Copernicus and the Aristotelian Tradition: Education, Reading, and Philosophy in Copernicus's Path to Heliocentrism (History of Science and Medicine Library 15/Medieval and Early Modern Science 12) [Illustrated] 9004181075, 9789004181076

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Copernicus and the Aristotelian Tradition

History of Science and Medicine Library VOLUME 15

Medieval and Early Modern Science Editors J.M.M.H. Thijssen, Radboud University Nijmegen C.H. Lüthy, Radboud University Nijmegen Editorial Consultants

Joël Biard, University of Tours Simo Knuuttila, University of Helsinki John E. Murdoch, Harvard University Jürgen Renn, Max-Planck-Institute for the History of Science Theo Verbeek, University of Utrecht

VOLUME 12

Copernicus and the Aristotelian Tradition Education, Reading, and Philosophy in Copernicus’s Path to Heliocentrism

By

André Goddu

LEIDEN • BOSTON 2010

On the cover: Reconstruction of Copernicus’s face. Reproduced with the kind permission of Prof. Dr. Jerzy Gąssowski, Director of the Institute of Anthropology and Archaeology of the Pultusk Academy of Humanities, Poland, who was responsible for the Copernicus program, the excavation of his grave, and the discovery of his remains. This book is printed on acid-free paper. Library of Congress Cataloging-in-Publication Data Goddu, André, 1945– Copernicus and the Aristotelian tradition : education, reading, and philosophy in Copernicus’s path to heliocentrism / by André Goddu. p. cm. — (History of science and medicine library, ISSN 1872-0684 ; v. 15) Includes bibliographical references and index. ISBN 978-90-04-18107-6 (hardback : alk. paper) 1. Copernicus, Nicolaus, 1473–1543—Knowledge and learning. 2. Copernicus, Nicolaus, 1473–1543—Sources. 3. Astronomy—History—16th century. 4. Cosmology—History—16th century. 5. Science—History—16th century. 6. Philosophy, Medieval. I. Title. QB36.C8G635 2010 520.92—dc22 2009047722

ISSN 1872-0684 ISBN 978 90 04 18107 6 Copyright 2010 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Hotei Publishing, IDC Publishers, Martinus Nijhoff Publishers and VSP. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Koninklijke Brill NV provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. printed in the netherlands

To Kayo and Seisei

CONTENTS List of Illustrations ............................................................................. Preface .................................................................................................. Acknowledgements ........................................................................... Introduction .........................................................................................

xi xiii xix xxi

PART I COPERNICUS’S EDUCATION IN POLAND

Chapter One Poland, Toruń, and Cracow in the Fifteenth Century ............................................................................................ 1. Early Education ......................................................................... 2. Cracow University .................................................................... 3. Curriculum and Texts, 1475–1500 .........................................

5 5 13 25

Chapter Two

Masters and Students in the 1490s ......................

35

Chapter Three The Teaching of Logic ......................................... 1. Aristotelian Logic—Introductory Orientation ..................... 2. The Teaching of Logic at Cracow ..........................................

51 52 72

Chapter Four Natural Philosophy ................................................ 89 1. General Orientation .................................................................. 89 2. Markowski’s Most Important and Relevant Conclusions ................................................................................ 97 3. The Quaestiones cracovienses on the Physics of Aristotle ... 99 4. Aristotle’s De caelo, De generatione, Meteorologica, and Metaphysics ................................................................................. 114 5. Johannes Versoris ..................................................................... 122 6. Albert of Saxony and John of Glogovia ................................ 128 Chapter Five Humanism and Astronomy ................................... 1. Introduction ............................................................................... 2. The Curriculum at Cracow ...................................................... 3. The Criticisms of Ptolemaic Astronomy ...............................

137 137 145 154

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4. Copernicus’s Teachers at Cracow .......................................... 159 5. Albert of Brudzewo’s Commentariolum ................................ 162 PART II COPERNICUS’S EDUCATION IN ITALY, 1496–1503, AND RETURN TO POLAND

Chapter Six Copernicus in Italy .................................................... 1. Introduction ............................................................................... 2. Copernicus’s Education in Canon and Civil Law ............... 3. Copernicus and Novara ........................................................... 4. Copernicus’s Study of Greek ................................................... 5. Copernicus in Rome ................................................................. 6. Copernicus’s Study of Medicine at Padua ............................ 7. Copernicus’s Degree from Ferrara .........................................

171 171 173 187 193 197 198 203

Chapter Seven Copernicus’s Reading and Progress towards his First Heliocentric Theory ........................................................ 1. Introduction ............................................................................... 2. Regiomontanus’s Epitome ........................................................ 3. Bessarion’s In calumniatorem Platonis .................................. 4. Ficino’s Translation of Plato’s Works ................................... 5. Plutarch, Pseudo-Plutarch (Aëtius) and Giorgio Valla ...... 6. Pliny’s Natural History and other Ancient Authorities ..... 7. Achillini ...................................................................................... 8. Commentariolus .........................................................................

207 207 215 220 225 229 237 238 243

PART III COPERNICUS AS PHILOSOPHER

Chapter Eight Copernicus as Logician ........................................ 1. Introduction ............................................................................... 2. The Sources of Dialectical Topics, 1490–1550 ..................... 3. Mereology—Logic and Ontology ........................................... 4. Logic in the Commentariolus .................................................. 5. The Use of Topics in the Preface of De revolutionibus ...... 6. The Rhetorical Framework of Book I .................................... 7. The Use of Topics in Book I ...................................................

275 275 279 285 291 292 300 304

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8. Hypotheses in Copernicus’s Method .................................. 9. The Logical Issues in the Relation between Mathematics and Natural Philosophy ......................................................... 10. The Logical Issues in his Discovery of the Heliocentric Theory ....................................................................................... 11. Concluding Remarks on Copernicus’s Relation to the Aristotelian Logical Tradition ..............................................

314

Chapter Nine Copernicus as Natural Philosopher .................... 1. Introduction ............................................................................. 2. Copernicus’s Critique of Geocentrism ................................ 3. The Motions of Celestial Bodies ........................................... 4. Impetus and the Motions of Elemental Bodies ................. 5. Infinity and the Finiteness of the Cosmos ......................... 6. Summary ..................................................................................

325 325 326 332 336 355 358

Chapter Ten Copernicus as Mathematical Cosmologist .......... 1. Introduction ............................................................................. 2. Hypotheses ............................................................................... 3. Spheres and the Nature of Celestial Matter ....................... 4. Equants ..................................................................................... 5. Summary ..................................................................................

361 361 362 370 381 384

Conclusion and Epilogue .................................................................. 1. Summary .................................................................................. 2. Copernicus’s Interpretation of Aristotle ............................. 3. Epilog: Reception of Copernicus’s Interpretation .............

387 387 389 403

317 321 323

Appendices ........................................................................................... 439 Bibliography ......................................................................................... 495 Indices Index of Names .............................................................................. 525 Index of Places ................................................................................ 536 Index of Subjects ............................................................................ 538

LIST OF ILLUSTRATIONS Maps Map 1 Map 2

Map of Poland ................................................................. Map of Eastern Pomerania and Varmia .....................

2 3

Plates Plate 1 Plate 2 Plate 3

Annotation from Copernicana 31, fol. sig. e5ra ......... Annotation from Copernicana 4, folio 269v ............... Annotation from Copernicana 4, folio 284v ...............

228 258 258

Tables Table 1 Table 2 Table 3

Copernicus’s Calculations in Uppsala Notebook ....... Comparison between Ptolemy and Copernicus ........ Calculation of a Sidereal Period from a Synodic Period ................................................................................

259 260 261

Figures Figure 1 Tusi’s device: spherical version with parallel axes and radii in the ratio of 1:2 ........................................... Figure 2 Tusi’s device: spherical version with oblique axes and equal radii ................................................................. Figure 3 Tusi’s device: plane version with equal radii ............. Figure 4 Reciprocation mechanism in Copernicus’s De revolutionibus ................................................................... Figure 5 Representation of Oresme’s Reciprocation Device ... Figure 6 Droppers’s Interpretation of Oresme’s Reciprocation Device ................................................................................ Figure 7 Hetherington’s Illustration of Straight Line Motion from Circular Motion ....................................................

263 265 266 268 481 482 483

PREFACE I began this study about 1990, or so I thought. In that year I was fortunate to have received a teaching position at Stonehill College that prompted me to focus on the history of science. Sixteen years later, as I wrote the first version of the conclusion of this study, however, I realized that I had begun this work in the mid-1970s. Manipulated, very mildly and willingly, by my doctoral adviser at UCLA, Amos Funkenstein, I added the history of science to a program in medieval history, and began to work on William of Ockham’s natural philosophy. In the meantime, I attended the seminars of Robert S. Westman who became my “second” adviser. Because of his support over many years, I owe my career almost entirely to him. For all sorts of mostly practical reasons, my profession became that of a historian of science, one trained in medieval history, philosophy, theology, church history, and paleography. But Funkenstein and Westman projected what had been in the background—the period of early modern science—into the foregound. As circumstances dictated, I worked on fourteenth-century natural philosophy but always with an eye on the sixteenth and seventeenth centuries. Westman, in particular, dissatisfied with what he saw as anachronistic readings of Kepler back into Copernicus, questioned me persistently about the logical issues that eventually led me to look more closely at the education in logic that students received at Cracow. Richard Rouse trained his students thoroughly in paleography, but even more he prepared them for a career. Similarly, Lynn White, Jr. inspired students to take risks. All of those influences, substantive and methodological, led to this study. Not 1990, but 1975 marks the beginning of this work. Robert Westman, of course, introduced me to Copernicus, and to Gingerich, Kuhn, Swerdlow, and so on. It was overwhelming, far too much to absorb in a few semesters. It has taken me thirty years to absorb it. Westman is not responsible for my own take on it. Yet I find that I have grown to agree more with my teachers’ insights than I did thirty years ago. Aside from my teachers at UCLA, there are many others to whom my debts are substantial but more recent. Michael J. Crowe was the

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first to introduce me to the mathematical technicalities, and Ernan McMullin influenced and stimulated my thinking about scientific theories. In the Boston area, Owen Gingerich, Stephen Brown, and John Murdoch are models of generosity and intellectual integrity. In several and various ways, they kept me engaged while not hesitating to point out deficiencies and errors. In Poland, Marian Zwiercan generously allowed me to consult a manuscript edition of a text by a major fifteenth-century scholar who may have taught Copernicus. Elżbieta Jung offered me an opportunity to publish two articles on fifteenth-century natural philosophy at Cracow. She and her student Robert Podkoński also kindly checked my reading of some articles published in Polish. I owe much of the detail in those papers and in this study to them and to archivists of the Jagiellonian Library in Cracow. I would be remiss if I did not mention the assistance of Michał Kokowski. Our differences of interpretation stem from our different reasons for studying Copernicus, but I am grateful to him for an invitation to give a talk at Cracow, for his editing of a paper from a conference, and for his generous gifts of books, especially a copy of the results of a commemorative conference on Ludwik Birkenmajer that was virtually impossible to find in the USA. That monograph from 2002 saved me from some embarrassing mistakes. Likewise, archivists at Uppsala University and in Stockholm provided indispensable assistance (and patience) in making early printed books with a Polish provenance available for my inspection. Without the opportunities in Poland and Sweden I could not have undertaken, let alone completed, this study. Similarly, Bennacer el Bouazzati provided an occasion to write a paper on Copernicus’s cosmological ideas. He single-handedly took on the task of editing and securing funding for the publication of the papers that he had “commissioned” for a conference in Rabat. To Hans Thijssen of Nijmegen I am beholden for an invitation to give a paper on Copernicus’s critique of geocentrism. It was a small but attentive and expert group to whom I owe thanks for comments and corrections. I must in particular mention Christoph Lüthy who on several occasions spurred me to examine my arguments more deeply. To John Cleary and participants at a conference at Maynooth, especially Franz de Haas, Michael Dunne, and Ernan McMullin, I am grateful for the opportunity to reflect on Copernicus and Kepler in the

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context of scientific method. The other papers and discussions were stimulating and indispensable in helping me arrive at defensible conclusions regarding the relation between natural philosophy and early modern science. To Alfonso Maierù I owe the opportunity to reflect on Copernicus’s achievement and address questions on continuity and revolution at the Sixth Congress of the Italian Society for the Study of Medieval Thought (Rome, 1996). Comments and criticisms, again, proved indispensable for recognizing limitations and achieving greater clarity. Dino Buzzetti arranged to have that paper translated into Italian by his daughter, and published it with others from the meeting. It was an unforgettable meeting for several reasons, but above all because it provided a baseline for further reflection on Copernicus’s role in the rise of early modern science. In recent months I have become increasingly dependent on exchanges with Dilwyn Knox of University College London. His familiarity with the sources of Copernicus’s intellectual world is astonishing, and I owe to him a major correction about how to understand and formulate Copernicus’s adaptation of Aristotelianism to heliocentrism. He read earlier versions of chapters four, nine, and the conclusion, correcting my mistakes, questioning my interpretations, and generously sharing his vast acquaintance with ancient, medieval, and early modern sources with me. Likewise, I am much indebted to Jennifer Ashworth. When I sent chapters three, eight, and the conclusion to her, she was in the process of leaving Canada and returning to the United Kingdom. Somehow, within a matter of weeks, she read the chapters, saved me from several errors, cautioned me to reconsider the historical developments more carefully, and by means of probing questions and precise references to relevant scholarship led me to a deeper appreciation for where and how John of Glogovia likely fits in the tradition of discussions about logical consequences and the paradoxes of implication. Owen Gingerich read chapters seven, ten, and the conclusion, corrected errors, and encouraged me to provide more pointers, at the risk of repetition, to guide readers to my conclusions about why Copernicus tied his heliocentric cosmology to the ancient goal of accounting for celestial motions in terms of uniform circular motions. These scholars almost certainly do not agree with me completely about matters on which they are expert, nor are they responsible for my mistakes and misunderstandings.

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Of course, financial support and time are also indispensable. The National Science Foundation, the International Research and Exchange Service, and Stonehill College supported the research. Bonnie Troupe and Kathy Conroy support the efforts of Stonehill scholars, and their advice was indispensable in securing outside funding. In addition to financial assistance and time, I am indebted to several of my colleagues for scholarly advice. Anthony Celano helped with paleographical matters, Nathaniel Desrosiers with translations, Martha Baldwin with her wide historical knowledge, and John Golden with assistance that helped me to improve my knowledge of Polish. Thomas Gariepy and Susan Mooney supported my work, but in their capacity as chairs (at what was then one of the only programs in the history and philosophy of science at a four-year college), they did what administrators do best— they let me get my work done. When that program was eliminated, administrators asked my chair in the Department of Physics, Michael Horne, what they could do for us; his answer was music to my ears: “Leave us alone.” Of course, without the support of higher administrators, several deans and two presidents, my department heads might have been more constrained. Glenn Everett was generous and expert in producing the plates and figures that make the arguments related to the origin of the heliocentric theory clearer than they would otherwise be. Any scholar who lives in the Boston area depends on major universities, but it was Stonehill College that paid for the stiff prices that Harvard College charges “special borrowers” to get lost in the bowels of Widener Library. Even Widener does not have everything, or its staff could not always locate catalogued items. The interlibrary-loan staff at Stonehill located and obtained, almost without fail, the items that I could not get otherwise. To Regina Egan earlier and to Heather Perry more recently I am deeply indebted for their tenacity in locating sources that I needed. There are dozens of former colleagues and fellow students, several in Germany, Jürgen Sarnowsky, Klaus Jacobi, and Marcus Wörner, who deepened my knowledge of medieval philosophy. To the editors at Brill and especially Gera van Bedaf, who corrected some mistakes that I missed, I am very grateful for their assistance and patience. As I wrote the first version of this introduction (20 July 2006), sectarian and other conflicts were erupting all over the world, and it is at

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the moment depressing to realize how little we seem to have advanced in our understanding of other cultures. The study of history provides an opportunity to develop the skills to understand other cultures, but every generation has to make the effort while being inundated on a daily basis by a materialistic life style that makes icons of the superficial and the ephemeral. Copernicus, like Ptolemy, advocated the study of astronomy as a pursuit worthy of the human mind and free individuals, and as a preparation for the understanding of what is beautiful and endures. In the Introduction that was suppressed in the 1543 edition and replaced by the Preface to the Pope, Copernicus refers to Psalm 92 and the vision of a chariot carrying him to the contemplation of the highest good. It was the same image that inspired Igor Stravinsky as he composed his Symphony of Psalms, ending it with Psalm 150, “Laudate Dominum.” Copernicus developed and cherished such thoughts about the time (around 1525) that he was embroiled in conflict with the Teutonic Knights. Perhaps his interests and goals were escapist, yet we remember him today primarily, not for his political and military activities, but for his intellectual and scientific accomplishments. Those facts to the contrary notwithstanding, it is astonishing to read about all of his administrative, legal, and political activities in the period from 1516 to 1542 while he was accomplishing his major revolution in cosmology. The evidence indicates that he was very worried about the reception of his theory, yet, thanks in part to Georg Joachim Rheticus and Tiedemann Giese, he seems to have finally achieved some peace with his ideas and with himself. I think that he would have shared, as I do, the sentiments (absent the title) expressed by Regiomontanus in his report of a disputation between himself and possibly Martin Bylica of Olkusz: Iam uero reuertens unde abii ne aliena delicta reprehendentem meipsum uidear eximere a grege isto ridiculo [historicorum] tanquam innocentem nullique errori obnoxium nunc profiteor aeque laturum imo gratias ingentes habiturum plerisque omnibus qui [meum] inspicient [librum] iudicabuntque quamuis insidiose. [quem] etsi sciam Horacii Quintilianique monitu non esse praecipitandas aliquid tamen in aetate uegetiori tentandum est ne uentri tantum more pecudum indulgere uidear. (Adapted from the Preface to Disputationum Joannis de monte regio contra Cremonensia delyramenta, Opera collectanea, 513–515.) Returning to my departure point I now confess that I will be most grateful to all who will examine [my book], even insidiously—as is proper

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preface if I am not to appear as one who exempts himself from the ridiculous crowd of [historians] and who is blameless and incapable of making mistakes when I blame others for theirs. Although I know, as Horace and Quintilian have admonished us, we should avoid being premature in what we produce, I must still try to do something while still active so that I may not appear to be like cattle that think only of being fed.

Stonehill College 21 May 2009

ACKNOWLEDGEMENTS All of the following are gratefully acknowledged for permission to use illustrations from their collection or publications: Uppsala University Library for plates from Copernicana 4 and Copernicana 31. Cambridge University Press for figures by George Saliba, and E. S. Kennedy from the following journal: Arabic Sciences and Philosophy, and to the editor Roshdi Rashed. Science History Publications and Mario di Bono for figures from the following journal: Journal for the History of Astronomy, and to the editor Michael Hoskin. Norriss Hetherington and Greenwood Press for a figure from Planetary Motions (Greenwood Press, 2006). The History Department of the University of Wisconsin for two diagrams from a dissertation by Garrett Droppers.

