was that which all bodies have in common when their peculiarities were removed by abstraction. Even if, for Gassendi, extramundane void space was a three-dimensional physical reality existing beyond the limits of the world, the author of the Syntagma philosophicum also conceived of extramundane void space in a way that made it akin to a geometrical entity. For Gassendi, mathematical objects were, indeed, conceived through an abstraction from sensible bodies. In the Syntagma philosophicum, Gassendi described this procedure of abstraction as follows: But truly, because matter and, through matter, every natural body, possesses, among other properties, magnitude or quantity which consists in threefold extension or dimension, namely length, width, and depth, for that reason the geometer or the mathematician who selects that property mentally separates it from matter, examines it separately, and produces demonstrations. And because the dimension of depth involves the two others and is such that it is understood to be involved in them, for that reason it is also called body, but mathematical or geometrical body, and the genus of quantity, and not to the genus of substance or matter from which it is understood to be abstracted by a mental or visual inspection. And this is the reason why you hear it said that the line is regarded by the geometer as a length deprived of width, and the surface as a width deprived

in quo concipere fas est puncta, lineas, & superficies in eodem imaginario intervallo permanentes [...].” Note that the relation between extramundane void space and mathematics can be dated back to the medieval period. Albert of Saxony already presents the idea that the parts of such void spaces could be distinguished by distance; see Albert of Saxony 2008, 131: “Quia Deus extra mundum talem lapidem creatum posset movere motu recto, et facere eum distare plus ab ultimo caelo quam prius; sed non posset talia facere nisi per spatium”; “si tales lapides non essent sibi invicem immediati, sicut Deus posset eos creare, tunc unus videretur distare ab alio, et per consequens extra caelum videretur esse distantia per quam tales lapides creati distarent.” 85  Toletus 1593, book IV, chap. V, qu. 8, ff. 121v-122r: “Est autem notatu dignum, locum, seu spacium imaginarium bifariam nos posse considerare. Vno modo, vt sit res ficta omnino, & fingamus esse, quod non est, vt extra caelum, vel in vacuo, vt diximus. Altero modo, in communi abstrahendo ab hoc, vel illo spacio vero singulorum corporum, spacium in communi totius mundi, in quo modo sunt corpora, abstrahendo, inquam, ab hoc, vel illo corpore: & haec consideratio non est ficta, sed vera […]. Sic ergo imaginamur illud spacium in communi totius mundi, tanquam quiescens, id est, abstrahendo a motu eiusdem, & a particularibus subiectis: & in communi similiter in eo distantiam consideramus, & situm in communi, & singularium partium eius positionem, omnia abstrahendo in communi, vt Mathematicus figuras […]. Et hinc est, quod spacium in communi omnes sic abstrahunt, quia vident illa accidentia in communi remanere, nam quamuis mutetur spacium, hoc tamen manet spacium, & aequale spacium.” See also Albert the Great’s Commentary on Aristotle’s Physics in Albert the Great 1651, vol. 2, 177a: “vacuum non dicatur esse nisi dimensiones mathematicae [...].”

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of depth; however, in reality, that is to say in matter or in material body, there is no length without width, nor any width without depth.86

Gassendi considered both mathematical objects and space incorporeal: “In fact even Aristotle does not seem to be able to give any other reason to explain why two contiguous surfaces coincide or are considered to be one and the same thing, than that they are incorporeal; which can also be said regarding several concurring points or lines [...].”87 From that point of view, I would say that, in comparison with the Coimbrans and Toletus, Gassendi’s conception of space can be seen as one more step forward towards the emergence of physical space with a geometrical structure. Indeed, let us try to summarize the properties of Gassendian space. Extramundane space “with its dimensions [is] extended to infinity in every direction.”88 Space is three-dimensional infinite extension. It is measurable: “a larger and a lesser portion of it can be designated, can be measured and can have, in short, all the relations [comparationes] that the body itself has, in so far as it has quantity.”89 From that point of view, Gassendi’s notion of imaginary spaces is close to that of Toletus, but departs from that of the Coimbrans as well as from that of Fonseca who claimed, in a refutation of Philoponus’ conception of space, that imaginary space cannot fall under the category of quantity because it is pure negation.90 Gassendi reshaped the notion of imaginary spaces by introducing quantification into it, which had been impossible while they were considered as non-dimensional, especially during the Medieval period.91 On the contrary, Gassendi’s space can be quantified, that is to say, measured. Distance from one point to another can be delineated within space. One can therefore claim that space has a metrical structure. Space is an entity in which the rules of geometry apply: “it will certainly be possible, by a geometrical postulate, to draw a straight line from one point to another or to understand it as  Gassendi 1658, vol. 1, 232a: “At verò, quia Materia, ac per ipsam corpus omne naturale, caeteras inter proprietates praeditum est Magnitudine, Quantitatéve, quae extensione, dimensionéve trina, vt putà longitudinis, latitudinis, & profunditatis consistit; ideò, Geometra, Mathematicúsve proprietatem hanc deligens, ipsam à materia mente separat, separatamque considerat, & de separata demonstrationes texit: Et quia dimensio profunditatis reliquas duas complectitur, talísque est, qualis inesse intelligitur; ideò ipsa quoque appellatur corpus, sed Mathematicum tamen, seu Geometricum, & de genere quantitatis, non item verò de genere substantiae, seu materiae, à qua intelligitur mente, considerationéve abstractum. Heinc est proinde, cur dici audias spectari à Geometra lineam, quasi longitudinem expertem latitudinis, & superficiem, quasi latitudinem, quae sit expers profunditatis; tametsi in re ipsa, hoc est in materia, materialíve corpore, nulla longitudo sine latitudine sit; nulla latitudo sine profunditate.” 87  Ibid., 219a: “Quinetiam Aristoteles non videtur posse aliâ ratione dicere duas superficies contiguas simul esse, seu pro vna eademque haberi, quàm quia illae sint incorporeae; quod quidem dici etiam potest de pluribus concurrentibus seu punctis, seu lineis; ac sanè tantò faciliùs, quantò puncta, lineae, superficies, aliud sunt à profunditate, cui tribuitur corporis nomen.” 88  Ibid., 183a: “quoquoversùm cum suis dimensionibus prolatatum in infinitum.” 89  Ibid., 184b: “potest illius portio maior, minórque designari, inque mensuram cadere, ac omneis prorsùs comparationes, quas ipsummet corpus, vt quantum est, habere.” 90  For the Coimbrans see fn. 82. See Fonseca 1589, book V, chap. XIII, qu. 7, section 1, 603–606. 91  See Grant 1981, 122–127. Henry of Ghent and Jean de Ripa are noteworthy exceptions. 86

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almost drawn in such a way that it can be defined by the application of an ell or another measure: therefore, although no body be found between those two points, extension or dimension which is incorporeal is nonetheless found [...].”92 This clearly presupposes some kind of homogeneous rectilinear space. Space is certainly isomorphic and isotropic because Gassendi rejected the Aristotelian (and the Epicurean) distinction between the up and the down. There is no reason to privilege one part of space over another by nature. What we perceive as differently oriented parts of the world is only a result of the constitution and order of the bodily parts which occupy this or that part of space.93 Space is characterized as immense, immobile, incorporeal and penetrable. Space is incorporeal in the sense that it is the negation of body: “with space and its dimensions, the word ‘incorporeal’ does not denote anything but the negation of body or of corporeal dimensions; and it does not denote any positive nature to which the faculties and the actions would belong, since […] space can neither act or be acted upon, but it only has the -resistance that allows other things to pass through it or to occupy it.”94 Because space has no positive nature it is not a threat to the uniqueness of God. However, does this statement not introduce some tension between a realist and a non-realist conception of space in Gassendi? If space is nothing positive, and is just the negation of body, this might seem to contradict what Gassendi said when he claimed that space and time were entia realia and not fictitious entities. However, that an entity could be a pure negation without being an ens rationis was precisely Fonseca’s conception of imaginary space. In his Commentary on Aristotle’s Metaphysics, Fonseca claimed that imaginary space is a non-resistance to receive bodies.95 This capacity is not a privation (because a privation is an ens rationis), but rather a “pure negation” (negatio pura), a negation without  Gassendi 1658, vol. 1, 190a: “poterit sanè recta linea vel per Geometricum postulatum, ab vno puncto ad aliud duci, seu quasi ducta intelligi, quae & vlnâ, aliáve mensurâ applicitâ possit definiri: Quare & licet inter illa duo puncta nullum intercipiatur corpus; intercipitur nihilominus extensio, seu dimensio, quae incorporea sit [...].” 93  Ibid., 220a. 94  Ibid., vol. 1, 183b: “in Spatio, eiusque dimensionibus vox Incorporei nihil aliud sonet, quàm negationem corporis, corporearúmve dimensionum; non autem praetereà positiuam vllam naturam, cuius facultates, actionésve sint; quippe cùm […] spatium neque agere, neque pati aliquid possit; sed habeat solùm repugnantiam, qua sinat caetera transire per se, aut se occupare.” The latter part of the quotation corresponds exactly to the Epicurean definition of body and void; see Lucretius, De rerum natura, book I, 440–444. I correct the 1658 edition by adding non before repugnantiam, just as in the text of the Animadversiones (Gassendi 1649, 616): “sed habeat solùm non repugnantiam, qua sinat caetera transire per se, aut se occupare.” This is consistent with the following passage: “corporeae sine resistantia recipiantur in incorporeis,” Gassendi 1658, vol. 1, 219a. See also Fonseca 1589, 606: “est non repugnantia quaedam capiendorum corporum commensurata corporibus locandis” and Goclenius 1613, 1068a: “Spatium Inane non est verum Ens, sed capedo quaedam corporum, sed quid corporum capedo? nihil aliud, quam repugnantiae negatio ad capienda corpora.” Gassendi is here at variance with Bartolomeo Amico, who had dismissed the very idea that imaginary space was the negation of body, i.e. vacuum. On Amico, see Grant 1981, 168–169. 95  Fonseca 1589, book V, chap. XIII, qu. 7, section 1, 605–606. 92

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a subject, because it is not the case that God could not create other worlds (in those imaginary spaces). Space, just like mathematical objects abstracted from things, is conceived by a combination of affirmations and negations. On the positive side, space is three-­ dimensional; it is a quantity. But on the negative side, those dimensions and that quantity are designated as incorporeal.96 This is precisely why space cannot really be divided. Whereas corporeal quantity can be divided at least up to a certain point, that is to say, in principle into atoms, incorporeal quantity cannot be subject to real division.97 The parts of space cannot be made really discontinuous, that is to say separated the one from the other, moved and permutated. The continuity of space in Gassendi’s view is based on the very impossibility to really separate its parts due to the fact that they are immovable: “But if something is extended in all directions, so that its parts cannot be conceived as separated from one another, nor are capable of contact and resistance, it is called space.”98 “Place cannot be interrupted by any force, but it always remains immovably continuous and identical [...].”99 Because space is immobile and immutable, and because this is true of all its parts, it is not possible to displace one part of it in order to separate it from the rest of space. This is the sense in which Gassendi understood the continuity of space. Division operated on space can be apprehended by the mind; some parts can be delineated in its extension, but they cannot really be separated from each other. It is possible to designate different parts in space, but these parts are not separate or naturally ­separable.100 Gassendi’s space is not really divisible. Notably, mathematical objects conceived by abstraction from sensible objects were considered indivisible by the mathematicians according to Gassendi. In the Disquisitio metaphysica, Gassendi mentioned “the ideas of geometric figures […] as they are conceived by geometers,

 As Mamiani remarks, “il suo spazio è una quantità pura dotata di dimensioni autonome e assolute,” see Mamiani 1979, 103. 97  Gassendi distinguished between corporeal quantity, which is divisible and separable, and incorporeal quantity, which can be determined but is not really divisible. Gassendi 1649, 621: “Dicendum est, quantitatem aliam esse corpoream, aliam incorpoream; ac proprium quidem esse corporeae, ita posse diuidi, vt partes abs se mutuò distrahantur; quod verò ad incorpoream, spatialemve attinet, ea nec diuidi, nec, vt ita loquar, discontiuari vlla vi potest; sed licet dumtaxat designatione dicere, hanc spatij partem non esse illam.” 98  Gassendi 1658, vol. 1, 131b: “Sin quidpiam ita extensum quoquouersum est, vt ipsius partes concipi non possint à se inuicem distrahi, neque esse capaces contactus, atque resistentiae, appelletur Spatium.” 99  Ibid., 224b: “Locus vi nulla interrumpi potest, sed immobiliter continuum, idemque semper permanet […].” 100  Ibid., 219b: “Heinc, cùm vrgent praeterea interuallo conuenire, vt quantitas sit, & quantitatem diuidi posse; dicendum est, quantitatem aliam esse corpoream, aliam incorpoream; ac proprium quidem esse corporeae, ita posse diuidi, vt partes abs se mutuò distrahantur; quod verò ad incorpoream, spatialémve attinet, ea nec diuidi, nec, vt ita loquar, discontinuari vlla vi potest; sed licet dumtaxat designatione dicere, hanc spatij partem non esse illam.” The similitude between place and what is placed is a similitude of dimension, see ibid., 219a. Their dimensions are superimposable. 96

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namely indivisible” because they have no real parts.101 In mathematics, indivisibility is just the result of a mental abstraction.102 However, one must recognize that Gassendi had a peculiar understanding of space’s continuity. Indeed, his conception does not amount to claiming that space is constituted of an infinity of mathematical, unextended, points. In a subsequent section of the Syntagma philosophicum Gassendi did not shy away from suggesting that space was constituted of indivisible parts in finite number which were not to be confused with mathematical points.103 Therefore, the continuity of space can only be understood, in Gassendi’s approach, as the perfect contiguity of innumerable extended parts which cannot be moved.

11.5  Conclusion Due to the outlined conception of space in Gassendi it is possible to consider Gassendi’s imaginary space a quasi-mathematical space physicalized or made real. This space has almost all the properties of geometrical extension as conceived by the mathematicians – except for continuity as we understand it today – but what Gassendi elaborated upon is nothing other but a physical or cosmological reality, namely what is to be found beyond the limits of our finite world. My claim is that he expanded on the scholastic notion of imaginary spaces in order to develop his theory of extramundane infinite three-dimensional void space. But the appropriation of imaginary spaces by Gassendi was far from an unreflected endorsement of a scholastic notion for the purpose of making his cosmological views immune to theological attacks. This notion was used by Gassendi as a tool to reshape

 Disquisitio metaphysica, in Gassendi 1972, 254: “It is false that the ideas of geometric figures are not drawn from the senses and that they can exist in the world as they are conceived by geometers, namely indivisible.” 102  Ibid., 257: “but that triangle composed of indivisible elements cannot exist except mentally and by hypothesis.” 103  Gassendi 1658, vol. 1, 341a–b: “An proinde est ad eas responsurus, negando illam tam potestate, quàm actu infinitatem partium; & concedendo insectilia, non Mathematica illa, atque infinita; verùm Physica, finitáque, ac numero solùm per mentem incomprehensibilia? Declaratum certè est quoque iam ante & infinitatem illam partium in continuo, & insectilitatem Mathematicam in rerum natura non esse, sed Mathematicorum hypothesin esse, atque idcirco non oportere argumentari in Physica ex iis, quae natura non nouit.” On this see Bloch 1971, 179–180; Palmerino 2011, 305– 306. Contrary to Bloch, I do not see a tension between the Syntagma philosophicum and the letter to Sorbière of 30 January 1644. Contrary to Bloch, in the latter Gassendi did not claim that space or place was “infinitely divisible” but that space had innumerable parts, i.e. that there were more parts in space than one could enumerate or count. Gassendi 1658, vol. 6, 179a: “Vtrumque [tempus et locus] etiam habens parteis inexhaustas” (“Both [place and time] have innumerable parts”). This is coherent with the passage just quoted from the Syntagma philosophicum, in which Gassendi suggested that the continuum could be made of finite physical indivisibles whose number went beyond the understanding (“numero solùm per mentem incomprehensibilia”). 101

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ontological categories according to the needs of epistemology and scientific requirements.104 Inheriting some of its late scholastic meaning, the notion took on a renewed conceptual dimension in Gassendi’s philosophy, since it allowed for the conception of a physical entity of the cosmos as an almost mathematical one. This is significant in regard to a broader process of mathematization of the natural world in the early modern period. Nevertheless, this did not amount to a mathematical approach to physics, since Gassendi maintained a rather clear-cut separation between mathematical entities as being continuous due to being abstracted by the human mind, and physical reality made up of discontinuous atoms and contiguous spatial parts. Rather than exactly providing later scientists like Newton the ontology of space that could fit their new science, as Koyré claimed, Gassendi’s theory represented only one more step towards a mathematical conception of space that would additionally require the abandonment of its constitution out of extended parts. This step would be made by Newton, who would give up the isomorphism of space and matter.105

References Albert of Saxony. 2008. Quaestiones in Aristotelis De caelo, ed. Benoît Patar. Louvain-la-Neuve: Peeters. Albert the Great. 1651. Opera Omnia, 21 vols, ed. Peter Jammy. Lyon: Claude Prost et al. Aversa, Raffaele. 1625. Philosophia metaphysicam physicamque complectens quaestionibus contexta. Vol. 1. Rome: Iacomo Mascardo. Bloch, Olivier. 1971. La Philosophie de Gassendi: Nominalisme, matérialisme et métaphysique. The Hague: Martinus Nijhoff. Brundell, Barry. 1987. Pierre Gassendi: From Aristotelianism to a New Natural Philosophy. Dordrecht: Reidel. Canone, Eugenio. 1993. Nota introduttiva: Le biblioteche private di eruditi, filosofi e scienziati in età moderna. In Bibliotecae selectae da Cusano a Leopardi, ed. Eugenio Canone, IX– XXII. Florence: Olschki. Clark, Joseph T. 1963. Pierre Gassendi and the Physics of Galileo. Isis 54 (3): 352–370. Conimbricenses. 1596. Commentarium Collegii Conimbricensis Societatis Iesu, in octo libros physicorum Aristotelis Stagiritae. Cologne: Lazarus Zetzner. Del Prete, Antonella. 2000. Pierre Gassendi et l’univers infini. Libertinage et philosophie au XVIIe siècle 4: 57–68. De Risi, Vincenzo. 2016. Francesco Patrizi and the New Geometry of Space. In Boundaries, Extents and Circulations: Space and Spatiality in Early Modern Natural Philosophy, ed. Koen Vermeir and Jonathan Regier, 55–106. Dordrecht: Springer. Descartes, René. 1991. The Philosophical Writings of Descartes, vol. 3: The Correspondence, ed. John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny. Cambridge: Cambridge University Press. ———. 1996. Œuvres de Descartes, ed. Charles Adam and Paul Tannery, 2nd ed. Paris: Vrin.

 The study of the notion of imaginary spaces I have presented here is therefore in agreement with Olivier Bloch’s more general statement about the use of theological arguments in Gassendi’s philosophy. See Bloch 1971, 316–317. 105  See Palmerino 2011. 104

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Fonseca, Pedro da. 1589. Commentarii in libros metaphysicorum Aristotelis Stagiritae. Vol. 2. Rome: Jacob Torneri. Galilei, Galileo. 1896. Le opere di Galileo Galilei: Edizione Nazionale. Vol. 6. Florence: G. Barbera. Gassendi, Pierre. 1632. Mercurius in sole visus et Venus invisa Parisiis anno 1631. Paris: Sébastien Cramoisy. ———. 1636. De vita et doctrina Epicuri, book XII. MS Tours 709, ff. 147r–166v. ———. 1637. De vita et doctrina Epicuri, book XIV. MS Tours 709, ff. 193r–214v. ———. 1641–1642. De vita et doctrina Epicuri, books XVII-XX. MS Tours 709, ff. 268r–500v. ———. 1642–1643. De vita et doctrina Epicuri, books XXII-XXIII. MS Tours 710, ff. 576r–720v. ———. 1649. Animadversiones in decimum librum Diogenis Laertii. Lyon: Guillaume Barbier. ———. 1658. Opera Omnia, 6 vols. Lyon: Anisson and Devenet. ———. 1727. Opera Omnia, 6 vols. Florence: Giovanni Gaetano Tartini and Santi Franchi. ———. 1972. The Selected Works. Trans. Craig Brush. New York/London: Johnson. Goclenius, Rudolph. 1613. Lexicon philosophicum. Frankfurt: Matthias Becker. Grant, Edward. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Helden, Albert van. 1985. Measuring the Universe: Cosmic dimensions from Aristarchus to Halley. Chicago: The University of Chicago Press. Henry, John. 1979. Francesco Patrizi da Cherso’s Concept of Space and its Later Influence. Annals of Science 36: 549–573. Henry of Ghent. 2007. Quodlibet XV, ed. Girard Etzkorn and Gordon A. Wilson. Leuven: Leuven University Press. Humbert, Pierre. 1936. L’Œuvre astronomique de Gassendi. Paris: Hermann. John Buridan. 1509. Acutissimi philosophi reverendi Magistri Johannis Buridani subtilissime questiones super octo Phisicorum libros Aristotelis diligenter recognite et revise a Magistro Johanne Dullaert de Gandavo antea nusquam impresse. Paris: Denis Roce. John Duns Scotus. 1895. Quaestiones quodlibetales. In Opera Omnia, vol. 25. Paris: Louis Vivès. Koyré, Alexandre. 1957a. Gassendi et la science de son temps. In Actes du Congrès du Tricentenaire de Pierre Gassendi (4–7 août 1955). Digne: R. Vial. ———. 1957b. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins University Press. Leijenhorst, Cees. 1996. Jesuit Concepts of Spatium Imaginarium and Thomas Hobbes’s Doctrine of Space. Early Science and Medicine 1 (3): 355–380. LoLordo, Antonia. 2007. Pierre Gassendi and the Birth of Early Modern Philosophy. Cambridge: Cambridge University Press. Mamiani, Maurizio. 1979. Teorie dello spazio da Descartes a Newton. Milan: Franco Angeli. McGuire, James E. 1978. Existence, Actuality, and Necessity: Newton on Space and Time. Annals of Science 35 (5): 463–508. Morin, Jean-Baptiste. 1631. Famosi et antiqui problematis de telluris motu, vel quiete, hactenus optata solutio. Paris: Apud authorem. Muccillo, Maria. 2010. La concezione dello spazio di Francesco Patrizi (1529–1597) e la sua fortuna nell’ambito della reazione anticartesiana inglese. In Dal cartesianismo all’illuminismo radicale, ed. Carlo Borghero and Claudio Buccolini, 49–71. Florence: Le Lettere. Nicole Oresme. 1968. Le Livre du ciel et du monde, ed. Albert D. Menut and Alexander J. Denomy. Madison: University of Wisconsin Press. ———. 2013. Questiones super Physicam (Books I-VII), ed. Stefano Caroti, Jean Celeyrette, Stefan Kirschner, and Edmond Mazet. Leiden: Brill. Paganini, Gianni. 2005. Hobbes, Gassendi und die Hypothese der Weltvernichtung. In Die Konstellationsforschung, ed. Martin Mulsow and Marcelo Stamm, 258–339. Frankfurt a.M.: Suhrkamp. ———. 2008. Le néant et le vide: Les parcours croisés de Gassendi et Hobbes. In Gassendi et la modernité, ed. Sylvie Taussig, 177–214. Turnhout: Brepols.

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Palmerino, Carla Rita. 1998. Atomi, meccanica, cosmologia: Le lettere galileiane di Pierre Gassendi. PhD dissertation. Florence. ———. 2001. Galileo’s and Gassendi’s Solutions to the Rota Aristotelis Paradox: A Bridge Between Matter and Motion Theories. In Medieval and Early Modern Corpuscular Matter Theories, ed. John E.  Murdoch, William R.  Newman, and Christoph H.  Lüthy, 381–422. Leiden: Brill. ———. 2004a. Gassendi’s Reinterpretation of the Galilean Theory of Tides. Perspectives on Science 12 (2): 212–237. ———. 2004b. Galileo’s Theories of Free Fall and Projectile Motion as Interpreted by Pierre Gassendi. In The Reception of the Galilean Science of Motion in Seventeenth-Century Europe, ed. Carla Rita Palmerino and Hans Thijssen, 137–164. Dordrecht: Kluwer. ———. 2011. The Isomorphism of Space, Time and Matter in Seventeenth-Century Natural Philosophy. Early Science and Medicine 16 (4): 296–330. Pantin, Isabelle. 2006. Teaching Mathematics and Astronomy in France: The Collège Royal (1550–1650). Science & Education 15: 189–207. Patrizi, Francesco. 1591. Nova de universis philosophia. Ferrara: Mammarelli. ———. 1943. On Physical Space. Trans. Benjamin Brickman. Journal of the History of Ideas 4(2): 224–245. Peiresc, Claude Nicolas Fabri de. 1893. Lettres de Peiresc publiées par Philippe Tamizey de Laroque. Vol. 4. Paris: Imprimerie nationale. Peter John Olivi. 1922. Quaestiones in secundum librum Sententiarum. Vol. 1. Ad Claras Aquas: Quaracchi. Pintard, René. 1943. La Mothe Le Vayer, Gassendi, Guy Patin: Études de bibliographie et de critique suivies de textes inédits de Guy Patin. Paris: Boivin & Cie. Richard of Middleton. 1591. Clarissimi theologi magistri Ricardi de Media Villa… super quatuor libros Sententiarum Petri Lombardi quaestiones subtilissimae, 2 vols. Brescia: De consensu superiorum. Rochot, Bernard. 1944. Les travaux de Gassendi sur Épicure et sur l’atomisme, 1619–1658. Paris: Vrin. Sakamoto, Kuni. 2009. The German Hercules’s Heir: Pierre Gassendi’s Reception of Keplerian Ideas. Journal of the History of Ideas 70 (1): 69–91. Schuhmann, Karl. 1994. La doctrine gassendienne de l’espace. In Pierre Gassendi 1592-1655. Actes du Colloque International Digne-les-Bains, 18-21 mai 1992, 233–244. Digne-les-Bains: Annales de Haute-Provence. Sturlese, Rita. 1987. Bibliografia, censimento e storia delle antiche stampe di Giordano Bruno. Florence: Olschki. Suárez, Francisco. 1861. Disputationes metaphysicae, part 2. In Opera Omnia, vol. 26. Paris: Louis Vivès. Suarez-Nani, Tiziana. 2017. L’espace sans corps: Étapes médiévales de l’hypothèse de l’annihilatio mundi. In Lieu, espace, mouvement: Physique, métaphysique et cosmologie (XIIe-XVIe siècles), ed. Tiziana Suarez-Nani, Olivier Ribordy, and Antonio Petagine, 93–107. Barcelona/ Rome: Fédération Internationale des Instituts d’Études Médiévales. Tack, Reiner. 1974. Untersuchungen zum Philosophie- und Wissenschaftsbegriff bei Pierre Gassendi (1592-1655). Meisenheim am Glan: Anton Hain. Thomas Bradwardine. 1618. De causa Dei contra Pelagium. London: John Bill. Toletus, Franciscus. 1593. Societatis Iesu, commentaria, una cum quaestionibus, in octo libros Aristotelis de Physica auscultatione. Cologne: Birckmann. Westfall, Richard S. 1962. The Foundations of Newton’s Philosophy of Nature. British Journal for the History of Science 1 (2): 171–182. William of Ockham. 1980. Venerabilis inceptoris Guillelmi de Ockham Quodlibeta septem, ed. Joseph C. Wey. St. Bonaventure: St. Bonaventure University.