INTRODUCTION Another book on Copernicus requires justification. Since 1973 when dozens of celebrations of Copernicus’s birth produced hundreds of articles and dozens of books on Copernicus and his times, there has not been a comprehensive review or assimilation of this material. Each chapter contains reactions to the most relevant of the contributions published from 1973 on, and either introduces new material, much of it from Polish scholarship that has been largely ignored outside of Poland, or proposes new interpretations or conclusions about Copernicus and his work. Although I have divided the study into three parts, it falls into two main divisions. Parts I and II are biographical and bio-bibliographical, trying to reconstruct Copernicus’s education and reading as much as the sources permit. Parts I and II argue that in Cracow Copernicus achieved some competence in astronomy and scholastic philosophy in the Aristotelian tradition. The curriculum of medieval universities required students to master logic, compare and analyze sources, and construct arguments. Two books that he purchased in Cracow along with some early annotations in them suggest that he acquired a foundation for the technical study of astronomy in Cracow. Part I covers Copernicus’s early period in Toruń and Cracow. Chapter one summarizes important results of mostly Polish scholarship on the socio-economic details of life along the Vistula River in the fifteenth century, and on Copernicus’s early education and knowledge of Polish. There are reasons for believing that Copernicus received some rudimentary instruction in astronomy as a very young student. Likewise, his knowledge of Polish may have been more than rudimentary, although German and Latin were his principal languages. Chapter two concludes that Copernicus received the equivalent of a typical medieval education in the liberal arts. He very likely followed a course of studies there towards a degree, although he left Cracow without one. Medieval scholars developed a strong commentary tradition and several schools of interpretation in both logic and natural philosophy. The fifteenth-century University of Cracow assembled representatives of several traditions, making it possible for students to understand the

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main problems, and compare a variety of solutions. Chapter three is on the teaching of logic, and chapter four on the teaching of natural philosophy in the fifteenth century. Copernicus developed a critical approach to natural philosophy but one that enabled him to modify Aristotelianism while remaining a participant in a broadly conceived Aristotelian tradition. Surprising to some perhaps, humanistic influences arrived at Cracow early in the fifteenth century, and promoted above all an interest in classical authors. It was here that Copernicus developed his desire for reformation and for assembling printed sources that he would use side by side for the remainder of his life. Chapter five shows the relationship between humanism at Cracow and Copernicus’s first efforts in astronomy. Readers may question the relevance of the details on the curriculum, teachers, and teaching at Cracow in the 1490s. Most scholars agree that Copernicus received a liberal arts education, but even the best studies have focused, understandably but narrowly, on natural philosophy and astronomy. A substantial portion of a medieval liberal arts education, however, was devoted to lectures and exercises on logic. Even much of the instruction on substantive topics and books applied scholastic techniques of textual explication and logical analysis. In an age when we pay lip service to critical thinking, we can barely appreciate the extent to which medieval students were drilled in theoretical and practical logic. Although he was already eighteen years of age when he matriculated at the university, his ability, demonstrated later, to construct arguments is strong evidence of instruction in scholastic techniques of logical analysis. In the chapters devoted to the curriculum and to the faculty (chapters one and two), I have tried to reconstruct the sort of instruction that would have been available to Copernicus. The same can be said for the details in logic, natural philosophy, and astronomy in chapters three to five. All of Part I, in other words, constitutes background, information about what Copernicus could have learned and about the teachers who may have taught him. In fact, most of the details provided in those chapters prove one point—his teachers in logic, natural philosophy, and astronomy were students of John of Glogovia and Albert of Brudzewo. Readers interested only in Copernicus’s works and annotations in books that he owned or used may skip Part I and turn immediately to Part II. They will lack background for Part III,

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but they can refer to the relevant chapters in Part I and perhaps then understand the relevance of that material. Most fifteenth-century Polish students who wanted a degree in law went to Italy or France if they had the financial means. Personal circumstances made it possible for Copernicus to recognize the limitations of further advance at Cracow, and to take advantage of residence in northern Italy. He attended the University of Bologna primarily as a student of canon law, but evidently improved and sharpened his skills as an astronomer under the guidance of Domenico Maria Novara. Through Novara, Copernicus attached himself, as it were, to the tradition of Greek humanism stemming from Cardinal Bessarion and applied to astronomy by Johannes Regiomontanus. In Bologna Copernicus formulated his intention to participate in the reformation of astronomy without the slightest idea at that time where it would lead him. Here too he began to learn Greek. Many scholars seem to assume that Copernicus learned natural philosophy at Bologna and/or Padua between 1496 and 1503, and that he became familiar with a number of Italian works on natural philosophy and cosmology. With exception of his acquaintance with a work by Pico della Mirandola, the evidence supporting his acquaintance with the works of other Italian authors is slim, and the hypotheses advanced seem to be based on a neglect, in part, of Copernicus’s education in the liberal arts and philosophy at Cracow, and, in part, of the books that we know he owned or that were probably available to him in Poland. Several studies also fail to distinguish clearly what Copernicus would have learned and read that is relevant to his writing of Commentariolus (ca. 1508–1512) from what is relevant to the writing of De revolutionibus (ca. 1525–1543). Here it is necessary to reflect on conjectures and speculation. The documentary evidence supporting conclusions about Copernicus’s education in Cracow and his later experiences in Bologna and Padua is sketchy. We are caught in a bind. Either we forego any effort to reconstruct Copernicus’s path to a heliocentric cosmology, or we must try to construct an account based on what we do know. If historians who work on early modern astronomy are honest, they will acknowledge that they all speculate to one degree or another, and that what leads one to accept or prefer one conjecture and question another is to some extent subjective. One of the tests that we can apply is whether a comment or argument in Copernicus depends on a unique source or whether it is reasonable to assume that the source

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amounts almost to common knowledge. If the latter is the case, then we have to examine all of the alleged sources and ask whether there is anything about one of them that is so unique that it must have been Copernicus’s source. I have speculated extensively about Copernicus’s education, but I have made few claims about sources except those that relate to annotations in the books that he owned or used or that are based on extensive and striking parallels between his comments and his source (as is the case with Regiomontanus’s Epitome). His education, as I have reconstructed it, provided background and training that help us to explain certain habits of mind, not sources that he quoted. Although I am skeptical that he would have attended scholastic disputations or read more scholastic philosophical sources during his years in northern Italy, I have not dismissed some of these supposed sources out of hand. It is possible that Copernicus did know them or rely on them, but I have also examined them critically, asking whether Copernicus could have drawn on sources that he probably knew in Cracow for assumptions, arguments, and conclusions. Chapters six and seven show above all how his education, contacts, and collection of books prepared him for his first heliocentric system, and prepared him to transform Ptolemaic geocentric into heliocentric models. Part II ends with Copernicus’s return to Varmia, the writing of Commentariolus, and a reconstruction of the origins of his heliocentric cosmology. In this part, I rely on De revolutionibus only in those cases where it echoes the same themes contained in Commentariolus. Part III, the second main division of the study, abandons the biographical approach of the first two parts and turns to an analysis of Copernicus as philosopher—the logic of his arguments, his views on natural philosophy, and, finally, his mathematical cosmology. This part treats De revolutionibus more extensively. The argumentative techniques employed can be traced to his early education, but I also consider sources that became available to him after 1514. By 1514 at the latest he formed the philosophical vision that would guide him in his restoration of the goals of ancient astronomy. Trained in scholastic forms of argumentation, Copernicus very likely reinforced the standard techniques through his study of law. He developed his own version of Aristotelianism, very much influenced by Renaissance Platonism, Neoplatonism, Stoicism, and the works of ancient authors newly published in the late fifteenth and early sixteenth centuries. The Aristotelianism that he developed was in numerous ways congenial with the Aristotelianism of the Middle Ages, and one of the many

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branches of Aristotelianism that flourished for at least two more centuries. It was also a version of Aristotelianism that was anti-Averroistic and more flexible in its approach to mathematics. On the other hand, other sources became available to him after 1514, and through 1542 he continued to reflect on the meaning of his reform of ancient astronomy. His heliocentric cosmology necessitated a drastic revision of Aristotelianism and scholasticism. For the revisions he turned primarily to other ancient traditions made available through new translations and editions of ancient works, and also through summaries contained in encyclopedias and dictionaries. For the most part, however, the other ancient authoritative figures on whom he relied were also geocentrists, hence he bent their criticisms of Aristotelian philosophy to his own purposes. It must be emphasized, however, that already in Cracow Copernicus developed humanistic interests, and there can be little question that he went to Italy in part to deepen and broaden his humanistic inclinations. My point is that while he was educated in scholastic contexts, he adopted humanistic goals, interests, methods, and style. He did not write like a scholastic, although we can say that he wrote like a scholastically educated humanist. Chapters eight, nine, and ten propose new solutions to questions about Copernicus’s logic, natural philosophy, and cosmology. Although controversial, his methods and views stem from respectable medieval traditions, but ones that he modified by reliance on sources that represented Neoplatonic and Stoic critiques of Aristotelian principles. As several experts have recently recognized, Copernicus’s understanding of mathematical models was not as robustly realist as earlier authors claimed. He was not an instrumentalist or fictionalist either. He rather adopted a principle of priority that ordered and distinguished several types and levels of hypotheses. Part III argues that Copernicus was a principled thinker who resolved principal questions while ignoring secondary, peripheral ones. In other words, he was not a systematic philosophical thinker, but he always maintained a clear sense of his principal goal, and distinguished between questions that he had to address and ones that he could leave aside. Even on those he had to address he sometimes remained doubtful or ambivalent about the correct solution. Accordingly, I have tried to show in chapter eight how he used standard argumentative techniques to argue for the greater probability of his assumptions over those of his geocentric predecessors and contemporaries. Chapter nine attempts to resolve questions about

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Copernicus’s views on mathematics, his account of the motions of the elements, and his commitment to a finite universe. Chapter ten tries to resolve controversial questions about his understanding of hypotheses, celestial spheres, celestial matter, and his criticism of the so-called equant model. For Copernicus’s texts and translations I have relied on the standard editions and versions. For the problems with editing Copernicus’s De revolutionibus, see Noel Swerdlow, “On Establishing the Text of ‘De Revolutionibus’,” Owen Gingerich, Review of De revolutionibus: Kritischer Text; idem, “Extended Errata List,” and Swerdlow “On Editing Copernicus.” Citations of De revolutionibus are usually from the Nobis and Sticker edition in the Gesamtausgabe, Volume 2, 1984. I checked all of the cited texts against the 1543 edition on which the German edition is based, and in some instances against Copernicus’s holograph copy. On problems with editing and translating Commentariolus, see Anthony Grafton, “Copernicus without Tears.” I have usually quoted the English translation of De revolutionibus by Edward Rosen because it is widely available, but where it is inaccurate or misleading, I have either corrected it or commented on it if relevant to my main argument. See Gerald Toomer, “Copernicus in Translation” on the inadequacy of the English translations. Rosen is usually though not always reliable for his translation of Book I, but not in the remaining parts of his translation and commentary that concern technical, mathematical matters. Anyone relying on Rosen’s translations of either Commentariolus or De revolutionibus must turn to Swerdlow, “The Derivation and First Draft of Copernicus’s Planetary Theory,” and to Swerdlow and Neugebauer, Mathematical Astronomy in Copernicus’s De revolutionibus. When I began writing this work in 2001, I relied on the then standard editions of documents relating to Cracow University in the fifteenth century. Polish scholars have since replaced those editions in part, but I refer to both the earlier and more recent editions because most of the secondary literature refers to the earlier editions. At an earlier stage of planning I had proposed a more comprehensive analysis of the reception of the Copernican theory down to 1600. In the meantime, however, many specialized studies appeared, making it clear that a study of reception even just to the end of the sixteenth century is another major project. My aim was to elucidate Copernicus’s philosophical connections with Aristotelianism and his own philosophical achievements. The conclusion fittingly restricts consideration of the

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reception of his ideas to their philosophical impact; however, even in this regard I do not attempt to be exhaustive. Instead, I develop a spectrum of views that describe typical reactions. It begins with a summary of Copernicus’s knowledge and understanding of Aristotelianism, and then turns to the reception of his efforts to adapt Aristotelianism to heliocentrism by leaning on other ancient sources. In this regard, the significant issues have to do with the status of hypotheses, the epistemic strength of conclusions in mathematical astronomy, the relation between mathematics and natural philosophy, and the role of theory in scientific explanation. The study draws conclusions about the role of data and hypotheses in the works of his readers down to Johannes Kepler. In particular the epilog draws conclusions about the rejection of geocentrism and the construction of a heliocentric system. There are some ironic consequences that modify Copernicus’s role in the scientific revolution, and require a more nuanced evaluation of his view of the relation between astronomy and natural philosophy.

PART ONE

COPERNICUS’S EDUCATION IN POLAND

Frombork Gdańsk Lidzbark-Warmiński Elbląg

Olsztyn

Chełmno Toruń

Warsaw

Vistula River

Cracow

Map 1. Map of Poland

Vistulan Sandbar

Braniewo Frombork

Gdańsk

Elbląg

Pienężno

Nogat River Malbork

Lidzbark-Warmiński

Varmia Olsztyn

Vistula River

Chełmno

Toruń

Eastern Pomerania Map 2. Map of Eastern Pomerania and Varmia

CHAPTER ONE

POLAND, TORUŃ, AND CRACOW IN THE FIFTEENTH CENTURY 1. Early Education1 For over one thousand kilometers the Vistula River2 flows from the southwestern mountains of Poland to the Baltic Sea. On a map, the Vistula looks almost like an elongated letter S.3 From the Berkidy range in Silesia it proceeds northeast through Cracow, continues eastwards and then veers to the northwest towards Warsaw. Just past Warsaw it turns sharply to the west, and continues northwest through Toruń.4 About forty kilometers northwest of Toruń, the Vistula again makes a sharp turn towards the northeast, passing through Chełmno.5 Just east of the port of Gdańsk,6 the Vistula enters the Gulf of Gdańsk and the Baltic Sea. Altogether around twenty-one rivers feed the Vistula, thereby joining many of the major cities of Poland; it was an important economic waterway, and remained so until Poland was partitioned at the end of the eighteenth century. During the fifteenth and sixteenth centuries, however, the Vistula served as a major link between Cracow and the Baltic Sea, uniting many Polish economic, educational, and

1 Section 1 relies primarily on the following: Hipler, Spicilegium, 303–311; Prowe, Coppernicus, I, A, Book 2: 86–116; Nowak, “Mikołaj Kopernik,” 9–33; Górski, “Royal Prussia Estates,” 49–64; Biskup, “Biography and Social Background,” 137–152; Biskup and Dobrzycki, Copernicus; and Schmauch, “Jugend,” 100–131. Rosen, “Nicholas Copernicus, a Biography,” 313–318, provides background and a review of many of the reconstructions of Copernicus’s early years but had nothing to add to speculation about Copernicus’s early education. 2 Wisła in Polish, Weichsel in German. I have used English versions of familiar Polish geographical locations (Cracow and Warsaw, for example) while retaining the Polish version for less well-known areas. Sometimes I have also used several alternative forms of Polish proper names to conform to the source that I cite. For example, “Szamotuły” is sometimes spelled “Schamotuli” and “Szamotuli.” The index of proper names lists them all. 3 See the maps of modern Poland and of Eastern Pomerania. 4 Thorn in German. 5 Kulm in German. 6 Danzig in German.

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political centers. For twenty-two years Nicholas Copernicus lived in towns located along the banks of the Vistula. On 19 February 1473, Copernicus was born in Toruń in the bishopric of Chełmno in the region of eastern Pomerania.7 Eastern Pomerania includes “Vistulan Pomerania,” the area of the Vistulan estuary and basin stretching roughly from Gdańsk in the west to Elbląg8 in the east, and from the Gulf of Gdańsk in the north to a little below Toruń in the south.9 After his years along the Vistula (1473–1495), except for seven years in Italy (1496–1503) and thereafter with only occasional visits to Cracow, Copernicus spent the remaining forty-one years of his life (d. 1543) entirely in northeastern Poland in the area known as Varmia, to the east of the Vistulan delta. Copernicus’s father, also named Nicholas, was born in Cracow, the capital of the kingdom of Poland from the eleventh to the end of the sixteenth century. Nicholas Sr. was a businessman who became entangled in the struggle between the Prussian Estates (union of clergy, nobility, and townspeople) and the Teutonic Order of the Knights of the Cross. The senior Nicholas moved to Toruń in 1456 or 1457, married Barbara Watzenrode, and lived to see Vistulan Pomerania become subject to the kingdom of Poland in the peace of Toruń (1466).10 By the terms of the treaty the kingdom of Poland regained access to the sea, and Vistulan Pomerania became part of the larger area known as Royal Prussia. Royal Prussia also included Varmia,11 a region that extended like a bell from Frombork12 and Braniewo13 into the part of 7 The date comes from Copernicus’s horoscope from around 1540, but the date of birth may be only approximate. See Hamel, Nicolaus Copernicus, 89. Poulle, “Les dates de naissance,” 5, says the horoscope can also be interpreted to read 19 January 1473. See Biskup, Regesta 34, no. 15, citing Munich, Bayerische Staatsbibliothek Cod. lat. Nr. 27003, f. 33v. I cite the English version of Biskup’s Regesta because the English version added some items not included in the earlier Polish version. See also Biskup, “Mikołaj Kopernik,” 99–109, at 101. 8 Elbing in German. 9 Biskup, Nicolaus Copernicus 5–18, esp. map on 10. 10 For a brief summary of family history, see Hamel, 90–92. For details on social and economic history, consult Biskup, U schyłku średniowiecza; and Czacharowski, “Kupiectwo toruńskie,” 21–39, at 24. See also Biskup, “Mikołaj Kopernik,” 100–101. The statement by Rabin, “Nicolaus Copernicus,” 1, describing Toruń as an inland port in the Hanseatic League, was based on a loose statement by Swerdlow and Neugebauer, Mathematical Astronomy 1: 3. Toruń had been a part of the Hanseatic League, but it was declared a free city under Polish administration in 1466. 11 Ermland in German. 12 German Frauenburg about 30 km northeast of Elbląg. 13 German Braunsberg about 10 km east-northeast of Frombork.

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Prussia held by the Teutonic Order and hence called “Order Prussia.” Varmia separated the two northern limits of Order Prussia, requiring the Teutonic Knights to travel through Varmia or to take a very circuitous route, a source of aggravation to them. Although required by the peace of Toruń to pay homage to the king of Poland, the Teutonic Knights would later attempt to take control of Varmia, leading to renewed conflict in which our astronomer would play a role. Much of the literature from the late nineteenth to the middle of the twentieth century about Copernicus’s nationality was tainted by jingoism—some German scholars reacting to Polish claims to prove that Copernicus was German to which Polish scholars in turn responded defensively. Arising out of modern conceptions of nationality and nation-states, the dispute is anachronistic.14 There was no German nor, strictly speaking, Polish state in the fifteenth century. The kingdom of Poland in the late fifteenth and early sixteenth centuries comprised a vast area that included Lithuania and part of modern-day Ukraine, extending from the Baltic to the Black Sea. Royal Prussia was a polyglot assemblage of commercial towns surrounded by lands controlled by aristocrats, gentry, and clergy. In the last quarter of the fifteenth century its population was loyal to the crown of Poland and resisted control by the Teutonic Knights. Its inhabitants, however, also resisted efforts by King Casimir IV Jagiellon (d. 1492) and his successors down to 1548 to consolidate their control over Prussia at the cost to church and local interests. This is a tangled history that concerns us only to the extent that it helps to explain Copernicus’s later support of the local and royal resistance to the Teutonic Knights in Varmia. Copernicus grew up in a Polish-German-speaking environment. His

14 An outrageous example of national-socialist historiography is represented by Kubach, Nikolaus Kopernikus. Kubach was the original editor of the Nikolaus Kopernikus Gesamtausgabe launched in 1943 and sponsored by the Deutsche Forschungsgemeinschaft. Schmauch, “Nikolaus Kopernikus—ein Deutscher,” 1–32, is more scholarly but still tainted by anachronistic nationalism. Schmauch argues persuasively that opposition to the Teutonic Knights was motivated more by local interests than Polish ones, but the same local interests argue likewise against German interests. Nevertheless, Schmauch was an outstanding scholar, and his work remains indispensable. For an excellent review of the debate over Copernicus’s nationality, see Poschman, “Beitrag,” 11–32. See also Gingerich, “Copernican Quinquecentennial,” 37–50, for his review of the nationalistic agendas and more examples.