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Zittel, Claus. 2013. Gassendis Astronomen-Viten. In Die Vita als Vermittlerin von Wissenschaft und Werk: Form- und Funktionsanalytische Untersuchungen zu frühneuzeitlichen Biographen von Gelehrten, Wissenschaftlern, Schriftstellern und Künstlern, ed. Karl Enenkel and Claus Zittel, 123–156. Berlin: LIT. ———. 2015. “Copernicus Found a Treasure the True Value of Which He Did Not Know at All”: The Life of Copernicus by Gassendi. In The Making of Copernicus: Early Modern Transformations of a Scientist and His Science, ed. Wolfgang Neuber, Thomas Rahn, and Claus Zittel, 251–286. Leiden: Brill.

Chapter 12

Space, Imagination and the Cosmos in the Leibniz-Clarke Correspondence Carla Rita Palmerino

Abstract  The famous correspondence between Leibniz and Clarke deals with fundamental physical and metaphysical questions, such as the soul-body interaction, the freedom of will, the composition of matter, the possibility of a vacuum, miracles, gravity, and the nature of space and time. With respect to most of these issues the disagreement between Leibniz and Clarke results from their conflicting views on God’s role in the world. While Clarke blames Leibniz for turning God into a necessary agent, Leibniz accuses Clarke of having a wrong notion of God’s power and wisdom. The aim of this chapter is to show how theological, metaphysical and cosmological considerations shape Leibniz’ and Clarke’s respective theories of space. In his letters, Leibniz repeatedly invokes the Principle of Sufficient Reason and the Principle of the Identity of Indiscernibles in order to argue, against Newton and Clarke, that space cannot exist independently from, and prior to, physical bodies. Clarke, in turn, appeals to imaginary scenarios of medieval origin in order to show that the metaphysical principles that underlie Leibniz’s theory of space imply a limitation of God’s freedom. The chapter analyses in detail the role that imaginary scenarios play in the discussion concerning the ontological status of space, and attempts to provide a new interpretation of the function of the Principle of the Identity of Indiscernibles in the Correspondence.

12.1  Introduction In the final year of his life, Leibniz engaged in what was to become one of the most famous epistolary exchanges in the history of science and philosophy with the Newtonian theologian Samuel Clarke. In November 1715 Leibniz wrote a letter to his former pupil Caroline of Ansbach – who had recently moved from Hanover to C. R. Palmerino (*) Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands e-mail: [email protected] © Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_12

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London with her husband, the future King George II – warning her about the negative religious implications of English philosophy and Newtonian physics. Caroline forwarded an extract of Leibniz’s the letter to Samuel Clarke, who promptly drafted a reply. Up to the moment of Leibniz’s death, in November 1716, the two thinkers exchanged ten increasingly intricate letters, which were published by Clarke in 1717. The Correspondence deals with fundamental physical and metaphysical issues, such as the soul-body interaction, the freedom of will, the composition of matter, the possibility of a vacuum, miracles, gravity, and the nature of space and time. On most of these issues, the disagreement between Leibniz and Clarke results from their conflicting views on God’s role in the world. As Steven Shapin has observed, “the Newtonian schema stressed God’s voluntary capacities, while the Leibnizian cosmology emphasized his intellectual attributes.”1 Leibniz’s intellectualist stance is already evident in the Discourse on Metaphysics (1686). There he criticizes voluntarist thinkers “who say that the eternal truths of metaphysics and geometry, and consequently also the rules of goodness, justice, and perfection, are merely the effects of the will of God.”2 In Leibniz’s opinion, goodness, order and rationality are coeternal with God and constitutive of his understanding and can hence be used to judge his creation. God deserves praise because he “does nothing which is not orderly and regular,” and because of all the possible worlds he has chosen the most perfect, that is to say, “the one which is at the same time the simplest in hypotheses and the richest in phenomena.”3 In the correspondence with Clarke, Leibniz repeatedly stresses that Newtonian physics does not do justice to God’s goodness and rationality. For example, to admit atoms and void in nature, like Clarke and Newton do, “is ascribing to God a very imperfect work”: why should God leave space empty if he can fill it with matter? and why should he prefer an atom to a corpuscle, which is “actually subdivided in infinitum and contains a world of other creatures which would be wanting in the universe if that corpuscle was an atom?”4 While Leibniz accuses Clarke of having “a mean notion of the wisdom and power of God,”5 Clarke blames Leibniz for turning God into a necessary agent. For “to assert that whatever God can do, he cannot but do is making him no governor at all, but a mere necessary agent, that is, indeed no agent at all, but mere fate and nature and necessity.”6 Clarke grants Leibniz that “nothing is without a sufficient reason why it is, and why it is thus rather than otherwise,” but he adds that “this

 Shapin 1981, 192.  Discourse on Metaphysics, in Leibniz 1989, 36. 3  Ibid., 39. 4  Both in the text and in the footnotes I use the letters ‘C’ and ‘L’ to indicate the respective author of the letter, roman numerals to indicate the number of the letter, and Arabic numerals to indicate the paragraph. L.IV, post scriptum, Alexander 1956, 44. 5  L.I.4, ibid., 12. 6  C.IV.22–23, ibid., 50. 1 2

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s­ ufficient reason is oft-times no other, than the mere will of God.”7 The “wisdom of God may have good reasons” for leaving some parts of space empty and for creating matter “in what quantity, and at what particular time, and at what particular spaces he pleases.”8 The clash between Clarke’s and Leibniz’ respective views on God’s omnipotence becomes particularly apparent in their debate concerning the nature of space and time. In the Correspondence Leibniz repeatedly invokes the Principle of Sufficient Reason (henceforth PSR) and the Principle of the Identity of Indiscernibles (henceforth PII) in order to argue, against Newton and Clarke, that space and time are not ontologically independent entities but exist only as relations among objects. Clarke, in turn, appeals to imaginary scenarios of medieval origin in order to prove that Leibniz’ theory of space implies a limitation of God’s freedom. In the present chapter, I shall try to shed light on the metaphysical, cosmological and theological considerations that shape Leibniz’ and Clarke’s respective theories of space, and on the role that imaginary scenarios play in their discussion. I shall, moreover, provide a new interpretation of the role that the PII plays in the Correspondence by arguing, against Fred Chernoff and Gonzalo Rodriguez-Pereyra, that Leibniz formulated both a logical and a contingent version of this principle, each applying to a different domain.

12.2  T  he Ontological Status of Space According to Leibniz and Clarke In his second letter to Clarke, Leibniz famously argues, in polemic with Newton, that natural philosophy must be grounded on metaphysical, rather than on mathematical principles. While the principle of non-contradiction constitutes the foundation of mathematics, “another principle is needed” for natural philosophy, namely that of sufficient reason, which requires “that nothing happens without a reason why it should be so rather than otherwise.”9 Leibniz illustrates this principle by means of a famous Archimedian example: L.II.1: Archimedes, in his book De Aequilibrio, was obliged to make use of a particular case of the great principle of sufficient reason. He takes it for granted, that if there be a balance, in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will be at rest. ‘Tis because no reason can be given, why one side should weigh down, rather than the other. Now, by that single principle, viz. that there ought to be a sufficient reason why things should be so, and not otherwise, one may demonstrate the being of a God, and all the other parts of metaphysics or natural theology.10

 C.II.1, ibid., 20.  C.IV.15, ibid., 49. 9  L.II.1, ibid., 16. 10  Ibid. 7 8

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Leibniz’s analogy could not sound anything other than inadequate to someone who, like Clarke, defined liberty as the “continual power” of choosing whether one “should act or forebear acting.”11 In Clarke’s view, by claiming that God “could in no case act without a predetermining cause, any more than a balance can move without a preponderating weight,” Leibniz takes away “all power of choosing” and introduces “fatality.”12 A balance in a state of equilibrium is bound to remain immobile, whereas God must be able to exercise his will in a situation of indifference: C.II.1: For instance: why this particular system of matter, should be created in one particular place, and that in another particular place; when, (all place being absolutely indifferent to all matter) it would have been exactly the same thing vice versa, supposing the two systems (or the particles) of matter to be alike; there can be no other reason, but the mere will of God.13

In his third letter, Leibniz turns his correspondent’s reasoning upside down. While Clarke regards the creation of matter in space as a paradigmatic example of God’s power of choosing in the absence of preponderating motives, Leibniz invokes the PSR to argue that God could not have created the world in an independently existing space: L.III.5: I say then, that if space was an absolute being, there would something happen for which it would be impossible there should be a sufficient reason. Which is against my axiom. And I prove it thus. Space is something absolutely uniform; and, without the things placed in it, one point of space does not absolutely differ in any respect whatsoever from another point of space. Now from hence it follows, (supposing space to be something in itself, besides the order of bodies among themselves,) that 'tis impossible there should be a reason, why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner, and not otherwise; why everything was not placed the quite contrary way, for instance, by changing East into West.14

In the lines just quoted, Leibniz argues that the creation of the world in a Newtonian space would entail a violation of the PSR, as God would inevitably face a choice between alternative, and yet equivalent, spatial configurations of matter. An East-­ West switch, for example, would produce two mirrored worlds, with a different location in absolute space, and yet the same spatial relations between their components.15 According to a relational theory of space, however, it would not be possible for God to find himself in a situation of indifference, as there would be no choice to be made: L.III.5: But if space is nothing else, but that order or relation; and is nothing at all without bodies, but the possibility of placing them; then those two states, the one such as it now is, the other supposed to be the quite contrary way, would not at all differ from one another. Their difference therefore is only to be found in our chimerical supposition of the reality of  Clarke 1998, 74.  CII.1, Alexander 1956, 21. 13  Ibid., 20–21. 14  L.III.5, ibid., 26. 15  Cf. Rickles 2008, 33. 11 12

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space in itself. But in truth the one would exactly be the same thing as the other, they being absolutely indiscernible; and consequently there is no room to enquire after a reason of the preference of the one to the other.16

In these lines, Leibniz invokes the PII in order to argue that, if space is nothing at all “without bodies,” then two symmetrical configurations are indiscernible, and hence identical. In the subsequent paragraph, he applies the same reasoning to time. The question why God chose to create the world in one given moment of time, rather than another, only makes sense if one believes, with Newton, that time flows independently from anything external. But if one agrees with Leibniz that “instants, considered without the things, are nothing at all,” then it would have been impossible for God to create the world sooner since “one of the two states, viz. that of a supposed anticipation, would not at all differ, nor could be discerned from, the other which now is.”17 Clarke’s reaction to Leibniz’s argument is very subtle and deserves to be analysed in detail. After reiterating his conviction that “mere will, without any thing external to influence it, is alone that sufficient reason,” Clarke explains why, in his view, the PSR cannot be used to criticize the Newtonian theory of space: in the framework of Leibniz’s theory of space and time one can, in fact, still conceive of spaces that “are really different or distinct one from another, though they be perfectly alike.” This, in turn, means that “even though space were nothing real, but only the mere order of bodies” it would still be possible to conceive of situations in which God would not be able to act according to the PSR, but would have to exercise his freedom of indifference: “It would be absolutely indifferent, and there could be no other reason but mere will, why Three equal Particles should be placed or ranged in the order a, b, c, rather than in the contrary order.”18 Then Clarke proceeds to observe the following: C.III.2: And there is this evident absurdity in supposing Space not to be real, but to be merely the order of bodies; that, according to that notion, if the earth and sun and moon had been placed where the remotest fixed stars now are, (provided they were placed in the same order and distance they now are with regard to one another,) it would not only have been, (as this learned author rightly says,) la même chose, the same thing in effect; which is very true: but it would also follow, that they would then have been in the same place too, as they are now: which is an express contradiction.19

Richard Arthur has recently claimed that Clarke’s argument is circular, as it “presupposes that the places of the earth, sun and moon are places in absolute space that are individuated independently of those bodies,” and thereby ignores Leibniz’s claim that, “given the homogeneity of mathematical space, the points can only be individuated by what is situated at them.”20 I would like to propose a more charitable interpretation of Clarke’s argumentative strategy. In my view, in the lines just quoted  L.III.5, Alexander 1956, 26.  L.III.6, ibid., 27. 18  C.III.2, ibid., 30–31. 19  Ibid., 31. 20  Arthur 2017, 118. 16 17

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Clarke uses conceivability as a guide to determine possibility. Taking his cue from Leibniz’s switch argument, Clarke suggests that the very fact that one can conceive of the entire world being rotated (with the East being switched to the West), or of the solar system being placed where the fixed stars are situated now, means that, even within a relational theory of space, the alternative locations are not indiscernible, and hence, that it must have been possible for God to assign to the world a different position. To this, Clarke adds a second argument: C III.4: If space was nothing but the order of things coexisting; it would follow, that if God should remove in a straight line the whole material world entire, with any swiftness whatsoever; yet it would still always continue in the same place: and that nothing would receive any shock upon the most sudden stopping of that motion.21

Both in C III.2 and C III.4 Clarke takes the actual state of the world as a starting point for a counterfactual reasoning. In the former scenario, he imagines two possible worlds with the same internal arrangement and yet in a different location relative to one another; in the latter he imagines that God intervenes to change the actual position of the world. As Chernoff has observed, with the former argument Clarke asks about two states that, “if distinct, must comprise parts of separate possible worlds,” whereas with the latter he asks about “two states that, even if distinct, might constitute parts of the same possible world.”22 In his own rendition of Clarke’s second argument Chernoff, like other scholars, simply speaks of the “entire material world” being “moved,” thereby omitting the role that God plays in the thought experiment.23 In my view, however, the scope of Clarke’s argument can only be fully understood if one takes into account its theological context. In his masterful book Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution Edward Grant briefly dwells on the Correspondence observing that Clarke’s argument of God displacing the world in a straight line “might have come straight from Nicole Oresme’s Le Livre du Ciel et du monde in the fourteenth century.”24 Grant is obviously thinking of the following passage of Oresme’s book: There is an imagined infinite and immobile space outside the world […] and it is possible without contradiction, that the whole world could be moved in that space with a rectilinear motion. To say the contrary is an article condemned at Paris.25