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loyalties were primarily local and incidentally Polish when local interests coincided with those of the Polish kingdom.15 There were several elementary schools in and around Toruń.16 Scholars have had to speculate about Copernicus’s early education because no known documents about his early education have survived. Leopold Prowe, Hans Schmauch, Marian Biskup, and, above all, Zenon Nowak have dispelled much of the speculation about Copernicus’s early education. Nowak has established that schools like the ones in Toruń did prepare students to enter university.17 After Copernicus’s father died in 1483, the younger Nicholas’s maternal uncle, Lucas Watzenrode (1447–1512), became his guardian and saw to his education.18 Of all the reconstructions, the likeliest is that Nicholas attended the parochial school of St. John in the old city of Toruń rather than the school of St. James in the new city or any other school until he was at least fifteen years of age.19 In the fourteenth century every town had its own school. The parochial school of St. John existed throughout the fifteenth century, including the years when Copernicus would have been a student from around 1480 to 1491.20 The director of the school of St. John held the title “rector,” and the school was administered and staffed by individuals some of whom had bachelor’s and even master’s degrees in the liberal arts. Their salaries were comparable to the salaries that university professors received.21 The records of the fifteenth-century curriculum at the school of St. John do not exist, but typically schools of this kind divided their students and instruction into three classes. In the first class students learned to read and write Latin. In the second they used the grammar of Aelius Donatus (probably both Ars minor and 15 For background on the history of Poland in the fifteenth century, see Górski, “Royal Prussia Estates,” who argues for a single state in this era but also, 58–61, notes local opposition to the kings of Poland. See also the collection entitled Poland, the Land of Copernicus containing the following articles: Kiełczewska-Zaleska, “Poland in Europe,” 9–24; Lesnodorski, “Commonwealth,” 25–39; and Biskup, “Royal Prussia,” 43–53, esp. 50, where Biskup notes that by patria or “motherland” the residents of Royal Prussia meant the province, not the kingdom, although they were subjects of the king of Poland. 16 Cf. Nowak, 13–22; Biskup and Dobrzycki, 31. 17 Nowak, 17–22. 18 Prowe, I: 85–90 and 108–109; Rosen, “Biography,” 314–315. 19 Nowak, 14–15 and 31; Prowe, I: 109–116; Hipler, 303–311, corrected by Prowe, I: 112–113. 20 Nowak, 16–17. 21 Nowak, 17.

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Ars maior), the Doctrinale of Alexander of Villa Dei along with the Disticha of Cato the Elder to learn the basics of grammar. In the third class they continued with instruction for two hours in the morning on the Doctrinale, and after lunch they were introduced as well to the fundamentals of logic and lectures mostly on the fables of Aesop and selections from the comedies of Terence. According to the pedagogy of the day, students would have spent most of their time in repetition and memorization. We may surmise that aside from learning to read and write Latin, Copernicus would have been taught the basics of arithmetic and probably some geography because Toruń was a commercial center. Scholars disagree about Copernicus’s mother tongue. German was the commercial language used in Royal Prussia, and so he almost certainly spoke German at home, although he likely had some acquaintance with Polish.22 What speaks especially for the school of St. John is that a rector at the school from around 1435 to 1450, Conrad Gesselen from Geismar in Hesse, was interested in astronomy and collected astronomical works. He may have left a successor who shared his inquisitiveness

22 Cf. Nowak, 22–23; Biskup and Dobrzycki, 32–33. Rosen, “Biography,” 315, claims that Copernicus spoke German at home, that his Polish was rudimentary at best, and that he wrote nothing in Polish. On p. 346, however, Rosen acknowledges Copernicus’s recording of farmstead names between December 1516 and August 1519. The seventy-five entries “show that he was not entirely unfamiliar with Polish, since he recorded baptismal names and did not convert them into the corresponding German forms.” Schmauch, “Nikolaus Kopernikus,” pp. 1–16, presents the evidence that Copernicus’s mother tongue was German. Małłek, “Hat Nicolaus Copernicus Polnisch Gesprochen?” 153–162, presents evidence for Copernicus’s knowledge of Polish. See especially Rospond, “Zu den Substitutions-schreibungen,” 65–80, for an authoritative linguistic analysis. See also Herbst, “Country and World,” 1–12, esp. 4 and 11; and Copernicus, Locationes, Introduction. The evidence for Copernicus’s knowledge of Polish is circumstantial yet persuasive. During Copernicus’s public career as a canon in Varmia, it is unlikely that he could have accomplished his duties without a working knowledge of Polish. He administered rural homesteads in a part of Varmia occupied by Polish settlers. He recorded names in Polish in a way that suggests acquaintance with the language. See Rospond, “Z badań,” 367–371, who maintains on the basis of Copernicus’s recording of Polish names that he knew and used the Polish language on a daily basis. At official meetings in Royal Prussia not all participants spoke German, and Małłek concludes that Copernicus acted as an interpreter. For additional evidence of the use of Polish at official meetings, see Acta statutum terrarum Prussia regalis, 6: 281–282 and 306. Finally, during the siege of Olsztyn in 1520–21, Copernicus administered and commanded the garrison of Polish soldiers. If Copernicus did speak Polish, then he would most likely have learned it as a child in his home and among his playmates. Rospond, “Z badań,” 367, adds that Copernicus also used Polish while studying in Cracow.

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about astronomy and transmitted it to interested students.23 A rector of the school in the 1460s, John Wohlgemuth, composed a text entitled Trilogium animae, in which he cites his sources24 and also provides details about the division of mathematics into arithmetic, music (i.e. mathematical ratios), geometry, and astronomy. As sources for the first three he names Pappus of Alexandria, Boethius, and Euclid respectively. He also cites Pappus on astronomy:25 According to Pappus, astronomy is the law of the stars because it teaches the path of the stars. The word “star” is composed of “nomos,” which means “law,” or “norma,” which means “rule,” or “noma,” which means “name.” Hence, astronomy is the science that teaches the law or rule of the stars, and because he names it “astronomy,” it, therefore, concerns continuous quantity in a narrow sense, namely, the celestial bodies in order with respect to motion. Astrology is an art and a part of astronomy, for the word “star” is put together with “logos,” which means “word,” as astrology is said to be the science that speaks about the stars. Astrology is partly natural and partly superstitious. The natural part describes the path of the sun and moon and the certain temporal stations of the stars. The superstitious part is what mathematicians follow who make predictions from the stars. They also distribute the twelve signs among each soul and the members of the body. They have learned to foretell the births of men and their characteristics from the path of the stars.

23 Biskup and Dobrzycki, 31. Nowak, 17–19, has identified astronomical tables owned by Gesselen. His ownership of such tables suggests that he was a practicing astronomer of at least amateur status. 24 Hipler, 309–310. Among the sources are Aristotle, St. Augustine, Hugh of St. Victor, Thomas Aquinas, Alexander of Hales, St. Bonaventure, Nicholas of Lyra, and John Gerson. 25 Hipler, 304–311; Nowak, 19–20; Prowe, I: 112–113: “Astronomia secundum papiam est lex astrorum: quia cursus syderum docet. Astrum enim componitur cum nomos quod est lex: vel norma: quod est regula: vel noma quod est nomen: inde Astronomia et est scientia docens legem vel regulam de astris: vel quia nominat ea Astronomia ergo est de quantitate continua contracto modo: scilicet de corporibus celestibus in ordine ad motum. Astrologia quedam est ars et pars astronomie. Astrum enim componitur cum logos quod est sermo et dicitur astrologia scientia loquens de astris. Astrologia partim naturalis partim superstitiosa est. Naturalis dum exequitur solis et lune cursus: vel stellarum certas temporum stationes. Superstitiosa vero illa quam matematici sequuntur qui in stellis augurantur. Quique etiam duodecim signa per singula anime et corporis membra disponunt. Siderumque ex cursu natiuitates hominum et mores predicare noscuntur. “He igitur sunt quattuor species mathematice, scilicet Arismetrica de numeris. Musica de proporcione. Geometria de spacio. Astronomia de motu. Elementum Arismetrice est vnitas: musice est vnisonum: geometrice punctum: astronomie instans.”

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There are four species of mathematics, namely, arithmetic of numbers, music of ratios, geometry of space, and astronomy of motion. The basic element of arithmetic is unity, of music unison, of geometry the point, and of astronomy the instant.

If the reconstruction of Copernicus’s education at the school is correct, it would mean that beyond the rudiments of reading and writing, he would have received basic instruction in logic, mathematics, music, and, although exceptionally in the case of the school of St. John, astronomy. His instruction at such a school might have begun at age seven and would have lasted eight years until he was fifteen in 1488. On the other hand, if he did not begin his study there until age ten in 1483 when his uncle assumed guardianship, then he would have completed his education in Toruń in 1491.26 It is a documented fact that Copernicus entered the University of Cracow in 1491.27 If Copernicus did leave the school of St. John at age fifteen, what did he do between 1488 and 1491? In 1489 Uncle Lucas was ordained Bishop of Varmia.28 Lucas decided that Nicholas and his older brother Andrew would enter the service of the church. If there was a gap between 1488 and 1491, it supports the speculation that Nicholas may have attended the school in Chełmno run by the Brethren of the Common Life.29 Chełmno is a day’s journey downstream on the Vistula from Toruń. At this school Copernicus could have completed his preparation for study at the university, although

26 Prowe, I: 112–113; Nowak, 19–20; and Biskup, U schyłku, p. 224. There is some confusion in the literature and sources about Uncle Lucas’s relationship to the school and to a John Teschner. Teschner was evidently a teacher and rector of the school in 1470. Lucas supposedly had a relationship with Teschner’s daughter who bore him a child for whom Lucas provided after he became bishop of Varmia in 1489. Some sources, however, maintain that Lucas himself was a master and rector of the school around 1469. He could have taught after his return from the University of Cologne where he received a master’s degree in liberal arts in 1469. We know that he was back in Toruń in 1469, but in 1470 he matriculated at the University of Bologna, and in December 1473 the University of Bologna conferred a doctorate in canon law on Lucas. See Schmauch, “Jugend,” 114, items 7, 8, and 13. In any case, all of these circumstances tend to support hypotheses about Nicholas’s connection with the school. 27 Metryka, 1: 498; Album studiosorum, 2: 12; Karliński, Żywot Kopernika, 40. 28 Schmauch, “Jugend,” 129–130, items 166–170. 29 Nowak, 24–30; Biskup and Dobrzycki, 32–33.

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its reputation has been questioned.30 The school was founded in 1473 at a time when the town had lost much of its commercial prosperity.31 The Brethren of the Common Life did not instruct the students themselves but rather supervised the dormitories where the students lived. They hired teachers who were not members of the Brethren, hence their basic instruction was not different from that in other schools for the most part.32 The Brethren accepted students up to the age of eighteen, and through their common life in the dormitories propagated their ideas. The teachers used many of the same textbooks as in parochial schools, but the students and instruction were divided into eight classes instead of three. If Copernicus started attending the school at age fifteen, then he would have entered in the fifth or sixth class when students were introduced to logic and music (both mathematical ratios and practice in singing and perhaps instruction on musical instruments, especially the organ). On the other hand, it is unlikely that students at Chełmno were taught the quadrivium. Instead, they received instruction on the Bible, textual exegesis, and theology. The possibility that Copernicus would have received a more humanistically slanted education in Chełmno and an introduction to

30 Prowe, I: 113–115, rejected the speculation about Chełmno as not well founded, and see Nowak, 29, for partial support, but see also note 32 below. Birkenmajer, Mikołaj Kopernik jako uczony, 8–12, speculated that because Lucas possessed a canonry in Włocławek (German Leslau) he moved Copernicus’s family there and that Nicholas completed his early education at its cathedral school. The hypothesis was refuted by Schmauch, “Jugend,” 100–108, who demonstrated that Lucas spent very little time in Włocławek. See also Biskup and Dobrzycki, 31. Nevertheless, Markowski, “Piętnastowieczna filozofia,” 23–37, at 24–25, revived the hypothesis based on the presence of Nicholas Wodka in Włocławek. Wodka learned astronomy in Cracow at a level that enabled him to lecture on the subject in Bologna in 1479–1480. He lived in Włocławek from 1485 on. If Copernicus was his student, he may also have received from Wodka one of his manuscripts of philosophical-theological content. See Markowski, Repertorium commentariorum . . . in bibliothecis Wiennae, 246–247. Markowsky based his conclusion on MS Vienna, Clw 4007, f. IVr, which attributes the manuscript to Nicholas of Marienwerder, that is, Nicholas Wodka of Kwidzyn and “Magistri Nicolai de Tho,” which Markowski interpreted as a short form for Nicolas de Thorun. To my knowledge Markowski’s conjecture has not been widely followed. 31 Prowe, I: 114; Nowak, 24. 32 According to Nowak, 24–28, a point that makes Prowe’s objection to the hypothesis less forceful. Schmauch, “Jugend,” 100–108, also supports the reputation of the school. Schmauch’s conclusion, 108–113, that Copernicus probably attended the school in Chełmno is based on two assumptions. The first is that Copernicus definitely ended his schooling in Toruń at age 15. The second, on Copernicus’s supposed living arrangements in Chełmno, however, does not agree with the type of school founded by the Brethren of the Common Life as described by Nowak.

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scholastic philosophy and theology in a way that is consistent with his later tolerance of the Reformation and Lutherans is attractive.33 The Brethren emphasized the religious writings of St. Jerome, Gregory the Great, Pope Leo I, Peter Damian, and John Gerson. They also showed a preference for some secular authors such as Aretino and Poggio as well as the humanist Aeneas Sylvius Piccolomini (Pope Pius II).34 Perhaps the school’s teachers influenced Copernicus’s views about biblical interpretation, but that is a subject that requires much further study. In sum, it is virtually certain that Copernicus attended the parochial school of St. John in Toruń. Attendance at the school in Chełmno cannot be excluded. Before he entered the university he possessed the ability to read and write Latin. He also knew grammar, read some classical poets and authors, and was introduced to the rudiments of logic. He knew some arithmetic, geometry, and music (the theory of ratios). He may have received some instruction in astronomy, musical practice, and perhaps scholastic philosophy and biblical theology of a humanistic strain. Although a matter of speculation, these modest but tentative conclusions about Copernicus’s early education are consistent with the precocity and intellectual dedication that his later years exhibit. Nicholas seems to have been stimulated to undertake intellectual pursuits at an early age when he may have acquired the habits that he continued to develop as a student at Cracow. 2. Cracow University35 At one time the year 1364 was accepted almost without exception as the founding year of Cracow University. The supposed fact should have raised suspicions largely because of a documented second founding in

33

Nowak, 28–31. Tiedemann Giese, later a good friend of Copernicus, was educated at the school in Chełmno, and he too exhibited the qualities of toleration attributed to Copernicus. 34 Nowak, 30. 35 For studies on the University of Cracow and Copernicus see the following: A. Birkenmajer, Études; Górski, Mikołaj Kopernik; Kopernicus-Forschungen; Das 500 jährige Jubiläum; Mikołaj Kopernik, Studia i materiały. For my interpretation of the early history of the university I have relied on the revisionist, comparative studies of Peter Moraw, Gesammelte Beiträge. Unlike the universities of Bologna and Paris, Cracow University and universities in German-speaking areas were founded from above and not created by organizing already existing schools and faculties. See Metryka, 1: XVII–XVIII and XLV.

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1400, but the first founding continued to be taken for granted. Revisionist, comparative historians have cast a far more skeptical eye on the standard accounts and their documentary sources. What happened in 1364 is difficult to judge. Perhaps there was a proposal to establish a university, but it seems to have been little more than wishful thinking. The perseverance of the standard history exposes the danger in relying on older histories, especially ones that were the product of celebrations. Criticism under such circumstances is in bad taste. The history of the university and Copernicus’s education in Cracow are sensitive issues. My approach is conditioned by recent comparative history and the fact that Copernicus did obtain an education in arts. Between those guiding lines we must try to reconstruct the education that he received. According to the standard account, in 1364 King Casimir III the Great founded the studium at Cracow after the models established at the University of Bologna and the University of Padua. While the aim was to staff faculties in arts, medicine, and law (but not theology), the study of law was presumably going to be its focus. Of course, students would have been expected to achieve a degree in the arts first, but most would probably have gone on to the study of law.36 Between 1397 and 1400, however, there was a second founding, as it were, this one perhaps modeled on both the University of Paris and Oxford University. On the other hand, it seems that the University of Prague, founded in 1348, was usually the model for the universities in German-speaking areas that were founded later.37 King Władisław Jagiello established the studium in this case with the intention of focusing on theology.38 In 1397 the papacy approved the formation of the faculty of theology. Although it has the appearance of a reformation, the establishment of the studium generale in 1400 amounted to a new foundation, a decision confirmed by Pope Boniface IX in 1401 and

36 Górski, 64. Documents that support such reconstructions are found in the following: Privilegia et acta, 53–71; Codex diplomaticus, 1–8; and Statuta nec non Liber, 7–8. On Bologna and Padua as models, see Privilegia, 61, lines 5–6. But see Moraw, 181–206. 37 Metryka, 1: XLV. 38 Privilegia, 74–75; on Paris as the model: lines 13–16 of Boniface IX’s document. On Oxford as model: Codex diplomaticus, Nos. XVI, XXI, and XXXI; Moraw, 190– 191.

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1403 or 1404.39 The statutes established all four faculties (arts, law, medicine, and theology), and despite the focus on theology, benefactors supported the study of the mathematical arts, astronomy especially. Around 1405 a Cracow citizen named Stobner funded a chair of mathematics and astronomy. Stobner professors interpreted the Alfonsine astronomical tables and prepared almanachs and ephemerides. A little later about mid-century, Martin Król of Żurawica funded a separate chair of astrology. The second chair in particular seems to have assured the training of students in practical astronomy. From about 1440 to 1460 the university prepared several competent astronomers who remained in Poland. The majority of astronomers trained from 1460 to 1475 spent their careers outside of Poland. The most notable was Martin Bylica of Olkusz who collaborated with Regiomontanus. After 1475 the astronomers with the greatest reputations remained in Cracow to teach, among them Albert of Brudzewo.40 Perhaps a reflection of the fact that the university benefited from the dissolution of Prague University in the period 1409–1417, philosophy, especially natural philosophy, occupied a major part of the curriculum. For the first half of the fifteenth century, the philosophers in the faculty of arts were partial to the fourteenth-century Parisian school of John Buridan. Influences from the University of Prague are especially striking during this period. By mid-century, however, a change becomes evident, namely, that scholars at the university began to rely more on other philosopher-theologians from the earlier medieval tradition.41 This trend continued until about 1475 when another major shift occurred marking a decline in the influence of Buridan (though not its disappearance by any means) and a corresponding increase in the influence of Albert the Great, Thomas Aquinas, and Giles of Rome.42 In the 1480s the philosophy of John Duns Scotus was also represented. In other words, the changes after mid-century demonstrate that

39 Privilegia, 76–82. The document, 76, is entitled “Vladislaii Regis Poloniae studii generalis cracoviensis reformatio.” For the approval by Boniface IX, see Codex diplomaticus, 32–33 and 57. 40 A. Birkenmajer, Études, 456–457, 472–473, 474–479, and 484–486; Moraw, 192– 197. On the Stobner chair and mathematics at Cracow, see Rosińska, “ ‘Mathematics’,” 24, n. 1. 41 Markowski, “Nauki wyzwolone i filozofia,” 91–115; Palacz, “Z badań,” 73–109; ibid. 13: 3–107; and 14: 87–198. 42 Markowski, “Kontakty personale,” 95–113.