 C.III.4, Alexander 1956, 32.  Chernoff 1981, 132. 23  Ibid. E.J. Khamara writes, along similar lines: “Hence Clarke allowed the following suggestion (which I shall call Clarke’s hypothesis) to be a coherent logical possibility: that the material universe as a whole should, for any period of time and without any internal alterations, be in a state of uniform rectilinear motion along a certain absolute direction” (Khamara 2006, 99). See also Alexander 1956, xxvii. 24  Grant 1981, 249. 25  Quoted in Grant 1979, 230 (my emphasis). 21 22

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Oresme here refers to the famous condemnation of 1277, when Etienne Tempier, the Bishop of Paris, compiled a list of 219 philosophical and theological theses which were not to be taught and discussed in the Faculty of Arts. This list includes a number of propositions which were condemned because they implied a limitation of God’s power. One of them stated that “God could not move the heavens with rectilinear motion and leave behind a void.”26 Grant has convincingly shown that the preoccupation with God’s absolute power which informed many articles of the condemnation acted as a “powerful analytic tool in natural philosophy.” In the wake of the condemnation, medieval natural philosophers formulated “a host of thought experiments that were, in one way or another, contrary to Aristotelian physics and cosmology.”27 These thought experiments, among them that of God displacing the world in a straight line, appealed to the distinction between the potentia Dei absoluta, that is to say, God’s power to do whatever does not imply a logical contradiction, and the potentia Dei ordinata, or the power which God exercised in the Creation. Given Clarke’s voluntaristic stance, it is no surprise that he invokes the medieval scenario of God displacing the world. His goal is to show that such a scenario, which is conceivable and hence should be regarded as possible, is incompatible with Leibniz’s theory of space, according to which God’s actions would have no effect, as the spatial relations among the parts of the world would remain unchanged. It is important to note that Clarke modifies the medieval thought experiment slightly by asking what would happen if God suddenly stopped the rectilinear motion of the world. As will become clear in the fourth letter, Clarke was convinced that such a stop would have the same noticeable effect on the bodies placed on the surface of the earth as the sudden deceleration of a ship has on its passengers. But how did Leibniz answer Clarke’s arguments? At the beginning of the fourth letter, he reiterates the conviction that a “will without motive” is “a fiction, not only contrary to God’s perfection, but also chimerical and contradictory; inconsistent with the definition of the will.”28 Then he starts discussing his opponent’s arguments one by one, dwelling on the conceivability and viability of Clarke’s imaginary scenarios. In response to Clarke’s observation that, even under the assumption of relative space, two orders (abc and cba) would be indifferent, Leibniz argues that L.IV.3: ‘Tis a thing indifferent, to place three bodies, equal and perfectly alike, in any order whatsoever; and consequently they will never be placed in any order, by him who does nothing without wisdom. But then he being the author of things, no such things will be produced by him at all; and consequently there are no such things in nature.29

 Grant 1996, 124. As Algra’s Chapter  2  in this volume recalls, the first extant version of this thought experiment is found in the work of the Stoic philosopher Cleomedes. 27  Grant 1976, 241. 28  L.IV.2, Alexander 1956, 36. 29  Ibid. 26

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In these lines Leibniz claims that, in the case of three equal bodies, it is impossible to distinguish between the spatial arrangements abc, acb, cba etc., because the arrangement would always be aaa. Hence God, who does nothing without wisdom, would not be able to decide in which order to place the three bodies. However, such a situation of indifference cannot occur, since God would not create three equal bodies.30 As a confirmation of this fact, Leibniz quotes the anecdote of the gentleman who ran all over Princess Sophia’s garden, looking in vain for two leaves perfectly alike.31 In the subsequent paragraphs, Leibniz addresses the question whether God could have created the world at a different time or in a different place than he did: L.IV.6: To suppose two things indiscernible, is to suppose the same thing under two names. And therefore to suppose that the universe could have had at first another position of Time and Place, than that which it actually had; and yet that all the parts of the universe should have had the same situation among themselves, as that which they actually had; such a supposition, I say, is an impossible fiction.32

According to Barry Dainton, Leibniz’s argument is not valid, as it is built on a premise that Clarke cannot accept. From a Newtonian point of view, the relations between material bodies and absolute space and time “are real features of the world,” and it is hence illegitimate to claim that alternative positions of the world in space and time would be indiscernible.33 In my view, this interpretation misses the point. In the fourth letter Leibniz is trying to respond to Clarke’s claim that, even within the context of a relational theory of space and time, one can imagine situations in which God would have to exercise his freedom of indifference. In IV.3 Leibniz argues that the situation envisaged by Clarke is indeed conceivable, but is incompatible with the PSR, and hence cannot occur in our world. In IV.6, by contrast, he claims that the scenario described by Clarke is conceivable within the framework of a Newtonian theory of space (according to which two different positions in absolute space are, indeed, discernible), but is an impossible fiction, and hence unconceivable, from the point of view of Leibniz’s own theory. Leibniz seems to make a similar point with respect to the scenario of God displacing the world in a straight line. In L.IV.13, he maintains that a rectilinear motion of the whole world without “any alteration in it is another chimerical supposition. For, two states indiscernible from each other, are the same state.”34 With respect to Clarke’s thought experiments, Leibniz observes that

 In the Confessio philosophi (1672–1673), Leibniz had admitted the possibility that two identical bodies, for example two eggs, might be distinguished only by their situation in space. In a letter to Casati, written in 1689, Leibniz used the same example of two eggs in order to argue that there are not two things in nature which differ only extrinsically. A close examination will reveal that two apparently identical eggs are discernible ‘in themselves.’ See Rodriguez-Pereyra 2014, 84–92. 31  L.IV.4, Alexander 1956, ibid., 36. 32  L.IV.6, ibid., 37. 33  Dainton 2010, 178. 34  Leibniz IV.13, Alexander 1956, 38. 30

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L IV.15: These are idola tribus, mere chimeras, and superficial imaginations. All this is only grounded upon the supposition, that imaginary space is real. L IV.16: If space and time were anything absolute, that is, if they were anything else besides certain order of things, then indeed my assertion would be a contradiction. But since it is not so, the hypothesis (that space and time are anything absolute) is contradictory, that is, it’s an impossible fiction.35

The parenthetical sentence “that space and time are anything absolute” was not part of Leibniz’s original letter, but was added by Clarke and maintained in all later editions of the Correspondence. In a recent article Martin Lin convincingly claimed that Clarke’s addition rests on a misinterpretation of the original text. What Leibniz regarded as contradictory was not the hypothesis “that space and time are anything absolute,” but rather “that God moves the world in a straight line.”36 I fully endorse Lin’s interpretation. By invoking the medieval thought experiment of God displacing the world in a straight line, Clarke wanted to show that Leibniz’s natural philosophy (just like the Aristotelian natural philosophy from Tempier’s point of view) imposed limits on God’s freedom and power. Leibniz understood that the only viable defensive strategy was to reject the scenario tout court by claiming that it was conceivable within the framework of Clarke’s own theory of space, but appeared as an impossible fiction from the point of view of Leibniz’s own theory. It is interesting to see, however, that Leibniz adduces two different reasons why Clarke’s imaginary scenario should be rejected. In section 13 of his fourth letter Leibniz invokes, as we have just seen, the PII in order to claim that the scenario would be “a change without any change,” and would hence not be brought about by God, who “does nothing without reason.”37 A few paragraphs later, however, he denies the premise of Clarke’s thought experiment, namely that the world is finite: “There is no possible reason that can limit the quantity of matter, and therefore such limitation can have no place.”38 Clarke, as was to be expected, was not satisfied with Leibniz’s answer. To claim, like Leibniz did, that “God cannot limit the quantity of matter, is an assertion of too great consequence, to be admitted without proof.”39 Once again, what he asked Leibniz was whether, supposing the world were finite, God could move it in a straight line. Clarke observed, moreover, that it was too easy a way out to invoke the PII in order to prove the impossibility of that motion. “Two places, though exactly alike, are not the same place. Nor is the motion or rest of the universe, the same state.” An “indiscernible motion of the universe” would still be real and would have real effects upon a sudden stop.40 Incidentally, it is interesting to note that both Leibniz and Clarke interchangeably speak of the “world” and the “universe” ­moving  Leibniz IV.15-16, ibid., 38–39.  Lin 2016, 455. 37  Leibniz IV.13, Alexander 1956, 38. 38  L.IV.21, ibid., 39–40. 39  C.IV.21, ibid., 50. 40  C.IV.13, ibid., 48. 35 36

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in space, which seems to indicate that neither of the two terms is meant to include a hypothetical extra-mundane space. Scholars have rightly observed that Clarke’s conclusion is at odds with Newton’s laws of motion. According to Corollary 6 to the laws of motion of the Principia mathematica “a sudden deceleration of all the bodies alike at the same time would not disturb their relative motions,” and hence could not be discerned.41 But this is not the answer Leibniz gave to Clarke. Instead of addressing the question what would happen if the world suddenly stopped, Leibniz limited himself to reiterating his previous arguments: L.V.29: I have demonstrated, that space is nothing else but an order of the existence of things, observed as existing together; and therefore the fiction of a material universe moving forward in an infinite empty space, cannot be admitted. It is altogether unreasonable and impracticable. For, besides that there is no real space out of the material universe; such an action would be without design in it: it would be working without doing any thing, agendo nihil agere. There would happen no change, which could be observed by any person whatsoever.42

A few paragraphs later, Leibniz writes in a similar vein: L.V.52: In order to prove that space, without bodies, is an absolute reality; the author objected, that a finite material universe might move forward in space. I answered, it does not appear reasonable that the material universe should be finite; and, though we should suppose it to be finite; yet ‘tis unreasonable it should have motion any otherwise, than as its parts change their situation among themselves; because such a motion would produce no change that could be observed, and would be without design […]. The author replies now that the reality of motion does not depend upon being observed […]. I answer, motion does not indeed depend upon being observed; but it does depend upon being possible to be observed. There is no motion, when there is no change that can be observed. And when there is no change that can be observed, there is no change at all. The contrary opinion is grounded upon the supposition of a real absolute space, which I have demonstratively confuted by the want of a sufficient reason of things.43

While in the fourth letter Leibniz dubbed Clarke’s scenario as “impossible” (L.IV.6) and “chimerical” (L.IV.13), in the fifth letter he describes it as “unreasonable and impracticable” (L.V.29; L.V.52). In his reply, Clarke stresses the ambiguous modal status of Leibniz’s claims concerning space and the cosmos. Leibniz grants “that God could make the material universe finite: and yet the supposing it to be possibly finite, is styled not only as a supposition unreasonable and void of design, but also an impracticable fiction.”44 Similarly, he sometimes admits the possibility of a void,

 Arthur 2017, 120. See also Arthur 1994, 221 and Vailati 1997, 132–133. Newton’s sixth corollary states that “If bodies are moving in any way whatsoever with respect to one another and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to one another in the same way as they would if they were not acted on by those forces,” Newton 1999, 423. 42  L.V.29, Alexander 1956, 63–64. 43  L.V.52, ibid., 74. 44  C.V.26–32, ibid., 100–101. 41

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whereas at other times he speaks as if a vacuum was “absolutely impossible in the nature of things; space and matter being inseparable.”45 Equally unsatisfactory, in Clarke’s eyes, is Leibniz’s analysis of the thought experiment of God displacing the world in a straight line: C.V.52–53: He must either affirm, that ‘twas impossible for God to make the material world finite and moveable; or else he must of necessity allow the strength of my argument, drawn from the possibility of the world’s being finite and moveable. Neither is it sufficient barely to repeat his assertion, that the motion of a finite material universe would be nothing, and (for want of other bodies to compare with) would produce no discoverable change: unless he could disprove the instance which I gave of a very great change that would happen; viz. that the parts would be sensibly shocked by a sudden acceleration, or stopping of the motion of the whole: to which instance, he has not attempted to give any answer.46

Clarke’s questions were doomed to remain without an answer as Leibniz’s death, in November 1716, put an end to the correspondence. In order to understand whether Leibniz regarded the scenario of God displacing the world in a straight line as impossible or simply as unreasonable, we must turn to a much-debated question, namely that of the modal status of the PII in the Correspondence.