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Cracow University depended on the University of Cologne, the University of Paris, and, to some extent, Oxford University for the direction and content of training in philosophy. The end effect was a much more diverse and flexible curriculum in philosophy where students were exposed to several major medieval traditions. Though devoted perhaps to one particular author, scholars were largely engaged in harmonizing the different schools. “Eclecticism” is a fair word to use to describe the philosophy taught at Cracow in the last quarter of the fifteenth century.43 Before turning in detail to the curriculum and teachers, and then in more depth to the teaching of logic, natural philosophy, and astronomy, we must address questions about Copernicus’s years at the university. Readers who fear that this is another attempt to prove that Copernicus’s education in philosophy at the university led him to formulate the heliocentric theory can set their minds at ease. Mathematical and astronomical goals and problems led Copernicus to formulate and work out the details of his theory, not philosophical speculation. While he developed the foundation of his mathematical and astronomical knowledge at the University of Cracow, Copernicus arrived at the heliocentric theory presented in the Commentariolus in 1506 at the earliest.44 Whatever he owed to his education, teachers, and the intellectual climate in Cracow falls under two categories—practical training in astronomy and the formation of intellectual habits. Habits of reading, argumentation, and scholarship served him in the task of presenting his theory to the world rather than in discovering it. I eschew even the word “preparation” for it connotes a goal or end of which Copernicus had absolutely no inkling by 1495. “Anticipation” is also objectionable for it supposes some early formulation that approximates the later theory, and we have absolutely no evidence to support such a conjecture.

43 The dominance of a particular author or tradition is a relative judgment. In fact, the ideas of Albert the Great, Thomas Aquinas, and Giles of Rome were represented in the first half of the fifteenth century. The point, then, is that the preference for Buridan was neither exclusive nor dogmatic. In turn, the increased influence of Albert the Great and others in the second half should be understood as relative to the first half of the century. See Markowski, Filozofia przyrody, 13. For a general summary, see Palacz, “Nicolas Copernic,” 27–40. For the greater importance of education in the arts at universities like Cracow, see Moraw, 409–432, esp. 425. 44 I will argue for a later “terminus a quo” in chapter seven.

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As with his earlier education, we find that many scholars regard conclusions about Copernicus’s education at the university as worthless. Their reasons deserve serious consideration. Copernicus did not graduate from the University of Cracow, and we possess no record of his attendance of classes. At the time it was not unusual for students to attend a university and leave without a degree. Scholars estimate that only a small fraction of matriculated students completed a degree. On what they have based their estimates is unclear, but Marian Biskup, for example, maintains that students from Toruń constituted about 15% of Prussian students overall who matriculated at the University of Cracow.45 In 1491 Toruń students accounted for 21% of matriculated Prussian students. Of the Prussian students from 1491 who received a bachelor’s degree, Toruń bachelors amounted to fewer than 15%.46 The general rate of promotion to the bachelor’s degree, according to Casimir Morawski, was between 25% and 33%, and to the master’s degree was around 5%.47 Perhaps Biskup and Morawski arrived at their percentages by dividing the average number of graduates by the average number of students matriculated in each year. A comparison between lists of graduates with lists of the matriculated is not always conclusive because the names recorded in the documents make it difficult to identify many individuals with certainty.48 My examination suggests that of the 218 students who matriculated in 1491, at most 65 (29.8%) and at least 56 (25.7%) received a bachelor’s degree from the University of Cracow within four years, that is, by 1495. The results are reasonably close to Morawski’s numbers whose results are general and not just for 1491. They indicate that 1491 was a typical year. Of the five Toruń students who matriculated in 1491, not one received a bachelor’s degree by 1495, although two other students from Toruń achieved promotion in 1493 and 1494 respectively.49

45

Biskup, U schyłku, 226. On the statistics and problems with them, see Moraw, 199–205. Today one can compare the results in Metryka with those in Księga. 46 For the numbers from 1491, see Perlbach, Prussia Scholastica, 60–61. 47 See Morawski, Histoire, 259. Peter Moraw and Rainer Schwinges have undertaken a project to produce a “who’s who” of graduates (1250–1550) at universities in German-speaking areas: the Repertorium Academicum Germanicum. See Moraw, 579–591. The results are at www.rag-online.org. When completed, more reliable statistics will be available. 48 Metryka, XLIX. 49 I compared the names in Album studiosorum and Metryka against those in the Liber promotionum and Księga. Where individuals were impossible to identify with certainty, I erred on the side of assuming their graduation so as not to keep the

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The reasons for such a low rate of graduation vary. Some students were unable to pay all the fees and might obtain a degree from another university where the fees were not so burdensome.50 Most students had no intention of remaining at the university to teach in any of the faculties or of teaching at local municipal schools, and so did not require a degree from the university. Others simply went to other universities where they either obtained a bachelor’s degree or matriculated in one of the higher faculties without a degree in arts. Copernicus later matriculated at Bologna in the faculty of law without ever having obtained a degree in arts. Copernicus’s decision to forego a degree in arts was typical, not unusual. Nevertheless, we may infer from Copernicus’s later demonstrated knowledge of numerous authors and subjects that he did receive an education in the liberal arts.51 There is, however, an even stronger reason to believe that Copernicus attended classes on a regular basis and according to the prescribed order. To follow the argument we must briefly return to 1483. Before Nicholas’s father died in that year and Uncle Lucas assumed his guardianship, important changes in the family’s financial situation had already occurred. The old patriciate in Toruń to which the Watzenrode and Copernicus families belonged was replaced by a new patriciate that earned its wealth in the grain trade in the last quarter of the fifteenth century. The old patriciate had amassed wealth for the purpose of buying land (perhaps to acquire the trappings of nobility). They sought to improve their position also by seeing to the education of their children, who then often pursued ecclesiastical careers, aspiring to benefices and their income. By the late 1480s the fortunes of both the Watzenrode and Copernicus families had definitely declined.52 numbers artificially low. For example, is “Michael Stanislai de Wratislauia” (Album, 8a) “Mich. de Wratislauia” (Liber promotionum, 115)? I included “Michael of Wratislavia” in my higher number. Of course, a few students may have taken more than four years to receive a degree or they may have received one elsewhere, but those cases are irrelevant for comparison with Copernicus. 50 Morawski, 257; Moraw, 349–351. 51 The statement by Albert Caprinus of Buk in 1542 that Copernicus by his own acknowledgement first acquired at Cracow the fundamentals of mathematics and other skills indicates at the very least that Copernicus did not deny his indebtedness to the university. See Rosen, “Biography,” 316; cf. Hilfstein, Starowolski’s Biographies, 39 and 90–91. I have taken Buk’s statement that Copernicus drew the admirable things that he wrote and would write in mathematics from the university as a source (ex fonte) to refer to his education at the university. 52 Compare Czacharowski, “Kupiectwo toruńskiej,” 21–36; Mikulski, Przestrzeń społeczeństwo, 124–125; Górski, 54–59; and Papritz, “Nachfahrentafel,” 132–142.

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Uncle Lucas was a talented and ambitious man, but rather than enter the family business he pursued a career in the church. When Nicholas Copernicus, Sr. died, Lucas sent one of his daughters to the Cistercian convent in Chełmno, and arranged a marriage for the other daughter to a businessman from Cracow.53 Lucas decided that both Andrew and Nicholas Jr. would enter the service of the church with the aim of securing benefices for them on their behalf. After 1489, when Lucas became bishop of Varmia, he even hoped that Nicholas would aspire to the bishopric.54 Acquiring benefices and canonries was a highly competitive and political enterprise. The candidates would eventually have to obtain degrees in canon law. Lucas himself had entered the University of Cracow in 1463, completed a bachelor’s degree in arts at the University of Cologne in 1466 and a master’s degree in 1468. He entered the University of Bologna as a student of law in 1470, was elected proctor of the German students of law in 1472, lectured on law at Bologna in 1473 and in that year was promoted to the doctorate.55 We do not know whether the Copernicus brothers entered the University of Cracow with the intention of obtaining degrees. Nor do we know when a decision was reached about going on to Bologna afterwards, perhaps even before Nicholas went off to Cracow. These are the facts as best as we can determine them. To study in Bologna, Nicholas would need a benefice or income as a canon in Varmia, and so he would have to wait for a vacancy. We cannot say with certainty what the calculation may have involved, but it was by no means a foregone conclusion. Even if vacancies appeared regularly, not even Bishop Lucas could guarantee a benefice or an appointment for his nephew. If none had become available, Nicholas would probably have obtained a degree in law at Cracow. In 1495 there was a vacancy in Varmia. We may reasonably assume that until then Nicholas was attending classes regularly just in case he would have to obtain degrees in arts from Cracow and perhaps even

53 Schmauch, “Jugend,” 111–113. Lucas’s stepsister Catherine Peckau was a nun in the convent in Chełmno. Some scholars have speculated that the Copernicus brothers lived with the married sister’s family in Cracow, but others maintain that her husband, Bartholomew Gertner, settled in Toruń. See Biskup, “Thorn,” 9–24, at 16 and 24. 54 In 1494 Lucas consecrated his stepsister abbess of the convent. After her death he consecrated Nicholas’s sister Barbara abbess of the convent in 1499. Lucas may not have considered Nicholas as a candidate for a bishopric until after 1504, but it is clear that he was ambitious for his nephew and the family earlier. 55 Schmauch, “Jugend,” 114, items 2, 5–6, 8, 10–13.

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complete his education in law there as well. Students could achieve a bachelor’s degree within two years, most took three years, and some, as we saw above, required four years. Those who completed the degree within two years could obtain a master’s degree within another two years. If he was working towards a degree, then Copernicus may have attended the required classes until 1495.56 And if that is correct, then by the end of the summer semester in 1493 he could have qualified for a bachelor’s degree and by the end of summer of 1495 possibly even for a master’s degree. Why, then, did he leave without obtaining any degree? The statutes of the Varmia chapter stipulated that the candidate could enjoy the income from the appointment for study only under specified conditions. The statute is crucial, so I quote it at length:57 (51) Item cum de literatis implenda sit indigencia ecclesie vt fructum suo tempore afferre valeant oportunum, Statuimus quod quilibet Canonicus de nouo intrans, Nisi in Sacra pagina Magister vel Bacalarius formatus, Aut in Decretis vel in Jure Ciuili aut in medicina seu phisica Doctor aut Licenciatus extiterit, post residenciam primi anni, Si Capitulo visum et expediens fuerit, teneatur ad Triennium ad minus in aliquo stu-

56 Hamel, 102–103, concludes that Copernicus studied at the university for three years until 1494, based on the Varmian statutes. As we shall see below, however, the statutes speak of “at least” three years, not “no more than” three years. 57 Hipler, “Statuten,” 246–265, at 261, number 51. Hipler set the date of the document as between June 1485 and February 1489. I quote it at length also because the source is difficult for some to obtain. My translation may miss some legal nuances, but it captures the principal intent: “(51) Item, because the completion of an education is desirable for the church that it may bear ripe fruit, we ordain that any newly entering canon—unless he is a master or formed bachelor in Sacred Scripture, or is a doctor or licensed in canon or civil law or in medicine as a physician,—after residence of one year, and if deemed advantageous to the Chapter, be required for at least three years to study in a licensed school in one of the said faculties, and to so work in that school that he take an oath that he continuously adhered to the course of study for the said three years. Nor should he take an absence, unless because of sickness from a pestilence or because of enemy hostility he is compelled to transfer to another licensed school. Whereas if he leaves school for another cause, as long as it is reasonable he will not have to account to the Chapter for the time of his absence. But if the reason is frivolous (and the Chapter will judge whether that is the case), he will be judged simply absent for the time of his absence. He will nonetheless be held to begin the said three-year period of study again and be allowed to continue up to the end, as if nothing had happened. Therefore, with respect to each and all of the above, before the newly elected canon be granted distribution of the income, he is held to provide assurances by means of proper oaths and by presenting written documentation with the seal of the Rector of the school where he studied. Moreover, if he conducts himself profitably in the school and petitions to be given a license to study longer, such license will not be denied.”

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dio priuilegiato in vna dictarum facultatum studere Sicque soli studio operam dare, vt iugiter et continue in ipso per memoratum triennium perseueret. Nec se inde absentare presumat, nisi pestilencie Infirmitatis famis aut hostilitatis causa ad aliud se duxerit priuilegiatum Studium transferendum. Quodsi ex alia causa, rationabili tamen, Studium deseruerit, pro tempore absencie eidem tanquam Studenti Capitulum minime respondebit. Si vero ex friuola causa (que an talis sit, Judicio Capituli stabitur) se duxerit absentandum, pro tempore absencie huiusmodi simpliciter reputabitur absens. Et nichilominus teneatur dictum Triennium reincipere Studiumque vt premittitur vsque ad finem continuare, ac si prius nihil esset actum in eodem. De premissis itaque omnibus et singulis, antequam ad percepcionem distributionum rediens admittatur, patentibus literis Sigillo Rectoris Studii in quo studuerit munitis et assertione proprii Juramenti teneatur facere plenam fidem. Preterea si is vtiliter se in studio habuerit petiueritque sibi dari licenciam studendi diucius, non erit sibi talis licencia deneganda.

The statute clearly stipulates that a new canon may enjoy the fruits of an appointment even if absent as long as the absence is for the purpose of studying at least three years towards an academic degree in law or medicine (phisica). That much is clear, but one scholar, Mieczysław Markowski, has also concluded that the canon was not permitted to enjoy the income if he had already obtained a degree.58 But the statute seems to limit that restriction to a degree in theology, law, or medicine. One clause is ambiguous: Nisi in Sacra pagina Magister vel Bacalarius formatus. It could be taken to mean a “master or formed bachelor in theology” or a “master in theology or a formed bachelor,” implying that it could be a bachelor’s degree in arts, but if that is what it means, then why does it not exclude any degree in arts specifically? The grammatical construction also supports the first interpretation. If that is correct, then it does not mean that the canon could not already have

58 See Markowski, “Doktrynalne,” 13–31, at 16–17, where Markowski emphasizes the tactical character of the decision vis-à-vis the statutes of the chapter in Varmia: “Była to wszakże świadoma decyzja Kopernika, która w przyszlości miała umożliwić taktyczne rozegranie z kapitułą warmińską sprawy jego dalszych studiów, gdyż statuty tej kapituły pozwalały kanonikom na studiowanie przy jednoczesnym korzystaniu z dochodów płynach z kanonikatu tylko wtedy, gdy nie nastąpiło zakonczenie studiów zdobyciem dyplomu. O ile na Uniwersytecie Krakowskim formalna promocja na niższym wydziale była potrzebna do dalszych studiów na jednym z trzech wyższych wydziałów, o tyle uniwersytety włoskie, przynajmniej niektóre z nich, okazywały w tum względzie daleko idące ustęptstwa.” Markowsky cites Sikorski, “Mikołaj Kopernik,” but I have been unable to locate that source or the following work by Sikorski: Mikołaj Kopernik. For the second reference, see Biskup, Regesta copernicana, 6, n. 11; and Thimm, “Zur Copernicus-Chronologie,” 173–198.

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a degree in arts, which is what Markowski implies. As we will see later, Copernicus used the statute to obtain permission to study medicine for two years at the University of Padua, and that he finally received a degree in law just before all of his allowed time had expired. The complications are hard to sort, but I suggest the following solution. The statutes did not prohibit a new canon from having a degree in arts, only a degree in theology, law, or medicine as an excuse to be absent. Copernicus could have obtained a bachelor’s degree in arts in 1493, and a master’s in arts in 1495 without violating the statute. Had Copernicus remained in Cracow, however, then he would have needed at least the bachelor’s degree to begin the study of law or medicine at the university. He could not possibly have known that a degree from Cracow was not necessary until the summer of 1495. Perhaps this is what Markowski meant when he asserted that Copernicus would not have been eligible for the income from his appointment if he had received a degree. It seems to me more precise to say that Copernicus delayed receiving a degree until he knew that he had to obtain one. The result, however, is virtually the same, namely, that Copernicus, uncertain about where he would complete his education, followed a course of studies in Cracow towards a degree in arts just in case he remained in Cracow. Of course, the argument also suggests that Copernicus wanted to study in Italy. We do not know when this became desirable to him, but it was very likely under the influence of his uncle, who had studied and even taught in Bologna. An education in canon law at the University of Bologna was more prestigious than one from Cracow, and perhaps Lucas was already grooming Nicholas to become a bishop himself and his eventual successor in Varmia.59 The simple fact of the matter is that students from German universities with the financial means went to Italy or France to complete their education and obtain degrees. This was especially true for degrees in law.60 Even in medicine, when he later had the opportunity, Copernicus requested permission to study at Padua rather than at Cracow. Copernicus was eighteen years old when he entered Cracow University, a fact that complicates my reconstruction. There are some classes

59 As we shall see, this hope was later frustrated. The plan is consistent with the pattern identified by Moraw, 349–351 and 425. 60 Moraw, 197.

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in subjects such as grammar, poetry, and rhetoric that he probably could have skipped, yet some of these might have introduced him to the very sorts of humanistic interests that also motivated him to go to Bologna. There are also other reasons for thinking that Copernicus’s desire to study in Italy was deepened by his experience in Cracow. There was a humanistic circle in Cracow that included Albert of Brudzewo and several individuals with whom Copernicus remained in contact in later years. Copernicus’s education in astronomy and mathematics, along with his humanistic leanings, may have stimulated him to be linked more closely and deeply with educational movements in Italy. He certainly learned from teachers in Cracow about problems in Ptolemy and about their criticisms of models and observations. Albert of Brudzewo died in 1495 when it became clear that Nicholas could study in Italy only if he left Cracow without a degree in law or medicine. Such obstacles evidently led Lucas and Nicholas to delay receipt of a degree at Cracow and to put off the costs until the situation became clarified. For us, however, the important variable is that they did not need to make a final decision until 1495. Keeping all of these variables in mind—the uncertainty about obtaining an appointment or benefice, the possibility that he might need a degree from Cracow, and his later demonstrated education in arts—we may reasonably conjecture that Nicholas followed the prescribed order and attended classes regularly for at least eight semesters. For reasons connected with Lucas’s plans and the canonical vacancies available, it was better for him to delay a degree. One standard tactic was for canons to request a leave of absence to attend another university for the purpose of obtaining a degree at the university selected. Shortly before promotion to a doctorate in canon law, the University of Bologna regularly granted dispensations to students who did not possess a diploma in liberal arts.61 In short, the skepticism about Nicholas’s education at the University of Cracow has been just as excessive as the claims made by others on behalf of the university. Aside from the circumstantial evidence of his acquaintance with ideas, authors, and texts as demonstrated in his later writings, we may appeal to the evidence of his canonical and

61 Windakiewicz, “Informacye,” 130–148, at 135, cites examples of other dispensations allowed.

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economic circumstances and conclude that Nicholas received an education in the liberal arts at Cracow. In sum, the trajectory of his career and the circumstances of ecclesiastical politics strongly support the following conclusions. Copernicus wanted to study in Italy because a degree in law from an Italian school was more desirable by far than one from Cracow. He pursued a course of studies towards degrees in arts at the University of Cracow for four years at the end of which it became clear that he did not need a degree from Cracow. He left the university without a degree because he did not need a degree in arts to study law at Bologna. Among even the most cautious scholars, we find that they concede that Copernicus acquired an educational foundation at Cracow.62 My purpose here is to unpack the content of the generally conceded foundation. We may now look more closely at the curriculum and teachers to examine the education students received at the university. In subsequent chapters we will examine the substance of instruction in logic, natural philosophy, and astronomy, and we will extract from them above all practical training in astronomy and in the formation of intellectual habits, that is, tools of thinking and writing, and techniques of expression and argumentation. These are the kinds of goals that we can reasonably believe students at medieval universities achieved. They might forget nearly everything of substance except in those cases where they retained notes and copies of lectures or where they continued to pursue a higher degree and only then because they would have encountered the same material at a higher level of instruction. In other words, from his substantive education in philosophy, especially natural philosophy, Nicholas would have retained generally impressionistic opinions and perhaps a few doctrines peculiar among Cracow natural philosophers. Jerzy Dobrzycki has fairly concluded in commenting on Copernicus’s path to his new theory: “Historians of science are rather inclined towards an interpretation that would link the development of the heliocentric theory with the internal problems of science.”63 On the other hand, Copernicus did not ignore philosophical issues and arguments. With these qualifications and limitations in mind, we turn

62 For example, Rosen and Dobrzycki assert that Copernicus received an education in arts at the University of Cracow and left the university with a firm grip on astronomy. See Rosen, Three Copernican Treatises, 315–316; and Dobrzycki and Hajdukiewicz, “Kopernik Mikołaj,” 3–16, at 4–5. 63 Dobrzycki, “Astronomy,” 153–157, at 156.

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to the curriculum and teachers at the University of Cracow in the last quarter of the fifteenth century eventually focusing on the years 1491 to 1495. 3. Curriculum and Texts, 1475–150064 The statutes of the University of Cracow from 1406 prescribe the books that students were to “hear” prior to receiving a bachelor’s and master’s degree in arts.65 We also possess a list of courses taught and of the instructors for the period 1487 to 1563.66 For the most part the information contained in these documents is reliable. The argument above has led us to look at the order of the curriculum. Almost everyone up to now has assumed that Copernicus could have designed his own education and chosen whatever courses he wanted. They have proceeded, then, to list all of the courses in astronomy and mathematics, and assumed that he would have attended these courses whenever it suited him.67 While he very likely received instruction privately or in extraordinary lectures, he probably followed the prescribed curriculum towards a degree.68 The books prescribed for the bachelor’s degree in arts provided instruction in grammar, poetry, rhetoric, logic, philosophy of nature, and computation of the ecclesiastical calendar (for example, the reckoning of Easter). The books assigned were standard medieval textbooks and the texts of Aristotle or, more likely, a summary of questions and answers on Aristotle’s texts. In grammar, for example, students received lectures on the second part of the Doctrinale of Alexander of Villa Dei. For poetry, students heard lectures on Poetria nova of Gualterus de Vino Salvo or on works of Vergil, Ovid, Statius, Horace, Terence, and Plautus. For lectures on rhetoric, masters selected Declaratio

64 This section relies on the following source: Statuta nec non Liber; Liber diligentiarum. 65 Statuta, I–XIII, at XII and XIII. 66 Liber diligentiarum, esp. 18–30 for the period in which Copernicus was a student; Karliński, Appendices II and III, 41–43, and Tables 1–8. 67 A good example is Zinner, Entstehung, 148–150. See also Palacz, “Naturphilosophie,” 153–164, esp. 156. 68 The claim about following the prescribed curriculum is supported below. Rosińska, “Identyfikacja,” 637–644, demonstrates Copernicus’s use of Bianchini’s Tabulae planetarum for his latitude theory. She also suggests that he would have received instruction on such matters in 1493 at the earliest and more likely in 1495.

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Donatii minoris de octo partibus orationis or Cicero’s Rhetorica. The requirement for the computus could be fulfilled by lectures on Computum chirometralem, the Calendarium of Regiomontanus, or even the Sphera mundi of John of Sacrobosco. For logic instructors lectured on the Tractatus (Summulae logicales) of Peter of Spain,69 the Parva logicalia,70 and on the texts of Aristotle, the Ars vetus (De interpretatione and Categories), the Prior and Posterior Analytics, and Sophistical Refutations. As one can surmise from this list, medieval universities did more than pay lip service to “critical thinking.” Classes and exercises on logic constituted nearly half of the curriculum for the bachelor’s degree. In natural philosophy students heard lectures on Aristotle’s Physics and De anima, and they studied John of Sacrobosco’s Sphera mundi. The curriculum for the B.A. corresponds to the medieval trivium with the addition of three books on natural philosophy.71 The curriculum for the master’s degree continued with more instruction in logic and natural philosophy, adding works in the rest of Aristotelian philosophy and the quadrivium, that is, the mathematical sciences. In logic the students attended lectures and exercises on Aristotle’s Topics, through which they received training in disputation. They continued their study of natural philosophy with classes on Aristotle’s De caelo, De generatione et corruptione, Meteorologica, and the Parva naturalia. Their study of philosophy was crowned with Aristotle’s works on metaphysics, ethics, politics, and economics. Finally, they studied the classic texts on arithmetic (Boethius), geometry (Euclid), music or theory of ratios (Johannes de Muris), astronomy (Theorica planetarum), and the mathematical account of vision known as “perspectiva” (Johannes Peckham). 69 The identification of Peter of Spain with Pope John XXI is now considered doubtful. See Spruyt, “Peter of Spain,” 1–10, esp. 1–2. 70 The version attributed to Peter of Spain contains the treatises on terms and the properties of terms (supposition, relatives, ampliation, appellation, restriction, distribution, and syncategorematics) and three treatises of the moderns (obligations, insolubles, and consequences). See Statuta, 447. There is also a version of Parva logicalia sometimes attributed to Marsilius of Inghen. 71 Compare Statuta, XII–XIII; Muczkowski, Mieszkania, 18–22 and 146–148; and Zwiercan, “Krakauer Lehrmeister,” 67–84, esp. 68–69. Ryszard Palacz, “Nicolas Copernic,” 32–33, maintains that an administrative decision of 1491 placed restrictions on instruction outside the regular courses, and that Albert of Brudzewo would surely have followed the decision. Conrad Celtes testifies to having received such instruction, but since this probably occurred before 1491, it does not contradict Palacz’s assertion. Unfortunately, Palacz does not provide a source, and none of the sources available to me mentions such a restriction.

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The statutes also specify the amount of time to be devoted to each book—the total instruction to be distributed normally over four semesters, about sixteenth months if we allow for vacations and holidays.72 There are exceptions, of course, for we occasionally encounter records for students who completed the requirements in less time and others who required more than two years. We may conclude that the typical student’s course of studies towards the bachelor’s degree looked as follows: the first semester on grammar, poetry, computation, rhetoric, and the beginning of logic; the second on logic; in the third they completed logic and began Aristotle’s Physics; and in the fourth they completed Physics and De anima. Aside from the regulations in the statutes, we know that the order corresponded to the pedagogical philosophy of John of Glogovia, the most important master of liberal arts at the university. As his modern Polish biographer has expressed it: “Jan took up the didactic principle of the medieval philosophers which proposed that the pupils’ mind should be introduced to easier branches of knowledge and then gradually to more difficult ones.”73 The Liber diligentiarum also specifies the classroom in which the lecture or exercise was to take place. The layout of the building remained remarkably stable for several centuries even when the names of the classrooms were later changed. For example, the rooms called “Theologorum” and “Ptolomei” were next to each other, and the rooms called “Socratis” and “Aristotelis” were also next to each other. In every case students could move from one class to another within five minutes, so the close scheduling of classes should not have presented a problem.74 At the end of the second year students could be admitted to examination for the bachelor’s degree, although only a small percentage did so. Even without a bachelor’s degree students could continue towards the master’s degree, which required a minimum of four semesters to complete. Here again the statutes are specific about the requirements, which were clearly more demanding, for students would have to distribute instruction and disputations over two-to-three years (sixteen 72 Statuta, XXIX. The statutes of 1451 require two years to complete the program, and to prevent students from completing the requirements in a perfunctory or evasive manner they added disputations and responsiones to the requirement. 73 Zwiercan, “Jan of Głogów,” 95–110, at 102–103. 74 Tomkowicz, “Gmach biblioteki jagiellońskiej,” 113–176, especially the sketches of blueprints after 176. The building still stands on the corner of ulica Jagiellońska and ulica Św. Anny.

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to twenty-four months). Typically, the students’ course of studies towards the master’s degree would probably have looked as follows: the first semester on logic, De caelo, and De generatione et corruptione; the second on Aristotle’s works on meteorology, metaphysics, and the beginning of ethics; in the third they completed ethics, politics, and economics; and in the fourth the so-called Parva naturalia of Aristotle and all of their quadrivial requirements (arithmetic and music, geometry, astronomy, and perspective). There were other requirements concerning payment of fees and attendance of other academic exercises such as disputations. In addition, there were “extraordinary” lectures and exercises in logic, classical authors, mathematics, and other subjects that were offered in addition to the classes specified above. Professors presumably offered these classes in the late afternoon or evening. As we may expect, teachers interested in certain books or subjects offered courses on them, and over time some of these could lead to changes in the curriculum as interests and fashions changed.75 The Liber diligentiarum provides a list of books read and the professors who lectured on them. It begins with the year 1487, and while it has a few unfortunate gaps and occasional additions introduced by the editor, they provide us with a reasonably complete picture. For each semester the Liber lists under the classroom where the lectures were held the hour at which it was held, the name of the instructor, and the book or topic of the lecture or exercise.76 Nicholas registered for the winter semester of 1491/1492, which began on October 19. That is the semester in which Nicholas would have attended classes on grammar, poetry, computation, rhetoric, and beginning logic. We do not know what additional courses outside of the requirements were offered in that semester. Beginning with the winter semester of 1491, we do have nearly all the classes and professors of required courses and evidently of some other courses that were not required. The hypothetical reconstruction that follows is not aimed at determining exactly when Copernicus took what course with what professor. In some instances we can make likely guesses. We can evaluate the importance of such hypotheses, however, only after we have described the curriculum in logic, natural philosophy, and

75 76

Statuta, XXVII. Liber diligentiarum, 18–30; Karliński, Appendix III.

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astronomy and compared them with Copernicus’s arguments and assertions from the Commentariolus and De revolutionibus in subsequent chapters. The principal aim of this chapter is to get a general sense of the instruction students received and of the faculty who taught them. At the end of this survey we will have a better feel for the time that Copernicus had available to study topics of interest to him. In the next chapter we will develop a profile of masters and students at the university in the 1490s. According to the Liber the first class is listed as beginning at hora 14, which, counting from sunset in winter at 5 p.m., would mean 7 o’clock in the morning.77 The last ordinary lecture was at hora 22, which would have been 3 p.m. In that semester Nicholas would have begun logic, probably Peter of Spain’s Tractatus or Parva logicalia and perhaps lectures and exercises on the Ars vetus. Only one teacher is listed as teaching Peter of Spain’s Tractatus—John Gromaczky at 7 a.m. John of Glogovia had been scheduled to teach it, but the Liber reads non legit, resignauit mgro Gromaczky, that is, he did not read it but assigned it to Master Gromaczky. At 8 a.m. there was a class on Vergil’s Georgics. At 9 a.m. there are two classes with exercises on the old logic, followed by a break at 10 a.m. At 11 a.m. he could have attended a class on the old logic. At 12 p.m. there were two classes on Donatus, that is, grammar. At 1 p.m. there is a class on Ganfredum (a class on the art of writing poetic verse), a class labelled Alkabicium, that is, Alcabitius (a Latin translation of an Arabic introduction to judicial astrology from the twelfth century), and a class on rhetoric. At 2 p.m. there is another class on grammar, one on Vergil’s Bucolics, and one on the Parva logicalia followed at 3 p.m. by exercises on the Parva logicalia. Among his teachers in that semester may have been John Gromaczky, Paul of Zackliczew, James of Gostynin, Michael Parisiensis of Biestrzykowa, John of Cracow, Nicholas Pilcza, John Premislia, John of Slupy, John of Lesznica, Albert of Pnyewy, Vitus de Brunna, James of Szadek, Stanisław Gorky, John Sommerfelt, and Bartholomew of Lipnica.78 What conclusions can we draw? From our knowledge of their careers, we know that several of these instructors were taught by John 77

I follow the interpretation of Morawski, 281, who reasons that when the sun set at 1700 hours in winter, for example, then hora 13 would correspond to 0600 hours. 78 For a complete list of textbooks and the order in which they were to be read, see Muczkowski, 18–22; Karliński, Appendix III, Table 1.

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of Glogovia, and that only two others were independent philosophical thinkers, James of Gostynin and Michael of Biestrzykowa, both of whom offered exercises on the old logic at the same time. The next chapter will fill out this information with more detail. The most important introductory text in logic by far was the treatise by Peter of Spain. Nicholas’s academic day of required courses may very well have begun with lectures on this treatise at 7 a.m. and ended with exercises on the Parva logicalia at 3 p.m. In between he would have attended classes on grammar, rhetoric, poetry, and Aristotle’s On Interpretation and Categories (Ars vetus).79 Perhaps half of these classes were exercises and repetition—the students needed time to study and learn these texts. We will turn later to teachers and the study of logic at Cracow, but we may conclude that this is the semester in which Nicholas began to learn scholastic logic. Of his possible teachers, the most notable are James of Gostynin, Michael of Biestrzykowa, Albert of Pnyewy, John Sommerfelt, and John Gromaczky, the latter a presumed student of John of Glogovia. In the summer semester of 1492, Copernicus probably continued to fulfill the extensive requirements in logic.80 In this semester classes began at 5 a.m. with a two-hour break starting at 9 a.m. Classes resumed at 11 a.m. and continued through 5 p.m. Students attended classes on Ars vetus and on the Prior and Posterior Analytics. With exercises these classes took up six hours out of the day, leaving perhaps two hours for other classes. Given assignments recorded, we may surmise that Nicholas studied these subjects with James of Gostynin, Albert of Pnyewy, Stanisław Biel, and Martin of Olkusz. The winter of 1492/1493 would ordinarily have been his last semester of courses in logic required for the bachelor’s degree. He needed to complete the Posterior Analytics and Sophistical Refutations. He would also have begun to fulfill requirements in natural philosophy, beginning with Aristotle’s Physics and possibly courses on Sphera mundi and the calendar, as there seems to have been no appropriate course listed in the previous semesters. If he attended the class on Physics given by Matthew of Kobylina in the previous semester, then he could have

79 It seems in fact that the Ars vetus was based on Boethius’s De syllogismis categoricis I. See Peter of Spain, Tractatus, lxxxviii–xciii. De Rijk, lxxxviii, distinguishes the logica antiquorum including both logica vetus and logica nova from the logica modernorum identified with the tracts discussing proprietates terminorum. 80 Liber diligentiarum, 20–21.

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completed work on the physics with Matthew in this semester. Otherwise his only option would have been to take Physics with Albert of Swolszowice. Among other possible instructors were Simon of Sierpc with exercises on the Posterior Analytics and Martin of Szamotuli with lectures on the Sophistical Refutations. In the summer semester of 1493, what would have been Nicholas’s last towards the bachelor’s degree in arts, students were required to complete natural philosophy by finishing the Physics and attending a class on De anima. If Nicholas completed all of the other requirements, then he would have qualified for the bachelor’s degree. He did not undergo examination for the bachelor’s degree, but he remained at Cracow for another two years. It has been assumed in the past that he might have attended Albert of Brudzewo’s class on De caelo in the summer semester of 1493. This assumption was based on a much later legend that he was a student of Albert and probably attended his extracurricular classes as well as the class on De caelo. De caelo was one of the courses required for the master’s degree, but Copernicus would not have begun classes towards that degree until the winter of 1493. If he did attend Albert’s class on De caelo, it would have been out of the ordinary, and we have no way of confirming it. On the other hand, he certainly knew of Albert’s reputation, and it is consistent with what we know of Nicholas’s interests that he would have taken the opportunity to attend Albert’s class. There would have been no conflict with the required courses scheduled in that semester, including exercises on De anima with Lawrence Corvinus.81 Some scholars have assumed that Copernicus would have taken three years for the equivalent of a B.A. degree, but they overlook one important variable. Nicholas was already eighteen years of age with a basic education behind him when he matriculated in 1491. He was probably a few years older than most of the students who matriculated in that year. It is not unreasonable to assume that he could have completed the requirements for a bachelor’s degree in the minimum time. In the next semester, winter 1493/1494, Copernicus could have begun attending classes that would normally lead to the master’s degree in arts. As we have been arguing and will substantiate in

81 Although the Liber, 24, comments: Sed aliud sepius exercitauit. Karliński, Appendix III, Table 4.

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subsequent chapters, we have reason to believe that Copernicus was educated in scholastic and Aristotelian logic and natural philosophy. The classes towards the master’s degree normally began with lectures on Aristotle’s Topics, probably to prepare students for the more intensive disputations of the master’s program. In winter 1493 he would have turned to Aristotle’s other standard works in natural philosophy, De caelo (if he did not take it in the summer semester), De generatione et corruptione, Meteorologica, and possibly the Parva naturalia. The records show only one class on Meteorologica, exercises with Albert of Pnyewy. Either the lecture-class has been omitted, or this was a continuation from the previous semester, in which Martin of Olkusch lectured on Meteora at 12 p.m., a time that would have fitted into Nicholas’s schedule. If he did take De generatione et corruptione in this semester, then it would have been with Albert of Brudzewo. In any event, he could have completed the remaining courses without any conflict.82 In the summer of 1494 Nicholas might have completed ethics and taken politics, economics, and metaphysics.83 None of his teachers is especially noteworthy except that Stanisław Ilkusch lectured on Sphera materialis (i.e., Sphaera mundi) at 1 p.m.84 One class on ethics (at 11 a.m.) and one on politics (at 2 p.m.) are listed along with metaphysics at 7 a.m. and exercises on metaphysics at 5 p.m. Of the others, he may have attended Albert of Szamotuli’s class on astrology at 3 p.m., and he could have attended Michael Falkener of Wrocław’s lectures on Meteorologica in this semester, also at 2 p.m.85 In the winter semester of 1494/1495, Nicholas could have completed courses on what we call social sciences and begun intensive work on the quadrivium. There were several classes in this semester on arithmetic, music, Euclid, Ptolemy, and Theorica planetarum. There were a number of able professors—Stanisław Kleparz on Euclid at 11 a.m., Albert of Szamotuli on Ptolemy at 1 p.m., and Stanisław Ilkusch on

82

Karliński, Appendix III, Table 5. We know from comments to be examined later in this study that Copernicus was familiar with Aristotle’s Metaphysics. In chapter two I comment on speculation that Copernicus may have known one of John of Glogovia’s Saturday disputations on the Metaphysics. 84 See McMenomy, “Discipline,” 140, for the titles of Sacrobosco’s treatise, Tractatus de sphaera, Tractatus de sphaera mundi, to which we may add Sphaera materialis. 85 Karliński, Appendix III, Table 6. 83

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Theorica planetarum at 2 p.m. He could have begun this long day at 7 a.m. with a class on arithmetic and music.86 Finally, in the summer of 1495 Copernicus could have attended numerous courses in the quadrivial arts. The demands of this semester along with requirements for disputations may explain why many students needed at least another year to achieve the master’s degree.87 To sum up, experts on Copernicus have assumed that Nicholas obtained an education in liberal arts at Cracow. It is likely that Copernicus counted among his teachers the leading masters in arts or their students. He may not have completed all of the requirements and attended all of the courses towards degrees, but an education in liberal arts at Cracow according to the standards of the day included instruction in grammar, rhetoric, poetry, logic, natural philosophy, metaphysics, ethics, arithmetic, music, geometry, and astronomy. Choices were limited. I have based the above reconstruction on the statutory requirements for degrees and on his age and previous education at matriculation. We know what books were read and, generally, the order in which they were read. We also know the sorts of introductory texts that masters used, and we will examine those in chapters three, four, and five. Before I summarize the education that students received in logic, natural philosophy, and astronomy, we may turn to biobibliographical profiles of the teachers and students at the university.