12.3  T  he Modal Status of the Principle of Identity of Indiscernibles in the Correspondence As we have seen in the previous section, in his polemic with Clarke Leibniz often invoked one of the fundamental principles of his metaphysics, namely the PII. Commentators have noticed, however, that the PII plays an ambivalent role in the Correspondence. In an influential article published in 1981, Fred Chernoff argued that, in his letters to Clarke, Leibniz used two conflicting versions of the PII: (1) a logical version, according to which two identical but distinct entities are inconceivable, and hence cannot exist; and (2) a contingent, or non-logical version, which simply tells us that two identical entities will not be found in the actual world. According to Chernoff, Leibniz makes exclusively use of the logical version of the PII in the third letter, while in the fourth letter he employs both the logical and the non-logical version; finally, in the fifth letter he disavows the logical version and only uses the contingent version. This situation demands, in his view, a “Darwinian interpretation”: the two conflicting principles “battle with one another for domination,” and the non-logical version eventually proves to be the fitter.47 In the recently published book Leibniz’s Principle of the Identity of Indiscernibles, Gonzalo Rodriguez-Pereyra also dwells on the ambiguous character of the PII in the  Ibid., 102.  C.V.52-53, ibid., 104–105. 47  Chernoff 1981, 137. Jolley 2005, 86, also points to a tension between a contingent and a necessary version of the PII. 45 46

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Correspondence: “For there Leibniz seems to assert and deny the necessity of the II, without seeming to be aware of his inconsistency. So, it might be thought, either Leibniz was really inconsistent in his correspondence, or else his views evolved within the correspondence. The former is maintained by Clarke himself, the second is maintained by Chernoff.”48 Rodriguez-Pereyra does not share either Clarke’s or Chernoff’s opinions. According to him, Leibniz never stopped regarding the PII as a necessary principle, but in the Correspondence he chose, for strategic reasons, to present the principle simply as true, without dwelling on its modal status (i.e. without specifying whether the principle was necessarily or contingently true). According to Rodriguez-Pereyra, there is only one passage in the Correspondence in which Leibniz commits himself to the necessity of the PII. Leibniz however regretted his commitment, and “his strategy was to try to convince Clarke that he maintained that the Identity of Indiscernibles was contingent (without actually saying so) in order to focus on the issue of the truth of the principle […]. The passages from the Correspondence with Clarke where Leibniz apparently commits himself to the contingency of the Identity of Indiscernibles give us little reason to think that Leibniz genuinely thought that the Identity of Indiscernibles was contingent.”49 In this section, I shall try to show that Leibniz neither changed his mind in the course of the controversy, nor chose, simply for argument’s sake, to defend a principle in which he did not believe. Rather, he formulated both a logical and a contingent version of the principle, each applying to a different domain. Clarke’s thought experiment of God displacing the world in a straight line, however, complicated matters, as it was not entirely clear to Leibniz which version of the principle should be applied to this imaginary case. As we have seen in the previous section, Leibniz first invokes the PII when, in the third letter (L III.5), he tries to prove that space is nothing other than an order of coexistence. There he claims that in creating the world God did not need to choose between two symmetrical spatial arrangements, as in relative space “the one would exactly be the same as the other, they being absolutely indiscernible.”50 Although Leibniz does not specify the modal status of the PII, I think that Chernoff is right in concluding that the logical version is intended here. Leibniz maintains, in fact, that within a relational theory of space it is impossible even to conceive of two opposite states, as these are indiscernible and hence identical.51 In his reply, Clarke tries to refute this argument by making an appeal to the imagination. He argues that, even within the context of Leibniz’ theory of space, it is conceivable that the world had been created in another place, or that God could displace it in a straight line. According to Rodriguez-Pereyra, however, the only passage of the Correspondence in which Leibniz commits himself to the necessity of the PII is section 6 of the fourth letter, where he denies that the universe could have occupied another position in time and space. Clarke’s envisaged scenario is an “impossible  Rodriguez-Pereyra 2014, 120.  Ibid., 25–26. 50  L.III.5, Alexander 1956, 26. 51  Cf. Chernoff 1981, 130; Rodriguez-Pereyra 2014, 163. 48 49

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fiction” for “two indiscernible states are the same state.”52 Rodriguez-Pereyra finds Leibniz’s argumentative strategy “odd.” The discussion between Leibniz and Clarke at the beginning of the Correspondence “centers on the right understanding of the principle of sufficient reason.” All Leibniz needs to do, in order to refute Clarke’s view about God’s freedom of indifference, is “to argue that a mere will cannot serve as a sufficient reason, and therefore indiscernibles are contrary to God’s wisdom and rationality – pointing out that they are contrary to his power, that is, that indiscernibles are impossible is not relevant to the issue that Leibniz and Clarke are discussing in those passages.”53 I do not agree with Rodriguez-Pereyra’s interpretation. To begin with, L.IV.6 is certainly not the only passage in which Leibniz commits himself to the necessity of the PII. There, Leibniz simply renders explicit what he has already claimed in L. III.5, namely that the counterfactual scenario of a world having the same internal arrangement as our world, but occupying a different position in space, is impossible, as there are no two such alternative positions. Moreover, Leibniz also seems to appeal to the absolute necessity of the PII in section 15 of the fourth letter, where he answers Clarke’s question whether God might have created the world sooner in time: L.IV.15: It is a like fiction, (that is) an impossible one, to suppose that God might have created the world some millions of years sooner. They who run into such kind of fictions, can give no answer to one that should argue for the eternity of the world. For since God does nothing without reason, and no reason can be given why he did not create the world sooner; it will follow, either that he has created nothing at all, or that he created the world before any assignable time, that is, that the world is eternal. But when once it has been shown, that the beginning, whenever it was, is always the same thing; the Question, Why it was not otherwise ordered, becomes needless and insignificant.54

The lines just quoted make clear why, in responding to Clarke’s imaginary scenario, Leibniz appeals to the logical version of the PII. In Leibniz’ view, space and time do not exist independently from physical bodies, and hence are not created by God. Therefore, it would make no sense for Leibniz to claim (as Rodriguez-Pereyra thinks he should have done) that two indiscernible points of space or two indiscernible instants of time are contrary to God’s wisdom or rationality. This is a claim which Leibniz can only make with respect to created things, and which, in fact, he makes with respect to material bodies. In section 3 of the fourth letter Leibniz maintains that atoms and vacuum are confuted “by the principles of true metaphysics.” No two perfectly equal bodies are produced “by him who does nothing without wisdom […] and consequently there are no such things in nature.”55 In his answer, Clarke grants Leibniz that “no two leaves, and perhaps no two drops of water are exactly alike; because they are bodies very much compounded.” This, however, does not imply that there cannot be two equal “parts of simple solid matter,” that is  L.IV.6, Alexander 1956, 37.  Rodriguez-Pereyra 2014, 122. 54  L.IV.15, Alexander 1956, 38–39. 55  L.IV.4, ibid., 36. 52 53

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to say two equal atoms. “And even in compounds,” Clarke adds, “there is no impossibility for God to make two drops of water exactly alike.”56 Clarke argues, in similar terms, that “it was no impossibility for God to make the world sooner or later than he did” or “to destroy it sooner or later than it shall actually be destroyed.”57 In his fifth letter, Leibniz accuses Clarke of playing “with equivocal terms”: L.V.4: For we must distinguish between an absolute and an hypothetical necessity. We must also distinguish between a necessity which takes place because the opposite implies a contradiction; (which necessity is called logical, metaphysical or mathematical;) and a necessity which is moral, whereby a wise being chooses the best […]. L.V.5: Hypothetical necessity is that, which the supposition or hypothesis of God’s foresight and pre-ordination lays upon future contingents.58

In his book Rodriguez-Pereyra argues that the distinction between absolute and hypothetical necessity is not relevant to the understanding of the PII as “Leibniz never doubted that the Identity of Indiscernibles was hypothetically necessary since for Leibniz even what is contingent in itself is necessary given the will of God.”59 Contrary to Rodriguez-Pereyra, I think that Leibniz introduces the distinction precisely in order to clarify the modal status of his claims regarding the non-existence of indiscernibles. From Leibniz’s point of view, the two cases mentioned by Clarke in the fourth letter are not equivalent: while it would have been absolutely impossible for God to create the world sooner or later than he did, the creation of two equal bodies is only impossible given the hypothesis of God’s wisdom. As far as the creation of the world in time and space is concerned, Leibniz observes that “things being resolved upon, together with their relations; there remains no longer any choice about the time and the place, which of themselves have nothing in them real, nothing that can distinguish them, nothing that is at all discernible.”60 Clarke’s claim that God “may have good reasons” to create the world “in what particular space and at what particular time he pleased” hence makes no sense within the framework of Leibniz’s theory, because time and space, “considered without the things,” are an “impossible fiction.”61 Here, as in previous letters, Leibniz uses the expression “impossible fiction” in order to indicate something which cannot be conceived. Two identical pieces of matter or two identical drops of water are, by contrast, conceivable, and this is why Leibniz considers their existence morally, but not absolutely impossible: L.V.21: I infer from that principle [i.e., the principle of sufficient reason], among other consequences, that there are not in nature two real, absolute beings, indiscernible from each other; because if there were, God and nature would act without reason, in ordering the one otherwise than the other; and that therefore God does not produce two pieces of matter  C.IV.3-4, ibid., 46.  C.IV.15, ibid., 49. 58  L.V.4-5, ibid., 56. 59  Rodriguez-Pereyra 2014, 28. 60  L.V.57, Alexander 1956, 76. 61  L.V.58, ibid., 76–77. 56 57

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perfectly equal and alike […]. This supposition of two indiscernibles, such as two pieces of matter perfectly alike, seems indeed to be possible in abstract terms; but it is not consistent with the order of things, nor with the divine wisdom, by which nothing is admitted without reason.62

In V.25 Leibniz makes clear, once more, that when he denies “that there are two drops of water perfectly alike, or any two other bodies indiscernible from each other,” he does not mean that it is “absolutely impossible to suppose them; but that ‘tis a thing contrary to the divine wisdom and which consequently does not exist.”63 Contrary to Rodriguez-Pereyra, I see no reason to doubt the sincerity of Leibniz’s claims. Leibniz’s scope, in sections 21 and 25 of the fifth letter, is not “to make Clarke believe that he maintains the contingency of the Identity of Indiscernibles,” but simply to clarify on which grounds he denies the existence of two indiscernible material bodies.64 The fact that in the fifth letter Leibniz admits the conceivability of two identical material bodies is, however, not sufficient reason to conclude, like Chernoff does, that he has abandoned the logical version of the PII in favour of the contingent version. For, as we have just seen, in the very same letter Leibniz uses the logical version of the PII in order to deny “that the wisdom of God may have good reason to create this world at such or such a particular time.”65 But although I believe that the logical and the contingent version of the PII coexist in the Correspondence, there is one passage of the fourth letter in which, as noted by Chernoff, Leibniz seems to invoke both versions of the principle at the same time. In commenting upon the thought experiment of God displacing the world in a straight line, Leibniz writes: L.IV.13: To say that God can cause the whole universe to move forward in a right line, or in any other line, without making otherwise any alteration in it: is another chimerical supposition. For two states indiscernible from each other, are the same state; and consequently, ‘tis a change without any change. Besides, there is neither rhyme nor reason in it. But God does nothing without reason; and ‘tis impossible there should be any here. Besides, it would be agendo nihil agere, as I have just now said, because of the indiscernibility.66

In the first part of the argument (which was briefly discussed in the previous section), Leibniz seems to suggest that the hypothesis of God moving the whole world in a straight line represents a logical impossibility because, due to the PII, the two positions are, in fact, one and the same. In the second part of the argument, however, he invokes the PSR in order to argue that God would have no reason to displace the world in a straight line. Contrary to Chernoff, I do not interpret this apparent inconsistency as a sign of a Darwinian struggle between the two principles, but rather as an indication that Clarke’s thought experiment represented a difficult test case for Leibniz’s theory of space.  L.V.21, ibid., 60–61.  L.V.25, ibid., 62. 64  Rodriguez-Pereyra 2014, 124. 65  L.V.58, Alexander 1956, 70–71. 66  L.IV.13, ibid., 38. 62 63

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As mentioned above, in the Correspondence Leibniz uses the contingent version of the PII when speaking about God’s potentia ordinata, that is to say the power exercised at the moment of creation. The fact that it is possible for us to conceive two equal atoms or two equal drops of water, means that, absolutely speaking, it would have been possible for God to create them. The existence of indiscernible bodies is, however, morally impossible, as the best possible world is one which maximizes variety. Leibniz uses the logical version of the PII when talking about God’s potentia absoluta, that is to say, about the possibilities that were open to him at the moment of creation. According to his theory of space, the question whether God could have created the world in another place does not arise as, in the absence of bodies, two points of space “would not at all differ from one another.”67 The scholastic scenario of God displacing the whole world brings some confusion into this distinction, as it entails a supernatural intervention in the created world. This explains, in my view, why Leibniz does not offer a straightforward solution to the thought experiment. He denies, on the one hand, that the world is finite and movable, and stresses, on the other hand, that even if it were finite, the situation described by Clarke could not occur. It is, however, not clear whether Leibniz regards the scenario as absolutely or rather as morally impossible. There are passages in which, as we have seen, he suggests that God could not move the world in a straight line for the same reason for which he could not have created the world in another place, namely that the successive positions the world would occupy during its motion are, in fact, one and the same, and absolutely indiscernible from one another. In other passages, however, Leibniz seems to maintain that the scenario of God displacing the world in a straight line is conceivable, and hence possible, but that God would have no reason to produce a motion which has no effect and cannot be observed. If considered from the point of view of Leibniz’s theory of space, the two counterfactual scenarios discussed in the Correspondence, namely that of God assigning another position to the world at the moment of creation and that of God displacing the world in a straight line, are not equivalent. Clarke’s first scenario takes place in what we might call a “pre-mundane” space, whereas the theatre of the second scenario is an extramundane space. Leibniz’s definition of space as “the order of bodies among themselves” (L.III.5) obviously rules out the possibility of a space existing prior to the creation of the world. But what about a space beyond the created world? As we shall see in the following section, it is not clear whether Leibniz was willing to allow the possibility of such an extramundane space.

67

 L.III.5, ibid., 26.