86 87

Karliński, Appendix III, Table 7. Karliński, Appendix III, Table 8.

CHAPTER TWO

MASTERS AND STUDENTS IN THE 1490S1 For the most part, the masters teaching between 1491 and 1495 had themselves been trained in the 1470s and 1480s. Three professors in particular stand out both for their productivity as scholars and also as teachers of most of the arts’ masters teaching at the university in the 1490s—John of Glogovia, Albert of Brudzewo, and James of Gostynin. John of Glogovia (ca. 1445–1507) matriculated at the University of Cracow in 1462, received the bachelor’s degree in 1465 and the master’s in 1468. Except for one academic year at the University of Vienna (1497–1498), John spent his entire career, about forty years, teaching liberal arts at the university. He was a scholar of wide interests who wrote on and taught grammar, logic, natural philosophy, metaphysics, astronomy, and geography. During his long career he performed numerous administrative duties. All of his writings are scholastic in method, several of which were printed in the early sixteenth century. The Jagiellonian Library in Cracow has preserved dozens of John’s treatises in manuscript. Among the most notable are exercises on Peter of Spain’s Tractatus (Summulae logicales) and on the old and new logic, commentaries on the Prior and Posterior Analytics, questions on Aristotle’s Physics, De anima, and Metaphysics, and a commentary on the Metaphysics and on Thomas Aquinas’s De ente et essentia.2 In astronomy he wrote a number of works of a practical nature—on the Alfonsine Tables, prognostications, almanachs, ephemerides, and astrological calendars. He also wrote an introductory compendium on the Sphera mundi of John of Sacrobosco.3 In geography he wrote an introduction to cosmography explaining Ptolemy’s Cosmographia. He 1

Chapter 2 relies on PSB, 45 volumes to date, and on the Liber diligentiarum. Copies of these works are preserved in the collection of the Jagiellonian Library in Cracow. See Markowski and Włodek, Repertorium commentariorum . . . in bibliotheca iagellonica Cracoviae: BJ, MS 25, MS 511, MS 689, MS 1902, MS 2017, MS 2088, MS 2089, MS 2090, MS 2173, and MS 2453—all commentaries on Aristotle’s works in logic and natural philosophy. 3 Zwiercan, “Jan z Głogowa,” PSB 10: 450–452: BJ, MS 1963, MS 2491, and MS 2729, all on astrology. Several of John’s works on logic and astrology were published in the early sixteenth century. 2

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counted humanists among his friends, but because of his scholastic style, some humanists regarded him as reactionary. Be that as it may, he was an important figure in reviving interest in the works of Albert the Great and Thomas Aquinas. His works in logic and natural philosophy were especially devoted to harmonizing the doctrines of several scholastic traditions. As a teacher, there is no other figure who exercised such an important influence on the liberal arts at Cracow in the period from 1470 to 1500.4 Although Copernicus may have attended only one of John’s courses (summer 1492 on Parva logicalia), it is very likely that John taught his instructors and that some of them probably used John’s exercises and questions in their classes.5 Albert of Brudzewo (ca. 1445–1495) entered the university in 1468, received the bachelor’s degree in 1470 and the master’s in 1474. Albert spent most of his career teaching liberal arts, although he did receive a bachelor’s degree in theology in 1490.6 He taught numerous courses in philosophy, but his main claim to fame rests on his reputation as the leading astronomer at Cracow in the second half of the fifteenth century. His reputation is due mainly to the publication of the most important work in astronomy published by a Cracow professor in the fifteenth century. The Commentariolum super Theoricas novas planetarum Georgii Purbachi was completed in 1482, and it appeared in print in 1495. One of the earliest biographies of Copernicus, Starowolki’s 4 See Zwiercan, “Jan z Głogova,” 450–452, with extensive bibliography and enumeration of editions and manuscripts. On John’s library, see Szelińska, Biblioteki profesorów, 176–181. See also the authoritative articles by Seńko, “Wstęp do studium,” 1: 9–59, and 3: 30–38. See also Zwiercan, “Krakauer Lehrmeister,” 67–84; Zwiercan, “Jan of Głogów,” pp. 95–110; Markowski, “Repertorium bio-bibliographicum,” 103– 162; Usowicz, “Traktaty Jana z Głogowa,”), 125–156; and Świeżawski, “Materiały,” 135–184. 5 Zwiercan, “Jan of Głogów,” 108–110, lists John’s students and humanist friends and supporters. The standard texts, however, were not John’s summaries, about which see Zwiercan, 99–100. Hilfstein, Starowolski’s Biographies, 43–44, following Ludwik Birkenmajer, Stromata copernicana, 121–122, speculates that Copernicus knew one of John’s Saturday disputations on Aristotle’s Metaphysics based on the spelling “Trimegistus” instead of “Trismegistus.” Unfortunately, the precise year or years in which John held the disputation is not known, nor did he lecture or conduct exercises on the Metaphysics between 1491 and 1495; Karliński, 41 and Appendix III, Tables 1–8. 6 Karliński, Żywot, 41; Hipler, Spicilegium copernicanum, 311–315 and 368–369; Birkenmajer, Stromata, 83–103; Palacz, “Wojciech Blar z Brudzewa,” 172–198; Markowski, “Repertorium bio-bibliographicum astronomorum cracoviensium medii aevi,” 111–163, at 117–133; Pawlikowska-Brożek, “Wojciech of Brudzewo,” 61–75; and Pakulski, “Wojciech z Brudzewa,” 661–681 [fasc. 4, 21–41]. PSB has not reached the letter “W” where Brudzewo’s biography will appear—Albert is Wojciech in Polish.

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Hekatontas, named Albert explicitly as one of Nicholas’s teachers.7 On the basis of this testimony and of the likelihood of contact between Copernicus and Albert, several scholars have speculated that Copernicus may have attended Albert’s lectures on De caelo in the summer semester of 1493. As we saw in chapter one, however, the one class that fits in my hypothetical reconstruction of Nicholas’s career as a student is Albert’s lecture-course on Aristotle’s De generatione et corruptione, not De caelo.8 We know from the education of Conrad Celtes that he received private instruction in astronomy from Albert, but because we have no record of extra-curricular courses taught by Albert or any other record of private instruction, we do not know what Nicholas may have learned from him. On the other hand, there are two passages in De revolutionibus that indicate Copernicus’s possible acquaintance with Albert’s Commentariolum.9 Even if Copernicus did attend Albert’s lectures on De caelo, we do not know details of Albert’s lectures. In other words, we must reconstruct Copernicus’s possible dependence on him from Copernicus’s own statements. The evidence is not strong, but Copernicus may have acquired his knowledge about the ancient axiom of the uniform, circular motions of the celestial spheres from the Commentariolum. Albert is also critical of Ptolemy’s lunar model, and perhaps he stimulated Copernicus to adopt a critical stance towards Ptolemy. In fact, however, Copernicus nowhere refers to Albert explicitly. It is likely that John of Glogovia trained most of the masters who taught logic, philosophy, and astronomy in the 1490s, and Albert also

7 Hilfstein, Starowolski’s Biographies, esp. 14, 30–39, 42–43, and 64. Starowolski evidently relied on Jan Brożek, a student who displayed a great interest in Copernicus at Cracow in the early seventeenth century, to reach his conclusion. Brożek’s testimony, however, is not always reliable even though he had correspondence from Tiedemann Giese, a close friend of Copernicus, in his possession. The letters were lost, and so we cannot say how much Brożek may have embellished the information available to him. Starowolski had also seen the correspondence. For further circumstantial evidence, see Wiszniewski, Historya literatury poslkiej, 4: 296, cited by Hilfstein, 43, who emphasizes the requirement that students were to select a master as adviser. 8 Although we have no example of Albert’s instruction on Aristotle, there is one book that he purchased for the library of the faculty of arts: BJ, MS1848 containing the “Quaestiones Cracovienses on Parva naturalia and De generatione et corruptione.” See Markowski and Włodek, 76. John of Glogovia was also one of Albert’s teachers. See Zwiercan, “Jan z Głogów,” 108. 9 Albert de Brudzewo, Commentariolum, esp. XVI–XVII, 55, 69, and 120. Birkenmaier’s beliefs to the contrary notwithstanding, we must add that the supposed textual parallels are slim.

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taught them astronomy and Aristotle’s works in natural philosophy such as De caelo and De generatione et corruptione.10 James of Gostynin (ca. 1454–1506) matriculated at the university in the fall of 1472, received the bachelor’s degree already in 1473, and four years later obtained the master’s degree. Although later a theologian, he lectured in the faculty of arts from 1477 to 1496. He began his study of theology in 1491, received the theological baccalaureate in 1493 and the master’s in 1499. His lectures on the liberal arts, especially on Aristotle, are marked by an emphasis on classical texts.11 Among the scholastically trained masters in Cracow, he was one of the professors who relied somewhat less on scholastic commentaries and more on a close reading of the Latin text of Aristotle in its own terms.12 As suggested in chapter one, Copernicus may have learned a good deal of what he knew about Aristotelian philosophy, especially of Aristotle’s logic, from James of Gostynin, who supplemented the sort of instruction provided by John of Glogovia and his students with greater reliance on Aristotle’s texts. Of the remaining scholars, Michael Falkener of Wrocław (ca. 1460–1534) merits consideration. Information about Michael is comparatively sketchy. His career as a student in higher education was unusually long—from 1479 to 1488.13 From 1488 to 1495 he taught in the faculty of arts at Cracow only as an assistant (extraneus de facultate), and in 1517 received a doctorate in theology. Initially inauspicious, Michael’s career turned out to be remarkably productive. He seems to have been a widely educated man especially gifted in teaching introductory courses. Aside from teaching all of the quadrivial subjects, he taught and wrote on mathematical astronomy and astrology. In philosophy he developed a reputation for producing textbook

10 Zwiercan, “Krakauer Lehrmeister,” 78. See also Markowski, “Szczyt rozkwitu,” 102–126, esp. 115–122. 11 Markowski and Włodek, Repertorium, list the following works preserved in Cracow: BJ, MS 505 (commentaries on the Physics and Metaphysics); BJ, MS 2010 (a commentary on the Physics); BJ, MS 2076 (marginal comments to the Prior Analytics, Posterior Analytics, Topics, Categories, and On Interpretation). 12 Seńko, “Jakub z Gostina,” PSB 10: 352; idem, “Jakub z Gostynina,” 183–210; Karliński, 41. 13 Barycz, “Falkener Michał,” PSB 6: 357–358; Palacz, “Michał Falkener z Wrocławia,” 35–91; and Palacz, “Michael Falkener,” 33–39. On Michael’s library, see Szelińska, Biblioteki, 201–217. See also Karliński, 42.

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summaries.14 These summaries are products of both the eclecticism that characterized the teaching of philosophy at the university in the last quarter of the fifteenth century but also of the growing influence of humanism in Cracow in the last decade of the century. He was on the cusp between scholasticism and humanism, and represents a transitional figure from scholasticism to humanism. The content of Michael’s work in philosophy affords us a glimpse into the state of philosophy at the university at the end of the fifteenth century. It is possible that Copernicus attended his lectures on Aristotle’s De generatione et corruptione or on Meteorologica. Of the remaining teachers of philosophy, the most important was Michael Parisiensis of Biestrzykowa (ca. 1450–1520).15 He matriculated at the University of Cracow around 1469 but received his bachelor’s degree in 1473 and master’s in 1475 from the University of Paris. He was trained as a Scotist, returned to Cracow around 1485 and began teaching in 1487.16 A productive scholar, he taught logic and philosophy primarily and remained the principal representative of Scotist philosophy at the university. His commentaries on logic show the influence of his teacher at Paris, Petrus Roselli, and he transmitted Parisian Scotism as represented by Peter Tartaret, John Magister, and Nicholas de Orbellis. He engaged in polemics with the work of fourteenth-century nominalists, for example, Marsilius of Inghen.17 It is possible that Copernicus attended his lectures on logic. Among his students who taught after Copernicus’s departure was John of Stobnicy (ca. 1470–1530) who received his master’s degree in 1498 and also taught philosophy primarily. Although humanistically inclined, Stobnicy wrote several works of philosophy in the Scotist manner. Like

14

Several of his works on astronomy and astrology and a handbook on logic, Congestum logicum, were published in the early sixteenth century. See, for example, BJ, Cim Qu. 5227. 15 Zwiercan, “Michał Twaróg z Bystrzykowa,” PSB 20: 621–622; Korolec, “Michał z Bystrzykowa,” 141–171; and Karliński, 41. 16 John Duns Scotus was a famous Franciscan philosopher-theologian who died in 1308, and the Scotist textual tradition is notoriously confused by the attribution of several inauthentic works to him. 17 Estreicher, “Michał z Bystrzykowa,” Bibliographia polska, 22: 332–334. For commentaries preserved in Cracow, see, for example, Markowski and Włodek, Repertorium, 96–97: BJ, MS 2061, a commentary on De anima. Many of his commentaries on works of Aristotle were published in the early sixteenth century.

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Michael Falkener, he provides another perspective on the state of philosophy at Cracow around the turn of the century.18 The list of possible instructors is extensive. In logic, natural philosophy, and mathematical sciences alone, I have identified twenty-two. For several of these individuals there is little published information available. Bartholomew of Lipnica (ca. 1465–ca. 1538) matriculated at the university in 1485 and in 1491 obtained a master’s degree in arts and also a bachelor’s degree in theology. He served as a parish priest and later became the first trustee of the Jagiellonian Library.19 In winter 1491 and summer 1492 he instructed students on the Parva logicalia.20 Bernard of Biskupie, also known as Bernard Kapustka of Cracow, (ca. 1457–1531) received the bachelor’s degree in 1477 and master’s in 1484. Around 1490 he occupied the Martin Król of Żuravica chair in astrology and produced a prognostication for 1489. He went on to the study of theology, receiving a bachelor’s degree around 1498 and a licentiate in 1503. He also served as dean of the faculty of arts and rector of the university on several occasions.21 He conducted exercises on De caelo in winter 1492, lectured on De generatione et corruptione in summer 1493, and led exercises on the Parva naturalia in winter 1494. He wrote no works on logic or natural philosophy.22 Martin Ilkusch, also known as Martin Biem of Olkusz (ca. 1470– 1540), a slightly older contemporary of Copernicus, received a bachelor’s degree in 1488 and master’s in 1491. He lectured as an assistant (extraneus non de facultate) in 1491 to 1494 on the works of Aristotle and on mathematics. Although interested in astronomy and astrology, he later went on to complete degrees in theology. He later made and reported several astronomical observations, and there is reliable testimony that he corresponded with Copernicus very probably about one of these observations.23 He owned some manuscripts containing

18 Tarnowska, “Jan ze Stobnicy,” PSB 10: 480–481. On John’s library, see Szelińska, Biblioteki, 248–249. 19 Barycz, “Bartłomiej z Lipnicy,” PSB 1: 315–316. 20 Liber diligentiarum, 19–20; Karliński, 43. 21 Barycz, “Bernard z Biskupiego,” PSB 1: 458–459. 22 Liber diligentiarum, 22, 24, and 30; Karliński, 41. 23 A. Birkenmajer, “Biem Marcin,” PSB 2: 68–69; Markowski, “Marcin Biem of Olkusz,” 5–21; Karliński, 42.

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commentaries on works of Aristotle.24 Martin may have taught Copernicus Ars vetus in summer 1492. He also lectured on Perspectiva in winter 1492, on Meteora and arithmetic and music in summer 1493, on the Calendar of Regiomontanus in winter 1493, and on the Parva naturalia in winter 1494. Stanisław Bylica of Olkusz, also known as Stanisław of Ilkusch (ca. 1460–1514), the nephew of Martin Biem of Olkusz, matriculated at the university in 1477, received the bachelor’s degree in 1478 and the master’s in 1484. He lectured as an assistant (extraneus de facultate) from about 1488 to 1490, held the Stobner chair in astronomy in the early 1490s. In the late 1490s he undertook the study of theology, and received the bachelor’s degree about 1500. He wrote mostly theological works and was one of the first to support the humanistic movement from Italy at the university. Aside from lectures on astronomy and astrology, he also lectured on the works of Aristotle. In winter 1492 Copernicus may have attended his lectures on the Posterior Analytics. In the summer semester of 1494 he lectured on the Sphera of John of Sacrobosco, and in winter 1494 on Theorica planetarum perhaps using the commentary by Albert of Brudzewo. As mentioned earlier, Copernicus may have been acquainted with Albert’s commentary. Because Albert did not lecture officially on his commentary between 1491 and 1495, we are led to conclude that Nicholas knew of the commentary either through his acquaintance with Albert or in Stanisław Bylica’s lectures on it, or otherwise from Albert of Pnyewy’s lectures.25 Matthew of Kobylina (ca. 1425–1492) received his master’s degree in arts around 1449, taught mostly logic from the 1450s, served as dean of the faculty of arts several times, and was the rector of the university who admitted Copernicus into the university as a student.26 In the summer and winter semesters of 1492 he lectured on Aristotle’s Physics.27 One of the oldest masters at the university, he was one of the few who possibly still taught natural philosophy under the influence of the fourteenth-century Parisian philosopher John Buridan and of

24 Markowski and Włodek, Repertorium, BJ, MS 714, MS 738, and MS 740. In the early sixteenth century he wrote marginal comments on Aristotle’s Sophistical Refutations preserved in BJ, MS 2175. On Martin’s library, see Szelińska, Biblioteki, 227–248. 25 Albertus, Commentarolium, p. XXXIII. On Stanisław’s library, see Szelińska, Biblioteki, 197–201; Karliński, 42. More on Albert of Pnyewy below. 26 Zathey, “Maciej z Kobylina,” PSB 19: 19–20. 27 Liber diligentiarum, 20–22; Karliński, 41.

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Albert of Saxony.28 He continued to lecture in the faculty of arts even after he received degrees in theology around 1465 and in law around 1480. Albert Piotrkow of Swolszowice (ca. 1466–1521) also taught in the 1490s and may have taught Copernicus Aristotle’s Physics in winter 1492 and summer 1493. The Liber diligentiarum lists no fewer than sixty variant spellings of his name. He was a book-collector, and evidence from around the turn of the century indicates that in his lectures on philosophy Albert adopted a Thomistic interpretation of Aristotle.29 He later went on to the study of theology. Annotations in several codices of works by Thomas Aquinas confirm his Thomistic orientation as well as his commitment to the so-called via antiqua in his collection of books that included works of Albert the Great and Bonaventure. He also possessed works of Duns Scotus, Antonius Andreae, Nicholas of Orbellis, and even a commentary on Peter of Spain’s logical works ad mentem Scoti. In addition, marginal notes in works by Lambert of Monte and Gerard of Harderwyck demonstrate his acquaintance with the tradition from Cologne. In short, Albert was familiar with the traditions of Thomism, Albertism, and Scotism in philosophy.30 His other books show that he was a well-read teacher who collected works of biblical exegesis, ecclesiastical history, hagiography, liturgy, casuistry, and ancient and Renaissance humanistic literature.31 Martin Kułab of Tarnowiec (ca. 1460–1538) matriculated in the faculty of arts in 1478, received the bachelor’s degree in 1486 and the master’s in 1489.32 He served in the faculty of arts from 1489 to 1523, and he was a scholar of wide interests. He lectured on grammar, Peter of Spain’s Tractatus, the Posterior Analytics in winter 1492, John of Sacrobosco’s Sphera, and Boethius’s De consolatione philosophiae. He also went on to study theology. As a teacher he held to the old scholastic forms and content but he also adopted the

28 He owned one manuscript of questions on the De caelo et mundo of Albert of Saxony. Markowski and Włodek, Repertorium, 28–29. He also gave a book to the library of the faculty of arts containing commentaries on the works of Aristotle by John Isner, a late fourteenth-century follower of Buridan. On Matthew’s library, see Szelińska, Biblioteki, 96–101. 29 Szelińska, Biblioteki, 217–227, esp. 218–219. 30 Szelińska, 219–222. 31 Szelińska, 222–226. 32 Szelińska, “Marcin znany Kułab (Kułap) z Tarnowca,” PSB 19: 574.

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new humanistic approaches to texts. In winter 1493 he lectured on Aristotle’s Metaphysics.33 Nicholas of Pilcza (ca. 1450–1515) matriculated in 1471, received the bachelor’s degree in 1473 and the master’s in 1477. He also later went on to study theology. In the winter semester 1491 he lectured on the Posterior Analytics.34 Lawrence Corvinus (ca. 1466–1527) matriculated at the University of Cracow in 1484, received the bachelor’s degree about 1486 and the master’s in 1489. He advocated Italian Renaissance humanism, came under the influence of the humanist poet Conrad Celtes and joined the humanistic circle known as the Sodalitas Vistulana. Aside from teaching classical poetry, he also lectured or led exercises on Peter of Spain’s Tractatus, Aristotle’s Posterior Analytics and De anima, Thomas Aquinas’s De ente et essentia, and Boethius’s De consolatione philosophiae. His first publications, however, were on geography, so he is representative of humanists in Cracow with mathematical interests, much like Copernicus himself. Among his most notable works is a didactic poem, Carmen elegiacum de Apolline et novem Musis (Wrocław, 1503), that demonstrates an acquaintance with Greek, the strong influence of Platonic and Neoplatonic philosophy, and a connection with astronomy at Cracow, although his main scientific interest was in geography.35 Of Silesian origin, Corvinus returned to Wrocław to teach and became a municipal notary, but moved to Toruń in 1506 where he had a stimulating if brief contact with Copernicus. They evidently knew each other from their time in Cracow. Corvinus played a role in the publication of Copernicus’s first work, the Latin translation of the letters of Theophylactus Simocatta, only the second translation of a Greek work into Latin published in Poland. In 1508, as Corvinus was planning on returning to Wrocław, Copernicus asked him for his assistance in publishing the translation.36 Corvinus not only agreed but also added a short elegiac poem at the beginning that indicates Corvinus’s awareness that Copernicus had devised a new and wonderful astronomical model.37 The work was published in Cracow in 1509, so

33

Liber diligentiarum, 26; Karliński, 42. Zathey, “Mikołaj Pych z Pilicy,” PSB 21: 131–132; Karliński, 41. 35 Barycz, “Corvinus Wawrzyniec,” PSB 4: 96–98. 36 Prowe, Nicolaus Coppernicus, 1, A: 400, note *. 37 Barycz, 97: Mirandum Omnipotentis opus rerumque latentes / Causae scit miris quaerere principiis. See also Prowe, 1, A: 387–390. 34

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we will examine it later especially with regard to Copernicus’s earliest formulation of the heliocentric theory.38 Perhaps in part because of his Renaissance humanist leanings, Corvinus declared himself a Lutheran supporter in 1522. In the Liber diligentiarum he is identified as “Laurentius de novo foro.” His name appears for the first time in winter 1489 when he lectured on Peter of Spain’s Tractatus, on Vergil’s Bucolics in summer 1490, and on Boethius in winter 1490. Unfortunately, except for exercises on De anima in summer 1493, there are no assignments during the rest of his tenure as a teacher that fit Copernicus’s schedule.39 In all of the assignments listed there is not a single repetition, so we cannot even suggest a pattern. It may be that Copernicus studied poetry or even rhetoric with Corvinus, but we will evidently never know. Nevertheless, their contact and acquaintance testify to Copernicus’s early interest in Renaissance humanism. John of Oźwięcimia (1443–1527) matriculated in 1459, received the bachelor’s degree in 1465 and the master’s in 1469.40 He spent several years in Italy, came under the influence of humanism, and was probably the student of the Greek scholar John Argyropulos. He returned to the University of Cracow where he served as dean of the faculty of arts in winter 1491,41 and supposedly lectured in arts as well.42 From 1492 until the end of his life he was active in the faculty of theology from which he received a doctorate prior to 1498. He was among the first advocates of humanism at the university and perhaps of the study of Greek as Copernicus began his education in Cracow.43 Leonard Vitreatoris of Dobzyc (ca. 1470–1508), a near contemporary of Copernicus, studied under John of Glogovia and Albert of Brudzewo in Cracow, and received his master’s degree in 1489 when he

38

Prowe, 1, A: 400, note *. Liber diligentiarum, 11, 13, 16, 19, 23, and 26; Karliński, 42. He is mentioned irregularly and only once among the roster of teachers as extraneus de facultate on p. 23. 40 Barycz, “Jan z Oźwięcimia,” PSB 10: 467–468. For his library, see Szelińska, Biblioteki, 190–197. 41 Liber diligentiarum, 18; Karliński, 41. 42 According to Barycz, PSB 10: 467. 43 The evidence that Copernicus first learned Greek in Italy is strong and persuasive, but only recently have scholars begun to realize the extent of education in Greek in Poland prior to 1500. Perhaps Copernicus received some instruction in Cracow or, at least, developed a yearning to learn Greek while still an undergraduate through his contacts with Corvinus, Oźwięcimia, and members of the Sodalitas Vistulana. 39

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began to lecture as an assistant (extraneus de facultate).44 He also studied law and theology but remained active in the faculty of arts where he lectured on treatises of Aristotle, mathematical astronomy, treatises of Ptolemy, astrology, and Euclid. He was interested in trigonometry, recorded several astronomical observations, and prepared astrological prognostications and horoscopes. In the early sixteenth century he was one of the first to publish several astronomical and astrological works, especially tables of solar, lunar, and planetary motions. Certainly not as original as Copernicus, Leonard was trained to succeed John of Glogovia and Albert of Brudzewo as the leading philosopher-astronomer in Cracow. Described by students and friends as astrologus summe experiencie, he died suddenly from an epidemic that ravaged Cracow in 1508 when he was about forty years of age. His name appears in the Liber diligentiarum as “Leonardus de Cracovia.” In the years that Copernicus was a student, Leonard taught Euclid, texts of Aristotle, and logic, but we do not know of any contact between them.45 Nicholas of Cracow (ca. 1465–1528), another slightly older contemporary of Copernicus, began studying at the university in 1483, received the bachelor’s degree in 1485 and the master’s in 1488. He lectured on grammar, poetry, rhetoric, Cicero’s De officiis, Peter of Spain’s Tractatus, and the works of Aristotle. Like Leonard, Nicholas was also a student of John of Glogovia and Albert of Brudzewo, and he shared their interests in astronomy and astrology. He later went on to the study of theology, which he taught at the university.46 In the years that Copernicus studied at the university, Nicholas of Cracow taught as an assistant (extraneus de facultate), lecturing on Aristotle’s Physics, Metaphysics, Ars vetus, Sophistical Refutations, the so-called Parva logicalia of Peter of Spain, and rhetoric.47 James of Szadek taught logic (Veteris artis) in winter 1491, Metaphysics in summer 1492, Meteorology in winter 1492, and De caelo in winter 1494. His personal collection included manuscripts of works of Thomas Aquinas, St. Augustine, Peter Lombard’s Sentences, and of other medieval authors. His collection also included incunabula, but 44 Friedberg, “Leonard Vitreatoris z Dobczyc,” PSB 17: 71–72. If his date of birth is even approximately correct, then he was a precocious student indeed. His date of matriculation is 1483, which would mean he entered the university at about age 13. For his library, see Szelińska, 187–190. 45 Liber diligentiarum, 18–19 and 21–22; Karliński, 42. 46 Szelińska, “Mikołaj Mikosz (Mikosch, Mykosz) z Krakowa,” PSB 21: 120–121. 47 Liber diligentiarum, 18, 20, 22–23, 26, and 29; Karliński, 42.

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his interests were primarily in theology and canon law. The dates of his instruction do not fit will with Copernicus’s likely undergraduate career.48 Of several instructors who may have taught Copernicus we know very little. The most important from this group are Albert of Pnyewy, Albert of Szamotuli, John Gromaczki, John of Słupczy (or Slupy), James of Iłzy, Simon of Sierpc, Stanislaus Kleparz, Martin of Zeburk, Paul of Zackliczew, and Bartholomew of Oraczew, only to select those who may have instructed Copernicus on logic, natural philosophy, and mathematics. Several of these individuals went on to become theologians and wrote nothing on logic, natural philosophy, or astronomy, for example, John of Słupczy.49 Others were active in astronomy or astrology, for example, James of Iłzy (d. 1526), a student of John of Glogovia and Albert Brudzewo. Some like Paul of Zakliczew, for example, developed reputations as humanists. Our information about the rest comes almost exclusively from the Liber diligentiarum. Albert of Pnyewy taught the Prior Analytics in summer 1492, conducted exercises on Meteorologica and lectured on Perspectiva in winter 1493, and he was an expert on astronomy. Albert of Szamotuli, likewise an expert on astronomy, taught De anima in winter 1492, astrology in summer and winter 1493 and summer 1494, and Phtolomeum (probably the Quadripartitum, Ptolemy’s work on astrology, or his Cosmographia) in winter 1494.50 Gromaczky substituted for John of Glogovia in winter 1491 on Peter of Spain’s Tractatus, and he taught the Prior and Posterior Analytics in that semester as well. Simon of Sierpc taught the Tabulas resolutas in summer 1494.51 Stanislaus Kleparz, Martin of Zeburk, and Bartholomew of Oraczew may have taught Copernicus mathematical subjects in winter 1494 and summer 1495. Above I have noted books owned by several professors. Such lists do not inform us directly of an owner’s opinion or even use, but in several cases the owners annotated the books. The annotations require further study, but the list alerts us to the survival of the books and 48

Szelińska, Biblioteki, 80–83; and Liber diligentiarum, 19–29; Karliński, 43. John may have commented on some works of Aristotle. See Markowski and Włodek, Repertorium, BJ, MS 2099. On James of Szadek, see Szelińska, Biblioteki, 80–83. Cf. F. Kiryk, PSB 10: 367–368; Karliński, 42. 50 Liber diligentiarum, 20–29; Karliński, 41–42. 51 Liber diligentiarum, 18–30; Karliński, 42–43. I have not listed all of the courses taught by these individuals. 49

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the possibility of their influence. Aside from the works of often-cited authors (Albert the Great, Thomas Aquinas, Giles of Rome, John Buridan, Marsilius of Inghen, Albert of Saxony, and John Versor), professors who taught in the 1490s owned works of every major author and tradition of the Middle Ages and later Middle Ages. The list includes works by Alexander of Hales, Bonaventure, Richard of Mediaevalia, William of Ockham, Walter Burley, Francis of Meyronnes, Robert Holcot, Nicholas Oresme, Gregory of Rimini, John Gerson, Gabriel Biel, Thomas of Strasbourg, Thomas Cajetan de Vio, Cajetan of Thiene, and Paul of Venice. Among other important contacts and friends from Copernicus's university days was Bernard Wapowski, a canonist interested in geography who later was in correspondence with Copernicus on astronomical matters. Wapowski (ca. 1470–1535) remained in contact with Copernicus from their days in Cracow, through their studies in Italy, and remaining years in Poland until Bernard’s death. He was probably also a student of Albert of Brudzewo and John of Glogovia.52 Copernicus and Wapowski apparently shared astrological and geographical information that contributed to Wapowski’s map of Poland. Wapowski inspired Copernicus to evaluate John Werner’s treatise De octava sphera. Copernicus dedicated his reply, Letter Against Werner of 1524, to Wapowski, and it provided Copernicus an opportunity to defend Ptolemy against Werner’s attacks.53 To control my speculative reconstruction of Copernicus’s course of studies, I have assumed that he attended classes towards degrees and that he followed the prescribed order and did not create his own academic program as it suited him. This still left him with choices, but we have no way of substantiating any private instruction that he might have received. My aim has been to establish the likelihood of his studies with John of Glogovia, Albert of Brudzewo, Michael Falkener of Wrocław, James of Gostynin, and Michael Parisiensis of Biestrzykowa, the best-known teachers at the university in this period. I have concluded that Copernicus may have attended only one class with John of Glogovia, Albert of Brudzewo, or Michael Parisiensis.54 It is likely,

52 Strzelecka, “Bernard Wapowski,” 23–59, esp. 25. Bernard, however, is not included among their students by Markowski, Burydanizm w Polsce, 241. 53 Strzelecka, 33–34. See Brożek, “Wojciech of Brudzewo,” 72, n. 16, for the reference to BJ, MS 560 and Jan Brożek’s note. 54 Goddu, “Logic,” 28–68; idem, “Consequences,” 137–188.

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however, that John, Albert, and Michael Parisiensis taught his teachers in logic, natural philosophy, and astronomy. Although his teachers did not use John of Glogovia’s commentaries and questions on texts in natural philosophy, they did use the standard Quaestiones cracovienses super octo libros “Physicorum” Aristotelis, and they were certainly acquainted with John’s version.55 Most of Copernicus’s likely teachers did not remain in the faculty of arts but went on to higher faculties, hence one may suppose a reliance by them on the texts of John of Glogovia and Albert of Brudzewo. Having come this far, however, I will not shrink from offering an opinion. It is likely that Copernicus learned Physics from Matthew of Kobylino or Albert of Swolszewice, De caelo from Albert of Brudzewo or Bernard of Biskupie, De generatione et corruptione from Albert of Brudzewo or Michael Falkener of Wrocław, De anima and probably Aristotelian logic from James of Gostynin, and Meteorologica from Martin Biem, Albert of Pnyewy, or Michael Falkener of Wrocław. Copernicus probably owed his knowledge of mathematics, astronomy (both theoretical and practical), and astrology to Martin Kułab of Tarnowiec, Albert of Szamotuli, Martin Biem, Simon of Sierpc, Stanisław Bylica of Olkusz, and possibly Albert of Pnyewy. His later contact with Lawrence Corvinus suggests instruction from him in poetry and rhetoric and possibly De anima. From comments in Copernicus’s works, we know that he was aware of the theory of impetus. Most of the questions on the Physics refer to the theory, and if Copernicus studied with Matthew of Kobylino, then he learned of it from a follower of John Buridan and Albert of Saxony. The extensive requirements in logic make it equally clear that he was trained not just in logical theory but also in the exercise and practice of constructing coherent arguments and in disputation. If he was trained by James of Gostynin in logic, then we cannot be certain that he was familiar with John of Glogovia’s views, for I am not aware of evidence that John taught James logic. On the other hand, while teaching arts at Cracow in the 1490s, James began work towards a degree in theology, and hence may very well have relied on John of Glogovia’s commentaries and exercises on logic. It may have been through James that

55 Even Zwiercan, “John of Głogów,” 99, does not regard John’s commentary on the Quaestiones cracovienses as the most important textbook on the Physics at Cracow in the 1490s.

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Copernicus developed his acquaintance with the works and remarks of Aristotle pertinent to logic. Because of his humanistic interests and contacts, it is likely that Copernicus rejected scholastic style already as a student in Cracow, but this was where he learned to construct logically sound arguments yet express them in a more literary manner. He no doubt became more proficient in style while a student in Italy. Aside from his knowledge of Aristotle’s Physics, he later demonstrated an intimate acquaintance with Aristotle’s De caelo and Metaphysics, texts that he first encountered in Cracow. Under Albert of Brudzewo and his students, Copernicus probably learned of the discrepancies between Aristotle and Ptolemy, between Averroes and Ptolemy, and of a number of technical problems with Ptolemaic astronomy. The many masters and students with interest in practical astronomy testify to the atmosphere and culture of the university, thus supporting Albert Caprinus of Buk’s comment in 1542 that Copernicus owed everything that he had achieved to the University of Cracow.56 It was a stimulating environment and one that whetted his appetite for direct contact with Italian Renaissance humanism. By way of summary we may conclude that most of Copernicus’s likely teachers did not write commentaries on works of philosophy or mathematics. They rather went on to the study of theology, medicine, or law. These instructors very likely leaned on masters like John of Glogovia, Albert of Brudzewo, and Michael of Biestrzykowa. We know that John and Albert taught most of the instructors at Cracow in the early 1490s. This pattern fits what we know generally about instruction at universities like Cracow, namely, that their emphasis was on undergraduate instruction, and that the instructors were students working towards higher degrees, usually theology.57 From the common materials and the teaching and writing of John of Glogovia, Albert of Brudzewo, Michael of Biestrzykowa, Michael Falkener of Wrocław, and James of Gostynin we may now turn to the curriculum and the education that students received in logic, natural philosophy, and astronomy in the 1490s.

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In chapter one I examined Buk’s statement, relying on Hilfstein, Starowolski’s Biographies, 91; and Rosen, “Biography,” 316. 57 Markowski, Burydanizm, pp. 241–242; Zwiercan, “Jan of Głogów,” 108–109; Moraw, Gesammelte Beiträge, 397.

CHAPTER THREE

THE TEACHING OF LOGIC 1. Aristotelian Logic—Introductory Orientation Scholastic professors devoted a great deal of attention to the part of logic that constitutes Aristotle’s most brilliant achievement as a logician, namely, syllogistic. The word “syllogism” can refer to one of the specific forms of valid deductive argument discussed in Prior Analytics I, 1–6, or to any valid argument with a conclusion different from any of its premises. The Prior Analytics challenged its readers to transform valid arguments into arguments using only syllogisms, at least for the purpose of making their reasoning more transparent.1 On the other hand, Aristotle himself suggests that not all arguments can be rendered syllogistically, and he probably wrote a treatise on the hypothetical syllogism that was lost. There has also been speculation about its relation to Stoic logic, and whether medieval scholars were influenced by Stoicism or independently rediscovered the connection of topics with hypothetical syllogisms.2 In fact, there are not many medieval authors who wrote about hypothetical syllogisms. Part of the explanation for this lack of consensus among scholars is that many treatises and manuscripts remain unedited, a consideration that feeds the worry that the standard interpretations are an artifact of selection and not fairly representative of the literature.

1 This is a brief, general sketch of the territory, not a summary of expert and scholarly analysis. I have consulted the literature but I have selected issues relevant to the sort of education that Copernicus received at Cracow. Cf. Robin Smith, “Logic,” 27– 65, esp. 27–35. In an earlier version of this chapter, I followed surveys that interpreted the development of topical inferences as absorbed into the logic of consequences (Otto Bird and Eleonore Stump) and as related to hypothetical syllogisms. E. Jennifer Ashworth raised doubts about these interpretations, and referred me to authors who proposed alternative interpretations that emphasized the literature on paradoxes and sophisms. I owe many of the references in the first section of this chapter to Ashworth. Judging from the literature, I have concluded that it is too early to write a definitive history of these developments. Instead, I present a selective survey with a tentative “trajectory” that led to the doctrines held by John of Glogovia and that are relevant to Copernicus’s arguments. Ashworth is not responsible for my reconstruction. 2 Ebbesen, “Theory of Loci,” 15–39, esp. 21–24.