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12.4  L  eibniz on the Possible Existence of Extramundane Void Space In a passage in the fourth letter to Clarke, Leibniz claims that “the same reason, which shows that extramundane space is imaginary, proves that all empty space is an imaginary thing; for they differ only as greater and less.”68 These lines have given rise to contrasting interpretations. While, according to Michael Futch, ‘imaginary’ must here be understood as meaning ‘impossible,’69 Gregory Brown attributes to Leibniz a view similar to that of Suarez, who called ‘imaginary’ a space that may be occupied by a body.70 Edward Grant, by contrast, believes that Leibniz uses ‘imaginary’ as synonymous with ‘non-existent,’ and thereby displays a wrong understanding of scholastic authors.71 Grant’s interpretation is implicitly confirmed by a passage from Clarke’s third reply, which was, in turn, written in reaction to an observation made in the private letter – now lost – which accompanied Leibniz’s third paper. In the letter Leibniz must have used the expression ‘imaginary space’ to deny the reality of both intramundane and extramundane void, as Clarke felt the need to specify that the ancients used the term ‘imaginary’ not to refer to “all space which is void of bodies, but only extramundane space. The meaning of which is not that such space is not real; but only that we are wholly ignorant of what kinds of things are in that space.” Clarke added that “those writers, who by the word imaginary meant at any time to affirm that space was not real; did not thereby prove, that it was not real.”72 Also in this case, Clarke did not manage to persuade his interlocutor. If we look at Leibniz’s fifth letter, we see that Leibniz uses again the adjective ‘imaginary’ to deny the reality of space. In L.V.29, quoted in section 2 above, he claims that one of the reasons why “the fiction of a material universe, moving forward in an infinite empty space cannot be admitted” is that “there is no real space out of the material universe.”73 A few pages later, Leibniz refers to both the void space out of the world and that within the world as ‘imaginary’. L.V.33: Since space is in itself an ideal thing, like time: space out of the world must needs be imaginary, as the schoolmen themselves have acknowledged. The case is the same with empty space within the world; which I take also to be imaginary, for the reasons before alleged.74  L.IV.7, ibid., 37.  Futch 2008, 50. Futch who, somewhat unexpectedly, does not discuss the thought experiment of God displacing the world in a straight line, maintains that according to Leibniz the PII is incompatible not only with Newtonian space, but also with empty space. Nicholas Rescher also attributes to Leibniz the view that void is impossible (Rescher 1967, 94). 70  Suarez 1597, Disputatio 51, sectio 1, 24. See Brown 2016, 209, n6. Ezio Vailati (1997, 117) believes, like Brown, that Leibniz regarded extramundane space as metaphysically possible. 71  Grant 1981, 412, n86. 72  C.III.2, Alexander 1956, 31. 73  L.V.29, ibid., 63 (my emphasis). 74  L.V.33, ibid., 64. 68 69

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The “reasons before alleged” are those which Leibniz had put forward in the fourth letter. They were grounded “upon the necessity of a sufficient reason,” according to which the universe is indefinitely extended, as “there is no possible reason, that can limit the quantity of matter,” and no vacuum is found in nature, “for the perfection of matter is to that of a vacuum as something to nothing.”75 But in Clarke’s view, an affirmation, like Leibniz’s, that there is no void space beyond the world or within the world does not amount to denying the possibility of an extramundane vacuum in which a finite world could be moved. This is why Clarke polemically observes, in the fifth letter, that Leibniz “must either affirm, that ‘t was impossible for God to make the material world finite and moveable; or else he must of necessity allow the strength of my argument [i.e., the argument of God displacing the world in a straight line] drawn from the possibility of the world’s being finite and moveable.”76 As we have seen, when challenging Leibniz’s interpretation of ‘imaginary space’ Clarke invoked the authority of the ancients. One of the arguments ancient philosophers had used in order to prove the existence of an extramundane empty space is the thought experiment of the man at the edge of the universe, which is mentioned in Frederik Bakker’s and Miguel Ángel Granada’s contributions to this volume.77 The thought experiment was a source of inspiration for several early modern thinkers, among them John Locke, who presented it in the Essay Concerning Human Understanding, Book II, Chap. 13, Sect. 2178: A vacuum beyond the utmost bounds of body. But to return to our idea of space. If body be not supposed infinite, (which I think no one will affirm), I would ask, whether, if God placed a man at the extremity of corporeal beings, he could not stretch his hand beyond his body? If he could, then he would put his arm where there was before space without body; and if there he spread his fingers, there would still be space between them without body. If he could not stretch out his hand, it must be because of some external hindrance […]: and then I ask, – whether that which hinders his hand from moving outwards be substance or accident, something or nothing? And when they have resolved that, they will be able to resolve themselves, – what that is, which is or may be between two bodies at a distance, that is not body, and has no solidity. In the mean time, the argument is at least as good, that, where nothing hinders, (as beyond the utmost bounds of all bodies), a body put in motion may move on, as where there is nothing between, there two bodies must necessarily touch. For pure space between is sufficient to take away the necessity of mutual contact; but bare space in the way is not sufficient to stop motion. The truth is, these men must either own that they think body infinite, though they are loth to speak it out, or else affirm that space is not body.79

Locke’s thought experiment, which took aim at the Cartesian identification of matter and extension, was based on the premise that material bodies were necessarily bounded and finite, a premise which, in his view, Descartes’ followers could not but accept.  L.IV.21, ibid., 39–40; L.IV. post scriptum, ibid., 44.  C.V.52–53, ibid., 104. 77  For an analysis of various ancient versions of this thought experiment, see Ierodiakonou 2011. 78  This and other Lockean thought experiments are discussed in Soles and Bradfield 2001. 79  Locke 1975, 175–176. 75 76

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It is interesting to point out that Leibniz, who in the New Essays extensively reacted to most of Locke’s thought experiments, did not comment on the scenario of the man at the edge of the universe, but limited himself to rejecting the premise on which it was based, namely the finitude of the world. When Philalethes, Locke’s spokesman in the dialogue, declares that “no one will venture to affirm that body, like space, is infinite,” Theophilus observes: Descartes and his followers, in making the world out to be indefinite so that we cannot conceive of any end to it, have said that matter has no limits. They have some reason for replacing the term ‘infinite’ by ‘indefinite,’ for there is never an infinite whole in the world, though there are always wholes greater than others ad  infinitum. As I have shown elsewhere, the universe itself cannot be considered to be a whole.80

In the New Essays, just as in the Correspondence, Leibniz speaks of the universe as being indefinite or unlimited, but not infinite, for, as he explains in the manuscript Quelques remarques sur le livre de Monsieur Locke intitulé Essay of Understanding, “the real infinite cannot be found in a whole composed of parts.”81 The reason behind this conclusion is that an infinite universe would violate the axiom according to which a whole must always be greater than its parts.82 In the last sentence of the passage quoted above Leibniz asserts, however, that even an indefinite or unlimited universe “cannot be considered to be a whole.” This claim is clarified by a passage of a letter to Des Bosses of 11 March 1706, where Leibniz observes that “it is of the essence of number, of a line, and of a whole to be limited.”83 According to Michael Futch, in the New Essays Leibniz denies that the world is an infinite whole, but not that “space is infinitely extended.” Futch interprets the fact that Leibniz did not directly respond to the thought experiment from the Essay as a sign that he tacitly approved “Locke’s conclusion, if not the route by which he arrives at it. […] Had Leibniz wanted to deny that space is infinite it is hard to imagine him passing on this opportunity.”84 However, as the title of Book II, Chap. 13, Sect. 21 of the Essay (A vacuum beyond the utmost bounds of body) indicates, the function of Locke’s thought experiment was not to demonstrate the infinity of space, but rather the existence of that extramundane void which, according to Futch’s own interpretation, Leibniz considered impossible. There were only two ways in which Leibniz could express his disagreement with Locke. The first was to propose an alternative interpretation of the scenario, by denying that the man at the edge of the world would be able to extend his hand into the void. The second – which Leibniz chose – was to refute the very premise on which the thought experiment was based, by denying that the world is bounded.

 Leibniz 1996, 150–151.  “Le véritable infini ne se trouve point dans un tout, composé de parties.” (Leibniz 1875–1890, VI.6, 7). 82  See Arthur 2001; Van Atten 2011. 83  Leibniz 1875–1890, II, 304, quoted in Arthur 2001, 112. 84  Futch 2008, 24. 80 81

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As we have seen, both in the New Essays and in the Correspondence Leibniz infers the non-existence of an extramundane void space from the non-finitude of the world. But what would happen if the universe were finite? Would the man be able to stretch out his hand into the void, and would God be able to move the world in a straight line? As far as Clarke’s thought experiment is concerned, Leibniz claims, as we have seen, that the motion of the entire world is an “impossible fiction,” since the successive positions would be indiscernible from one another and hence coincide. Such a conclusion is supported by the fact that, according to Leibniz’s relational theory of space, there is no stable frame of reference in respect to which the entire world would move. This is why Leibniz claims in the fifth letter that “what is moveable, must be capable of changing its situation with respect to something else, and to be in a new state discernible from the first: otherwise the change is like a fiction. A moveable finite, must be therefore part of another finite, that any change may happen which can be observed.”85 This answer would, of course, not be applicable to Locke’s thought experiment, in which the moveable finite (i.e. the hand of the man) is part of another finite (i.e. the world). This explains, in my view, why Leibniz did not comment on Locke’s thought experiment, but limited himself to claiming that the universe “cannot be considered to be a whole.” Had he granted that the world is finite, it would have been difficult for him to deny the conceivability, and hence the possibility, of the scenario described by Locke. As Edward Khamara has observed, Leibniz rules out “the possibility of a spatial world containing no material objects at all,” but he “does not rule out the possibility of unoccupied places” in a world in which material objects exist. For if an actual frame of reference is given, then “all the possibilities of being situated relatively to that frame of reference are also given. This at once guarantees, a priori, both the continuity and infinite extent of relative space.”86 Put differently: while before the creation of the world no space existed, and hence no frame of reference was given, the actual physical objects constitute the very frame of reference in relation to which unoccupied places can be located. This means that, if the world is finite, it must be possible to individuate a place in the extramundane void space in which a man would be able to extend his hand. But if this is true, should one not also conclude that it is possible for God to individuate a point in the extramundane void space towards which he could move the entire world? And is then Clarke not right in claiming that his proposed scenario is “drawn from the possibility of the world’s being finite and moveable”?87 Leibniz’s answer that one “ought not to admit a moveable universe; nor any place out of the material universe” is based on the observation that motion depends “upon being possible to be observed” and that “when there is no change that can be observed, there is no change at all.”88 At the same time, however, Leibniz grants Clarke that  L.V.31, Alexander 1956, 64.  Khamara 2006, 42. 87  C.V.52–53, Alexander 1956, 104. 88  L.V.52, ibid., 74. 85 86

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there is a difference between an absolute true motion of a body, and a mere relative change of its situation with respect to another body. For when the immediate cause of change is in the body, that body is truly in motion; and then the situation of other bodies with respect to it, will be changed consequently, though the cause of that change be not in them.89

Scholars have proposed various interpretations of the latter passage, none of which explicitly links Leibniz’s concession to Clarke’s thought experiment.90 As a matter of fact, Leibniz is reacting here to a point made by Clarke in the fourth letter, according to which God would impart to the world a “real motion” having “real effects.” In his answer Leibniz looks at the thought experiment from two different points of view, namely that of God’s action and that of the resulting motion. The very conceivability of Clarke’s scenario makes it difficult for Leibniz to deny that it would be possible for God to exert a force on the world. At the same time, however, he stresses that God’s action would be without effect and would result in a non-motion, as there would be no change in the relative position of physical bodies.

12.5  Conclusion As we have seen in this chapter, imaginary scenarios play a central role in the debate between Leibniz and Clarke concerning the nature of space and time. In order to stress the, in his view, absurd implications of Leibniz’s theory, Clarke argues that “if space was nothing but the order of things coexisting,” (C.III.4) then it would follow that God could neither have created the world in a different place, nor could remove the entire world in a straight line. In both cases the spatial relations among objects would, in fact, remain unchanged. In his reaction Leibniz invokes the PII in order to argue that Clarke’s thought experiments are “impossible fictions” (L.IV.6; L.IV.13). He points out that, according to a relational theory of space, the alternative locations and the successive positions of the world would, in fact, be indiscernible, and hence coincide. However, while Leibniz is adamant that it would have been impossible for God to assign to the world a different location in space, he seems not be able to decide whether the rectilinear motion of the entire world would be “impossible,” (IV.6) or simply “unreasonable” (L.V.29; L.V.52). Fred Chernoff has interpreted this hesitation as a sign of the fact that in the course of the Correspondence Leibniz changed his mind regarding the modal status of the PII, abandoning a logical version of the principle in favour of a contingent version. In the present chapter I have argued against Chernoff, but also against a more recent interpretation of the PII proposed by Rodriguez-Pereyra, that two different versions of the PII coexist in the Correspondence. Leibniz uses the logical version of the principle when talking about the possibilities that were open to God prior to the act of creation (potentia absoluta), and the contingent version when talking 89 90

 L.V.53, ibid.  See, among others, Alexander 1956, xxvi; Cook 1979, 50ff; Vailati 1997, 131; Arthur 1994, 231.

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about the created world (potentia ordinata). The thought experiment of God displacing the world in straight line, which was used by medieval authors in order to prove that God should be able to do anything that did not imply a logical contradiction, represents a difficult test case for Leibniz, as it implies a divine intervention in the created world. Within the framework of a relational theory of space Clarke’s first thought experiment is simply impossible, as there are no alternative locations from which God would be able to choose. But once the world is assumed to be in place, as in the second thought experiment, it is not unconceivable that God would impart a motion to it. However, as Leibniz notices, this would be an action without effect (agendo nihil agere), as the motion of the entire world would produce no observable change. This explains why, in the fifth letter, Leibniz labels Clarke’s scenario as “unreasonable” and “impractical” rather than as “impossible.”

References Alexander, Robert Gavin, ed. 1956. The Leibniz-Clarke Correspondence, With Extracts from Newton’s Principia and Opticks. Manchester: Manchester University Press. Arthur, Richard. 1994. Space and Relativity in Newton and Leibniz. The British Journal for the Philosophy of Science 45: 219–240. ———. 2001. Leibniz on Infinite Number, Infinite Wholes, and the Whole World: A Reply to Gregory Brown. The Leibniz Review 11: 103–116. ———. 2017. Thought Experiments in Newton and Leibniz. In The Routledge Companion to Thought Experiments, ed. Michael T. Stuart, Yiftach Fehige, and James Robert Brown, 111– 127. London: Routledge. Brown, Gregory. 2016. Leibniz on the Possibility of a Spatial Vacuum, the Connectedness Condition on Possible Worlds, and Miracles. In Leibniz on Compossibility and Possible Worlds, ed. Gregory Brown and Yual Chiek, 201–226. Dordrecht: Springer. Chernoff, Fred. 1981. Leibniz’s Principle of the Identity of Indiscernibles. The Philosophical Quarterly 31: 126–138. Clarke, Samuel. 1998. A Demonstration of the Being and Attributes of God. And Other Writings, ed. Ezio Vailati. Cambridge: Cambridge University Press. Cook, John W. 1979. A Reappraisal of Leibniz’s Views on Space, Time, and Motion. Philosophical Investigations 2: 22–63. Dainton, Barry. 2010. Time and Space. 2nd ed. London/New York: Routledge. Futch, Michael J. 2008. Leibniz’s Metaphysics of Time and Space. Dordrecht/Boston: Springer. Grant, Edward. 1976. Place and Space in Medieval Physical Thought. In Motion and Time, Space and Matter, ed. Peter K. Machamer and Robert G. Turnbull, 136–166. Columbus: Ohio State University Press. ———. 1979. The Condemnation of 1277, God’s Absolute Power, and Physical Thought in the Late Middle Ages. Viator 10: 211–244. ———. 1981. Much Ado about Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. ———. 1996. The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional and Intellectual Contexts. Cambridge: Cambridge University Press. Ierodiakonou, Katarina. 2011. Remarks on the History of an Ancient Thought Experiment. In Thought Experiments in Methodological and Historical Contexts, ed. Katarina Ierodiakonou and Sophie Roux, 37–49. Leiden: Brill.

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Jolley, Nicholas. 2005. Leibniz. London/New York: Routledge. Khamara, Edward J.  2006. Space, Time and Theology in the Leibniz-Newton Controversy. Frankfurt: Ontos. Leibniz, Gottfried Wilhelm. 1875–1890.  Die philosophischen Schriften, ed. Carl Immanuel Gerhardt, 7 vols. Berlin: Weidmann. ———. 1989. Discourse on Metaphysics. In Philosophical Essays, eds. and trans. Roger Ariew and Daniel Garber. 35–68. Indianapolis: Hackett. ———. 1996. New Essays on Human Understanding, eds. and transl. Peter Remnant and Jonathan Bennett. Oxford: Oxford University Press. Lin, Martin. 2016. Leibniz on the Modal Status of Absolute Space and Time. Noûs 50: 447–464. Locke, John. 1975.  An Essay Concerning Human Understanding, ed. Peter Nidditch. Oxford: Clarendon Press. Newton, Isaac. 1999. The Principia: Mathematical Principles of Natural Philosophy, ed. and trans. I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press. Rescher, Nicholas. 1967. The Philosophy of Leibniz. Englewood Cliffs: Prentice-Hall. Rickles, Dean. 2008. Symmetry, Structure, and Spacetime. Amsterdam: Elsevier. Rodriguez-Pereyra, Gonzalo. 2014. Leibniz’s Principle of the Identity of Indiscernibles. Oxford: Oxford University Press. Shapin, Steven. 1981. Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes. Isis 72 (2): 187–215. Soles, David, and Katherine Bradfield. 2001. Some Remarks on Locke’s Use of Thought Experiments. Locke Studies 1: 41–61. Suarez, Francisco. 1597. Metaphysicarum disputationum, in quibus et universa naturalis theologia ordinate traditur, et quaestiones omnes ad duodecim Aristotelis libros pertinentes accurate disputantur tomus prior. Salamanca: Renaut. Vailati, Ezio. 1997. Leibniz and Clarke: A Study of Their Correspondence. Oxford/New York: Oxford University Press. Van Atten, Marc. 2011. A Note on Leibniz’s Argument against Infinite Wholes. British Journal for the History of Philosophy 19: 121–129.

Correction to: The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe Frederik A. Bakker

Correction to: Chapter 3 in: F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_3 Owing to an oversight on the part of Springer, Chapter 3 was initially published as a regular chapter. However, this is an Open Access chapter.

The updated version of this chapter can be found at https://doi.org/10.1007/978-3-030-02765-0_3

© Springer Nature Switzerland AG 2019 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0_13

C1

Index

A Acerbi, F., 226 Aertsen, J., 70 Aëtius, 53 Agostini, I., 71 Agrippa, H.C., 206 Aiguillon, F. d’, 188 Albert of Saxony, 241–243, 252 Albert the Great, 73, 74, 77, 121, 137, 252 Alberti, L.B., 181 Albertson, D., 108, 120 Alessandrelli, M., 160 Alexander of Aphrodisias, 12, 34–37 Alexander, R.G., 262, 264–270, 272–275, 277, 280, 281 Al-Ghazali, 121 Algra, K., 4–7, 11–14, 16, 21, 23, 25, 27–31, 34, 38, 44, 46, 48, 160, 187 Allen, J., 59 Amato, B., 158, 168 Ambrose, Saint, 70 Amico, B., 254 Anfray, J.-P., 71 Annas, J.E., 115 Archimedeans, 218, 224 Archimedes, 263 Archytas, 6, 45 Ariew, R., 138 Aristotelianism, 2, 5, 12, 16, 18, 24–26, 28, 31, 32, 36, 37, 70–73, 76, 79, 80, 82, 85, 86, 91–93, 95, 100, 108, 124, 129, 133, 142, 143, 149, 152, 153, 158–160, 173, 174, 180, 190, 193, 195, 203, 208, 224, 225, 235, 240

Aristotle, 2, 4–7, 11–38, 42, 45, 50, 61, 72, 73, 76–80, 84, 85, 91–93, 95, 96, 98–100, 102–104, 107, 108, 110–115, 117, 118, 120–123, 127–129, 134, 136, 142–145, 147–149, 152, 159–161, 163, 165, 168, 170, 174, 175, 180, 184, 185, 188, 190, 193, 194, 196, 221, 234, 240, 242, 243, 246, 252–254, 267, 269 Arius Didymus, 48 Arnim, H.F. von, 45, 48 Arrighetti, G., 43, 44 Arthur, R., 265, 270, 279, 281 Asmis, E., 42, 44, 45, 58, 59 Atomists, 3, 5, 7, 29, 30, 42, 45, 53, 56, 98, 108, 129, 225 Augustine of Hippo, Saint, 70, 77, 109, 110, 113, 122, 126, 182, 183, 190, 202 Augustinianism, 183, 196 Avempace (Ibn Bajja), 13, 26, 35, 85 Averroes (Ibn Rushd), 13, 15, 21, 30, 34, 35, 80, 82, 85, 93, 97, 99, 101, 102, 104 Aversa, R., 234, 241–243, 250 Avicenna (Ibn Sina), 117, 121 Avotins, I., 42, 45 B Bacon, F., 190, 207 Bailey, C., 43, 44, 46, 49, 55, 60, 62 Bailhache, P., 212 Baius, M., 183 Bakker, F.A., 6, 7, 44, 45, 47, 49–53, 56, 59, 61–63, 278 Bakker, P.J.J.M., 85, 108

© Springer Nature Switzerland AG 2018 F. A. Bakker et al. (eds.), Space, Imagination and the Cosmos from Antiquity to the Early Modern Period, Studies in History and Philosophy of Science 48, https://doi.org/10.1007/978-3-030-02765-0

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286 Baldi, B., 224 Baliani, G.B., 226 Baldini, U., 185, 221 Barcaro, U., 226 Barker, P., 184 Beaulieu, A., 207 Bede, Saint, 195 Bellis, D., 5–8, 143 Beltrán, M., 140 Bénatouïl, T., 59 Bergson, H., 13 Bernes, A.-C., 180 Besler, H., 169 Biancani, G., 184 Biard, J., 70, 71, 79, 80 Bloch, O., 240, 246, 256, 257 Blumenberg, H., 164, 224 Bodin, J., 227 Boer, S. W. de, 85, 108 Boethius, 108, 110, 118–120, 122, 124, 127 Bonaventure (Bonaventura), 27, 72–74, 78 Bostock, D., 14, 34 Boulier, P., 221 Boulliaud (Boulliau), I., 143, 226 Boulnois, O., 76 Boute, B., 183 Boutroux, P., 211 Bradfield, K., 278 Brahe, T., 180, 184, 190, 192, 193, 207, 208, 210, 214, 223, 225, 234–238 Brown, G., 277 Brundell, B., 234, 236–238, 240 Brunianism, 246 Bruno, G., 5, 6, 8, 56, 129, 151, 152, 157–176, 202, 213, 214, 234, 235, 238, 239, 244 Bucciantini, M., 218 Buccolini, C., 203, 204, 213, 218, 223 Burkert, W., 118 Burley, W., 121 Burnyeat, M., 33 Büttner, J., 226 Buzon, F. de, 211, 212 C Cabbala, 207 Cafiero, L., 206 Calenus, H., 183 Cambridge Platonists, 146 Campanus of Novara, 126 Canone, E., 239 Čapek, M., 2, 3 Capella, M., 118, 190

Index Cappelletti, L., 78 Caroline of Ansbach, Princess, 261, 262 Carraud, V., 202 Casati, P., 268 Cassiodorus, 118 Castelli, B., 190 Castellote Cubells, S., 134, 140 Cazre, P. le, 226 Cesalli, L., 111 Ceyssens, L., 180 Chalcidius, 113, 164 Chaldean Oracles, 72 Charleton, W., 246 Chatelain, A., 74 Chernoff, F., 263, 266, 271, 272, 275, 281 Chrysippus, 49 Cicero, 44, 52, 54, 57, 63 Clark, J.T., 234 Clarke, S., 6–8, 14, 33, 92, 261–282 Clarke, W.N., 57 Clavelin, M., 71 Clavius, C., 184 Clement of Alexandria, 195 Cleomedes, 6, 32, 45, 49, 50, 57, 92, 147, 267 Cohen, F.H., 217 Coimbrans (Coimbra Jesuits / Conimbricenses), 6, 134, 240, 242, 249–251, 253 Conti, A., 111 Cook, J.W., 281 Copernicanism, 184, 190, 192, 195, 196, 213, 220, 226 Copernicans, 180, 186–192, 208, 210, 218, 234, 236–238 Copernicus, N., 4, 180, 184, 192, 195, 213, 236–239 Cornelli, G., 118 Cornford, F.M., 62, 164 Corsi, F.G., 63 Costabel, P., 218, 222 Coujou, J.-P., 138, 140 Courtenay, W.J., 163 Cross, R., 70, 92, 93 Croy, Cardinal Guillaume de, 181 Ctesibius, 224 Cusa, Nicolas/Nicholas of, 64, 108, 129, 172 Cyril of Alexandria, 195 D Dainton, B., 268 Damascius, 14 Darling, D., 42, 56

Index Dear, P., 214, 221, 226 Deitz, L., 134, 147, 150, 207 Delle Colombe, L., 203 Del Prete, A., 151, 163, 171, 213, 239 Demange, D., 78 Democritus, 7, 42, 53, 98, 110–112, 126 Denifle, H., 74 De Risi, V., 134, 137, 144, 145, 150–153, 234 Des Bosses, B., 279 Descartes, R., 6, 13, 14, 71, 82, 138, 143, 146, 202–204, 212, 214, 218, 221, 222, 224–226, 240, 248, 278, 279 Desclos, M.-L., 12 De Smet, I., 181 De Vittori, T., 145, 148, 150 Dick, S.J., 42, 56 Diels, H.A., 45 Diogenes of Oenoanda, 46, 54, 63 Dowd, M.F., 42 Drabkin, I.E., 221 Drake, F.D., 56 Druys, J., 182 Duba, W., 5, 7, 95, 98, 99 Duhem, P., 27, 70, 81, 82, 92, 98, 101, 102, 161 Duvergier de Hauranne, J., 182 E Edelheit, A., 147 Einstein, A., 3 Epicureanism, 2, 3, 159, 162, 234, 246 Epicureans, 2, 8, 42–65, 159, 160, 233, 236, 238, 239, 244–246, 254 Epicurus, 4, 7, 14, 21, 41–65, 162, 163, 233, 238, 239, 244, 246 Erasmus, D., 181 Esmaeili, M.J., 78 Étienne Tempier, Bishop of Paris, 7, 32, 101, 240, 242, 267, 269 Euclid, 2, 108, 113, 126, 128, 150, 216 Eudemus of Rhodes, 12, 26, 32, 37 Evans, G.R., 70 Evans, J., 62 F Fabbri, N., 6–8, 202, 211, 212, 218 Fabri, H., 226 Faes de Mottoni, B., 73 Fantechi, E., 158, 162, 164, 169, 172 Favaro, A., 188 Ferdinand of Austria, Cardinal-Infante, 183

287 Ferrara, Duke of, 150 Ficino (Ficinus), M., 152, 164 Fienus, T., 190, 195 Fludd, R., 202–204, 206–208, 210, 214, 227 Fonseca, P. da, 249, 250, 253, 254 Fortenbaugh, W., 12 Fowler, D.P., 56 Fraenkel, C., 175 Franciscans, 81, 92, 94, 97, 98 Francis of Marchia, 75, 78, 81–84 Froidmont (Fromondus), L., 6, 179–196 Funkenstein, A., 3, 4, 71 Furley, D.J., 12, 13, 42, 45, 47, 49–51 Futch, M., 277, 279 G Gaffurio (Gaffurius), F., 206, 217 Galilei, G., 2, 71, 80, 82, 86, 129, 140, 162, 180, 184, 185, 202–204, 210, 213, 214, 218–222, 224, 226, 227, 234, 236, 238, 239, 246 Galilei, V., 217 Gallanzoni, G., 218 Galluzzi, P., 218, 221, 226 Gassendi, P., 2, 5–8, 71, 140, 145, 162, 204, 206, 207, 222, 233–257 Gaultier de La Valette, J., 206 Gays, G., 190 George II, King of England, 262 Gerald Odon (Gerardus Odonis / Guiral Ot), 85, 98, 108 Gilbert of Poitiers (Gilbert de la Porée), 114, 137 Giles of Rome, 72, 80, 81, 84 Giorgi, A., 224 Giorgi, F., 206 Giovannozzi, D., 71 Glauser, R., 138 Gloriosi, C., 193 Goclenius, C., 181 Goclenius, R., 242, 254 Goris, W., 98 Gottschalk, H., 12 Grafton, A., 185 Granada, M.Á., 5, 6, 8, 158, 163, 165, 184, 191, 213, 278 Grant, E., 2, 3, 8, 13, 31, 33, 70, 71, 107, 108, 158, 161, 165–167, 169, 173, 174, 176, 223, 240, 242, 251, 253, 254, 266, 267, 277 Gregorius XIII, Pope, 183 Gregory of Rimini, 79, 80, 84, 85

288 Gregory the Great, 190 Grellard, C., 70, 98, 99 Grienberger, C., 184 H Hamesse, J., 100 Hammerstaedt, J., 54 Harrison, P., 214 Harvey, W.Z., 175 Hasdai Crescas, 108, 161 Heider, D., 137 Helden, A. van, 239 Henry, J., 137, 143, 144, 148, 152, 158, 214, 234 Henry of Ghent, 5, 74–77, 242, 253 Henry of Harclay, 98 Heraclides, 189 Hero of Alexandria, 224 Hesiod, 18, 170 Hilary of Poitiers, Saint, 70 Hissette, R., 74 Hobbes, T., 71, 140 Homer, 174 Horky, P.S., 118 Hugh/Hugo of St. Victor, 73 Humbert, P., 236 Hume, D., 58 Hussey, E., 14, 22, 34 I Iamblichus, 14 Ierodiakonou, K., 6, 45, 278 Ingoli, F., 219, 239 Innocent X, Pope, 183 Inwood, B., 44 Ioannes Baptista Rasarius, 137 Irigaray, L., 13 Itard, J., 145 J Jacobi, F.H., 175 Jaffro, L., 71 Jammer, M., 3, 71 Jansen, J.E., 182 Jansenism, 196 Jansenius, C., 179, 181–183, 195–196 Jerome, Saint, 70, 195 Jesuits, 133, 134, 140, 182–184, 188–189, 195–196 Joachim of Fiore, 202

Index John Buridan, 13, 15, 79, 242 John Duns Scotus, 5–7, 74–78, 80–83, 92–94, 97, 99, 101, 102, 104, 105, 137, 223, 242 John of Damascus (Damascenus), 73, 138 John of Ripa (Jean de Ripa), 8, 32, 71, 253 John Wyclif, 5, 7, 107–129 Jolley, N., 271 Joly, B., 214 K Kaluza, Z., 113 Kambouchner, D., 146 Kechagia, E., 53 Kelter, I.A., 195 Kepler, J., 184–185, 188, 191, 202–204, 207–208, 210–214, 216–218, 226–227, 234, 236, 238, 239 Khamara, E.J., 266, 280 King, P., 120 Kircher, A., 227 Kirschner, S., 108 Konstan, D., 44–46, 51, 162 Koyré, A., 1–2, 4, 71, 129, 158, 162–163, 234, 239, 257 Kranz, W., 45 Kretzmann, N., 109, 125 L Lafleur, C., 92, 101 Lahey, S.E., 110 Lamæus, R., 183 La Mothe Le Vayer, F. de, 208 Lansberg (Landsberg), P., 186, 226 Lapide, Cornelius a (Cornelius van den Steyn), 195 Laplanche, F., 191 Leibniz, G.W., 6–8, 14, 33, 92, 145, 150, 261–282 Leijenhorst, C., 71, 140, 249 Leinkauf, T., 145 Lenoble, R., 204, 212, 221, 222 Leone, G., 63 Lerner, M.-P., 184, 185, 218 Lettink, P., 13, 21, 26, 34, 35 Leucippus, 42 Levin, F.R., 118 Levy, I.C., 110 Lewis, N., 121, 122, 223 Liddell, H.G., 61

Index Lin, M., 269 Lincei, Accademia dei, 220, 221 Lipsius, J., 180, 181, 188 Locke, J., 6, 278–280 Lohr, C.H., 137 LoLordo, A., 235, 246 Long, A.A., 43, 44, 51, 59 Lovejoy, A.O., 56, 163 Lucian (Lucianus), 181, 185 Lucretius, 6, 42–59, 61, 63, 64, 159, 162, 163, 224, 236, 254 Lüthy, C., 71 Lyceum, 12, 23 M Machamer, P.K., 3 Macrobius, 118 Magni, V., 224 Mahoney, E., 74 Maier, A., 70, 92, 98, 121 Maimon, S., 175 Maimonides, 175 Makovský, J., 150, 151 Mamiani, M., 2, 246, 255 Margolin, J.-C., 213 Marion, J.-L., 211, 212, 218 Mash, R., 42, 56 Matthew, T., 190 Matthew of Aquasparta, 74, 78 Maury, J.-P., 221 McGuire, J.E., 234 McMullin, E., 191 Mehl, É., 138, 151, 206 Mendell, H., 120 Mersenne, M., 6–8, 143, 201–228, 248 Methuen, C., 212 Metrodorus, 42 Meyer, E., 226 Michael, E., 109, 112 Miller, D.M., 2, 4 Molanus, J., 183 Molina, L. de, 182, 195 Monantheuil, H. de, 224 Monchamp, G., 180, 188 Moraw, P., 70 More, H., 71, 145, 146 Morin, J.-B., 237 Morison, B., 13, 31–33, 36 Muccillo, M., 145–146, 234 Mueller, I., 128 Müller, I., 111 Murdoch, J.E., 98, 121

289 N Nannius, P., 181 Nardi, B., 72 Neoplatonism, 14, 57, 72, 118, 127, 134, 143, 152, 169, 194, 202, 216 Neopythagoreanism, 5, 108, 109, 111, 116, 118–123, 127, 128 Newton, I., 3, 4, 7, 8, 14, 71, 145, 146, 162, 234, 235, 246, 257, 261–265, 268, 270, 277 Nicholas Bonet (Bonetus), 5, 81–82, 92–94, 97–105, 108 Nicholas of Autrécourt, 98, 108 Nicole Oresme, 33, 108, 147, 241–243, 249, 266–267 Nicomachus of Gerasa, 118–119, 124, 127 Normore, C., 71 O O’Keefe, T., 51 Ophuijsen, J. van, 12, 13, 34 Orcibal, J., 182 Osiander, A., 237 Oviedo, Francisco de, 142 Owen, G., 14 P Paganini, G., 71, 249, 250 Palisca, C.V., 217 Palmerino, C.R., 6–8, 86, 221, 226, 234, 237, 238, 256, 257 Panti, C., 74, 121 Pantin, I., 6, 7, 181, 185, 188, 189, 237 Pascal, B., 145 Pasnau, R., 71 Patrizi, F., 5–7, 133–134, 137, 142–153, 158, 207, 214, 234, 242, 243, 246 Paz, F., 190 Peiresc, Nicolas-Claude Fabri de, 206, 236 Pena, J., 184, 188 Pépin, J., 167 Peripatetics, 12, 23, 24, 99, 142, 173, 235 Petagine, A., 2, 71 Peter Abelard, 120, 121 Peter Auriol (Petrus Aurioli), 5, 92–97, 103–105 Peter John Olivi, 74, 78, 242 Peter Lombard, 70, 73, 77, 190 Peterschmitt, L., 2, 3 Petronius, 181 Philip, J.A., 118

290 Philoponus, J., 5, 12, 13, 16, 21, 23–25, 27, 30, 34–36, 85, 108, 137, 161, 194, 253 Piccolomini, A., 224 Piché, D., 74 Pico della Mirandola, Gianfrancesco, 161 Pines, S., 175 Pintard, R., 240 Pius V, Pope, 183 Plato, 4, 5, 14, 38, 42, 55, 57, 61, 62, 64, 97, 109, 110, 113, 118, 119, 122, 126–128, 134, 148, 152, 164, 165, 168, 175 Platonism, 47, 57, 78, 99, 108–111, 116–118, 129, 143, 146, 151, 163, 168, 173, 174, 211, 218, 222, 226 See also Neoplatonism Platonists, 47, 57, 146, 168, 173 Plutarch, 49, 50, 57, 59 Popkin, R.H., 214 Presocratics, 42, 57 Prins, J., 147 Proclus, 14, 127–129, 150, 216 Ptolemaic system, 72, 203, 208, 210, 225, 236, 237 Puliafito Bleuel, A.L., 134 Puteanus, E., 181 Pythagoras, 126, 217 Pythagoreanism, 6, 45, 78, 118, 122, 128, 129, 202 See also Neopythagoreanism R Raban Maur (Rabanus/Hrabanus Maurus), 72 Raphael, R., 218, 221 Rashed, M., 12 Redondi, P., 188, 221 Regier, J., 2 Relihan, J.C., 181 Rescher, N., 277 Rey, J., 213, 220 Ribordy, O., 2, 5, 7, 71, 136 Richard of Middleton, 72, 74, 78, 242 Rickles, D., 264 Robert, A., 5, 7, 70, 78, 84, 98, 108, 120 Robert Grosseteste, 110, 117, 121–123, 125–128, 202 Roberval, G.P. de, 7, 204, 222, 248 Robson, J.A., 121 Rochot, B., 221, 244 Rodriguez-Pereyra, G., 263, 268, 271–275, 281 Roger Bacon, 69, 74 Rohde, M., 70

Index Rommevaux, S., 70 Roques, M., 108 Roseman, P.W., 70 Ross, W.D., 174 Rothmann, C., 184 Rouse, W.H.D., 42, 46, 47, 50, 52, 53, 55, 56, 58, 59 S Sacré, D., 181 Sakamoto, K., 234 Sambursky, S., 14, 49–51, 226 Scapparone, E., 164 Schabel, C., 83, 92, 95, 97 Scheiner, C., 184, 188 Schmidt, J., 49 Schmitt, C.B., 161 Scholastics, 3, 5–7, 13, 92, 97, 99, 133, 134, 139, 163, 180, 194, 196, 201, 205, 223, 224, 233–235, 240, 242, 245, 249, 251, 252, 256, 257, 276, 277 Schuhmann, K., 158, 246 Scott, R., 61 Sedley, D.N., 43, 44, 47, 49, 53, 56–59, 62, 65, 161 Seneca, 180, 181, 188 Serarius, N., 195 Sextus Empiricus, 12, 21, 24, 43, 50, 57 Shapin, S., 262 Sharples, R., 12 Shea, W.R., 218, 221 Simplicius, 12–14, 16, 26, 27, 30–36, 137, 194 Singer, D.W., 164 Siorvanes, L., 12, 13 Smith, A.M., 221 Smith, M.F., 42, 46, 47, 50, 52–56, 58, 59, 63 Snellius, W., 193 Soles, D., 278 Sorabji, R., 12, 14, 25, 27, 31, 70, 71, 85, 187, 194 Sorbière, S., 244, 256 Speer, A., 70 Spinoza, B., 8, 157, 175, 176 Spoerri, W., 53 Stabile, G., 219 Steuco, A., 151, 152 Stobaeus, 48, 49 Stoicism, 3, 4, 6, 12, 21, 32, 41, 42, 45, 47–53, 57, 61, 64, 65, 147, 151, 158–161, 164, 179–181, 187, 188, 196, 224, 239, 267 Strabo, V., 72

Index Strato of Lampsacus, 12, 13, 23 Striker, G., 59 Sturlese, R., 239 Suárez, F., 5, 6, 133–142, 151–153, 242, 243, 249, 251, 277 Suarez-Nani, T., 2, 5, 7, 8, 70, 71, 73–76, 78, 81, 82, 140, 146, 147, 242 Sylla, E., 71 Syrianus, 14 T Tack, R., 234 Taub, L., 59 Taussig, S., 206 Telesio, B., 158 Themistius, 12, 16, 35, 175 Theophrastus of Eresus, 12, 14, 21, 33, 37 Thijssen, J.M.M.H., 71 Thomas Aquinas, 13, 27, 30, 72–74, 77, 80, 81, 97, 152, 163, 195, 242 Thomas Bradwardine, 32, 242 Thomson, W.R., 111 Tirinnanzi, N., 169 Todd, R., 12, 32 Toletus, F., 252, 253 Torricelli, E., 224 Traphagan, J., 42 Trevisano, M., 78 Trevisi, A., 182 Trifogli, C., 70 Trigault, N., 188 Turnbull, R.G., 3 U Urban VIII, Pope, 183 Urmson, J.O., 12, 13 Usener, H., 44, 50, 51, 59 V Vailati, E., 270, 277, 281 Valois, Louis de, 244 Van Atten, M., 279 Vanden Broecke, S., 186

291 Van Nouhys, T., 188 Vanpaemel, G., 181, 193 Van Wymeersch, B., 212 Védrine, H., 142–144, 148, 150–152 Veneziani, M., 71 Venier, L., 98 Verde, F., 59, 60, 62, 63 Vermeir, K., 2 Vermij, R., 190 Vignaux, P., 8, 71, 72 Vitelleschi, M., 184 Vitruvius, 224 Vives, J.L., 181 W Wallace, W.A., 71 Walter Chatton, 78, 84, 108 Warren, J., 56, 58, 60 Waterfield, R., 14, 24, 34 Weill-Parot, N., 70, 79, 86 Weinbrot, H.D., 181 Wendelin, G., 226 Westfall, R.S., 234, 246 Wildberg, C., 12, 13, 194 William Crathorn, 108 William of Champeaux, 120 William (of) Ockham, 13, 242 Wils, J., 182 Wisan, W.L., 226 Wolff, M., 27, 49–51 Wolfson, H.A., 161 Wöller, F., 97 X Xenarchus of Seleucia, 12, 13, 23 Xenophon, 56 Z Zarlino, G., 217 Zeno of Elea, 17–19, 36, 37 Zhmud, L., 118 Ziegler, J., 184 Zittel, C., 234, 237