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Recent scholarship suggests that the followers who reported and developed Aristotle’s views unwittingly conflated his account of the hypothetical syllogism with Stoic accounts. The process of conflation was evidently so complete that by the time Boethius translated Aristotle’s works in logic and wrote his own treatises, he was unaware of the conflation. As a consequence, Boethius transmitted to the Middle Ages the conflated account. The handbook treatment of the Topics introduced further confusions.3 According to some authorities, medieval masters picked up on these traditions to develop a theory of consequence or conditional argument derived from Stoic logic by way of Boethius. Some of them apparently concluded, however, that Aristotle’s Topics contains a broader doctrine of hypothetical syllogism, which they may have regarded as compatible with the logic of consequences.4 Experts on the history of consequences have not reached consensus on the medieval developments. Otto Bird, Jan Pinborg, and Eleonore Stump related the development to the dialectical tradition of topics, arguing that topics were absorbed into the theory of consequences in the fourteenth century.5 Niels Green-Pedersen, Franz Schupp, and Sten Ebbesen noted that while some medieval commentators did indeed draw a close relationship between topics and consequences, there is considerable evidence that topics appear in the sophistical literature (treatises on insolubles, obligations, paradoxes, and the like) where they played a major role in training students in disputation.6 My account is driven by the teaching at the University of Cracow between 1490 and 1495, especially the views of John of Glogovia, one of Copernicus’s likely teachers. According to Mieczysław Markowski, an authoritative expert on the curriculum and instruction at the university in the fifteenth century, discussion of the sophistical literature

3

Speca, Hypothetical Syllogistic. Wagner, Seven Liberal Arts, 11; Slomkowski, Aristotle’s Topics, 3–6 and 95–132; Chojnacki, “L’essor,” 889–894, esp. 893; Green-Pedersen, Tradition, 15–28. For a cautionary note about Slomkowski’s analysis, see Speca, Hypothetical Syllogistic, 26. 5 To adopt Eleonore Stump’s view of their relation. See Stump, “Dialectic,” 125–146. On Bird, see, for example, “Formalizing,” 138–149; idem, “Topic and Consequence,” 65–78; and idem, “Re-discovery,” 534–539. On Pinborg, see “Topik und Syllogistik,” 157–178. See Weijers, “L’enseignement,” 57–74. 6 Green-Pedersen, Tradition, 266–271 and 343; idem, “Early British Treatises,” 285–307; Schupp, Logical Problems, 21–30 and 86–91; Ebbesen, “Theory of Loci,” 27–29; and idem, Commentators and Commentaries, 106–126. 4

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played an unimportant role in teaching.7 As we saw in chapter two, moreover, Peter of Spain’s Summulae logicales was the principal textbook in the 1490s. Even as they began their work towards a master’s degree, students were required to attend a presumably more advanced or complete discussion of Peter of Spain’s Summulae. John of Glogovia’s most important works on logic are commentaries on the handbook summaries by Peter of Spain. John did comment on some of Aristotle’s works in logic, but they are less innovative than his commentaries on Peter of Spain. Three cautionary statements are in order, however. First, Cracow professors also commented on all eight books of Aristotle’s Topics. Second, John of Glogovia did comment on the treatises related to sophistic, a fact that may require some qualification of Markowski’s observation. Third, Cracow professors did prepare students for the master’s degree for disputations. These qualifications to the contrary notwithstanding, my focus is on topics, consequences, and the paradoxes of implication for reasons that will become clearer in the second part of this chapter. John of Glogovia and others at Cracow in the 1490s reacted to several medieval schools, and developed their own (possibly peculiar) doctrines about topics and their relation to the paradoxes. I will propose a hypothesis about the origin of John’s doctrine, but whatever its origin, Copernicus may have found features of it congenial to his effort to break the impasse to which Ptolemaic astronomy and Aristotelian natural philosophy had brought medieval cosmology. In this section, I provide a very brief review of Aristotle’s texts in logic, and trace the principal relevant developments through Boethius to Peter of Spain. In the second section, I survey the teaching at Cracow, and explain what John of Glogovia contributed to these discussions. The chapter concludes with a discussion of the relation between logic and astronomical hypotheses. In chapter eight I show how such ideas very likely influenced Copernicus’s rhetorical strategies and dialectical arguments. Aristotle’s text On Interpretation provides a theory of the structure of propositions and their truth-conditions. His theory of syllogistic relies on the account of assertions in that treatise. His text Categories answered questions about a thing and its various conditions. Medieval

7 Markowski, “Dialektische und rhetorische Argumentation,” 577–587, esp. 578 and 587.

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students began their university study of logic by studying propositions, the meaning of terms out of which propositions are composed, and the categories as preparatory to the study of syllogistic (Prior Analytics), demonstration (Posterior Analytics, which also discusses inductive arguments), and dialectical arguments (Topics).8 Through lectures and exercises on the logical texts of Aristotle as transmitted through the translations and interpretations of Boethius and later medieval masters, students learned the language, rules, and formulas of Aristotelian logic and scholastic discourse. Students were also trained in the uses of argument, and the topics included accounts and uses of demonstrative science, of definition and division, of predicables, of the categories, of dialectical arguments, of sophistical refutations, and of rhetorical arguments.9 Aristotle’s theory assumes that for a conclusion to count as science there must be first truths that are known without demonstration. Aristotle believed that the human mind has the capacity to recognize a universal present in a series of perceptions. Accordingly, he believed that our perceptions, when examined carefully, are reliable and give us reliable knowledge where repetition and memory lead to an intuition of the universal. This part of his theory is controversial, some emphasizing its intuitionist side, others its empiricist side. For our purposes its important feature is the assumption that we can arrive at a reliable knowledge of essences and qualities by means of our senses. “Reliability” is ambiguous, for if it refers to our pragmatic negotiation of the experienced world, then it is unobjectionable, but if it means “apprehension of unqualified universal truths,” then it begs the question of how we can ever justify such an apprehension. With the last sentence we anticipate one of Copernicus’s strategies in his critique of geocentrism to be discussed in detail in chapter nine.10 In speaking of essences and qualities, we are speaking of “forms,” and in logic this refers to definition and division. Division is the procedure used to arrive at a definition. Probably the most famous example is found in the first six chapters of the Poetics. By dividing a genus

8

Smith, 29–35. See Mignucci, “Albert the Great’s Approach,” 901–911, esp. note 2 for an extensive bibliography. 10 Smith, 47–51. For a sympathetic and persuasive explanation of Aristotle’s doctrines of perception and intuition as actualizing of a potentiality, see Bayer, “Coming to Know Principles,” 109–142. 9

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(imitation, for example) into parts according to relevant differences, we arrive at a definition (of tragedy, for example) that consists of the genus and its differentiae. Definitions can function in demonstrations as principles, and so are not demonstrable.11 In medieval accounts the method of division was an important method for establishing the principles in demonstrations, and the method as adapted from legal discourse had an enormous influence on the scholastic style of argument and writing. The account of predicables (On Interpretation) discusses the ways in which terms are predicated of subjects—definition, proprium (unique or essential property), genus, differentia, and accident. Sometimes differentia is not included in this list. Aristotle distinguished ten categories (whose relation to the predicables is not entirely clear) that answer the questions, what is it, what kind, how much, in relation to what, where, when, in what position, having what, doing what, and affected how? Knowledge of predicables and categories is essential to dialectical argument, which involves critical examination of commonly held opinions.12 Such examination can lead us to a deeper understanding of our most deeply held beliefs. Aristotle may also have meant the method to reach the indemonstrable first principles of demonstrations, but this too is a major point of contention among experts.13 Sophistical Refutations treats fallacies, and trains students to recognize them in arguments. Rhetorical arguments (a part of dialectical argument according to Aristotle) rely on techniques of persuasion that appeal to emotions, the moral character of the speaker, and logic for their effectiveness.14 Now this suggests an overlap between dialectic and rhetoric, namely, that the logical effectiveness of a rhetorical argument belongs properly and specifically to dialectic. Throughout the Rhetoric Aristotle refers readers to the Topics. Aristotle says of rhetoric that it is an offshoot of both dialectic and ethical studies.15 The aim of a dialectical argument is primarily to provide reasons in support of a conclusion; a rhetorical argument aims to achieve agreement on the acceptability of a conclusion. Both aim at persuasion, but dialectic

11

Smith, 51–53. Smith, 53–57. 13 Smith, 57–62. Cf. Stump, “Dialectic”; Pinborg, “Topik und Syllogistik,” 158–160. 14 Aristotle, Rhetoric I, 1–2; Smith, 63–64; Goddu, “Copernicus’s Mereological Vision,” 318–319. 15 Aristotle, Rhetoric I, 2, 1356a20–30. 12

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relies primarily on logic and on the authority of experts in their fields, whereas rhetoric relies also on emotive language and the moral character or reputation of the speaker to achieve consensus. To this point we have discussed these matters as if students learned logic directly from Aristotle’s texts and according to his intentions. Medieval students were required to attend lectures and exercises on all of Aristotle’s logical works. In fact, what they often encountered was Aristotle refracted through Boethius and other intermediary sources.16 Students at Cracow began their study of logic with lectures and exercises on introductory texts written by Peter of Spain.17 These provided students with a brief, handy outline of the major parts of Aristotelian logic (as interpreted by Boethius and perhaps influenced by Stoic logic), and they were especially useful in preparing students for critical thinking and dialectical argument. Before we turn to Boethius and his influence on medieval masters especially Peter of Spain, I address briefly why the following material will focus more on dialectical argument than on demonstration. The term “dialectic” has many connotations. In the Middle Ages it was often used interchangeably with “logic.” When considered as a distinct part of logic, “dialectic” may refer to all logic that is not strict demonstration. Sometimes “dialectic” refers to all reasoning that begins from premises that are not necessarily true but probably true, true for the most part, or accepted by experts in their field. The interpretation of “necessary” and “probable” introduced further complications. If taken logically, “necessity” refers to “formally valid inferences,” and may appear in what are called “formal consequences.” If taken metaphysically, “necessity” refers to “essential relations,” where semantic considerations enter. Such metaphysically necessary premises may appear in what are called “material consequences,” and are usually judged to be materially valid inferences. Material consequences may or may not be “epistemologically” necessary, because what philosophers take to be necessarily true many educated individuals may judge to be a matter of opinion. As can be surmised from these considerations, medieval philosophers usually focused on the logic of ordinary language, not

16

Stump, “Dialectic,” 138–141. Not all universities began their instruction with Peter of Spain. Not all English students began with Peter; packages of English texts on logic were used in Prague and Italy, and Paul of Venice’s Logica parva was also very popular. I owe these observations and qualifications to Jennifer Ashworth. See Ashworth, “Manuels,” 351–370. 17

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abstract variables. One more relevant connotation involves the use of topics as a means to find middle terms for arguments. Additionally, some authors used topics to interpret and qualify the paradoxes of implication, and some of those authors regarded the paradoxes in the context of disputation and treatises on insolubles and obligations.18 As we shall see, John of Glogovia eventually rejected the paradoxes of implication on grounds that rely on topics. However, he may also have recognized that sophistical arguments (as in disputations) often begin with a proposition that is contradictory but accepted as true for the sake of argument. It is often difficult to keep all of these connotations of “dialectic” distinct, but in what follows I will try to explain how developments in the Middle Ages influenced John of Glogovia to discuss consequences, hypothetical propositions, the paradoxes, and topics in the same or related contexts. In addition, the discussions that emphasized relevance in their evaluation of the paradoxes resorted to topics, and thereby also played a role in dialectical strategies, that is, the construction of probable arguments to support a thesis contrary to a standard and traditional opinion or belief. From a theoretical perspective Aristotle gave priority to demonstration among the types of reasoning and argument, and scholastic commentators followed him to some extent. Yet the emphasis on demonstration does not seem to correspond to practice where dialectical and rhetorical arguments prevail. The requirements for demonstration, especially scientific demonstration in the strictest sense, are so rigorous that meeting them seems to be a seldom-achieved ideal. The ideal also made some medieval philosophers uneasy, a concern arising out of theological motives. In most disciplines the premises from which arguments begin are widely shared assumptions or opinions that are probable and hence the arguments are dialectical, not demonstrative. In a number of cases, however, medieval philosophers held some conclusions so universally that they were accorded a certainty appropriate to demonstrative conclusions when in fact they did not actually satisfy the strictest requirements. We may dub such claims a sort of “creeping demonstrability.”19 In scholastic contexts, such a tendency is surprising 18

I owe several of these distinctions to Jennifer Ashworth, who, of course, is not responsible for any oversimplification or confusion on my part. 19 I have adapted the felicitous expression “creeping infallibilism” here from a source that I read over thirty years ago and can no longer recall.

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on two grounds. First, scholastic method was routinely dialectical in character. The scholastic methods of textual commentary and oral disputation put into practice the techniques that Aristotle taught in the Topics and in Sophistici elenchi. At Cracow, such techniques were also summarized and illustrated by Peter of Spain in his Tractatus or Summulae logicales. This apparent discrepancy between theoretical ideal and practical reality may be due to nothing more than an inclination to regard our arguments and conclusions as more certain, indubitable, and persuasive than they really are. It may be as well that the techniques taught in the Topics were intended to achieve propositions that were true, necessary, certain, appropriate to the phenomena, and universal, but the results of actual practice suggest again that the achievement fell short of the ideal.20 Second, as noted above, some medieval philosophers, concerned to preserve divine free will, were not consoled by the conditions specified by Aristotle, under which an essential nature always necessitates the phenomena exhibited. On some accounts there is a hypothetical character to Aristotelian science that tends to get obscured by the emphasis placed on necessity and certainty.21 Some modern interpreters see in Aristotle’s views on deduction a distinction that corresponds to the deductive systems of the mathematical sciences, on the one hand,

20 Serene, “Demonstrative Science,” 496–517. See also Wallace, “Aristotle and Galileo,” 47–77. For an excellent review of Wallace’s important discovery of the source of Galileo’s method, see Laird, “Galileo and the Mixed Sciences,” 253–270. Speaking of the “indubitable principle” in a mixed science that naturally accelerated motion is in fact equally accelerated, and that the principle is both mathematical and physical, Laird, 268–269, says the following: “Although this principle lay outside of the deductive structure of the science—no science can prove its own principles—it nevertheless was not merely an arbitrary assumption or hypothesis. Like the corresponding principles of astronomy, optics, harmonics, and mechanics, it had to be established from ‘sensory experiences’, in this case from experiments with inclined planes, and through an intricate logic of inference. Perhaps here, as Wallace has argued, Galileo followed the method of regressus, developed by Paduan Aristotelians such as Zabarella and passed on through lectures by Jesuits at the Collegio Romano. But whether he was also indebted to Zabarella for his confidence in the demonstrative certainty of the mixed sciences remains in doubt, for he would not have found it in his Jesuit sources.” 21 Serene, p. 510, expresses the point thus: “Aristotelian science was designed to explain a particular phenomenon by showing it to be a token of a type whose essential nature always necessitates that exact kind of phenomenon under the specified conditions.” It is clear from this assertion that a thing may not exhibit the phenomenon if the conditions are not satisfied. It is also clear that particular terms that appear in a scientific demonstration, as in the case of a body interposed between two other bodies during an eclipse, are to be understood as tokens of a type whereby the universality requisite of a scientific demonstration is preserved.

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and to the hypothetico-deductive systems of the empirical sciences, on the other.22 The demonstrations that derive from premises that hold necessarily and without exception belong to strictly deductive systems. Demonstrations derived from premises that hold usually or for the most part belong to hypothetico-deductive systems. Aristotle was explicit about the conditions that premises in deductive systems must satisfy, but not about the premises of hypothetico-deductive systems. Dialectical method leads the scientist to the principles that are appropriate for the object of the science in question. If the principles hold universally and necessarily, then the system is strictly deductive, corresponding to what is meant by scientific demonstration—demonstration in the strictest sense where the conclusions possess certainty. If the principles hold usually or for the most part, then the system is hypothetico-deductive, and the conclusions are likely or probable.23 These views are all controversial matters in the literature. Aristotle adopted scientific demonstration as the ideal, yet he cautioned readers to adopt the principles and methods appropriate to the scientific object in question. Despite their misgivings about the ideal of demonstration, medieval professors did teach their students all of the technical features of Aristotelian logic as they understood them, and they taught students how to analyze and evaluate the arguments of others and how to construct their own arguments. How is it that Boethius came to exercise such a large influence on the interpretation and teaching of Aristotelian logic? Until scholars began routinely to learn Greek and return to the originals, medieval masters and students depended on Latin translations of Aristotle’s works. In late antiquity Boethius had translated numerous Greek works into Latin and he wrote his own treatises on logic. The purpose of Aristotle’s Topics is to provide rules that will make it easier for debaters in dialectical disputation to discover arguments.24 This notion of discovery influenced the ancients, but Aristotle’s text is very long and unwieldy. Although it is organized according to four predicables (genus, property, definition, and accident), the same topic is often

22

Koutras, “Aristotle and the Limitations,” 153–160. Koutras, pp. 154–157. In fact, Koutras speaks of a “degree of probability,” but this suggests a statistical notion not yet developed before the seventeenth century. 24 Compare Green-Pedersen, 37–126 with Stump, “Dialectic,” 131; and Stump, Dialectic, 3. 23

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found in all four groups. Followers began to systematize the topics in different ways to make them easier to use. The story about to be sketched is confusing for reasons that go back to changes introduced already by Greek interpreters of Aristotle. Aristotle’s basis for distinguishing demonstrative, dialectical, and sophistical syllogisms is not syllogistic structure but the truth content of the premises. Accordingly, his distinction between topics or dialectic and analytics or demonstration is based not on purely formal but rather on semantical criteria.25 During the Middle Ages some interpreters expressed the rules for syllogisms as a formal, metalinguistic description of syllogistic structure. They reserved the topics as rules for all other forms of inference or argument including implication, conjunction, disjunction, conversion, and equivalence, all of which can be interpreted as enthymemes.26 As a result, topics functioned both as rules of inference and as inquiry into the semantical relationships between predicates. Late medieval commentators reflect all of this confusion in the way that they alternatively emphasized dialectic and demonstration, consequences and syllogisms, topics and formal rules, truth and validity, propositional logic and predicate logic, formal and semantic analysis, and syllogism as proposition and syllogism as rule.27 With this caution (and apology for the complications that follow) we may resume the sketch. In his definitive work on dialectic, De topicis differentiis, Boethius regards the finding of arguments as its main task. “Topic” means place. The notion here is that by means of a topic we can find a term that will mediate between two given terms in an argument.28 Boethius divides topics into maximal propositions or principles that are self-evident, 25 According to Pinborg, 160: “Der Unterschied zwischen Topik (Dialektik) und Analytik (Demonstration) besteht somit nicht in rein formalen, sondern in mehr inhaltsmäßigen Kriterien.” 26 Pinborg, 162. 27 Pinborg, 178: “Ein Schluß ist nur ‘gut’, wenn zwischen seiner Termini eine semantische Beziehung (ein locus) besteht. Aber wie kann diese formal beschrieben werden? Die Topik versucht diese semantischen Beziehungen zu beschreiben (metasprachlich) und zu formalisieren. Aber die eigentliche Kontrolle scheint in der Einzelwissenschaft zu liegen, d. h. in der Analytik, die den Prädikatsinhalt untersucht. In der hier angedeuteten Problematik liegt wohl die tiefste Ursache dafür, daß die mittelalterlichen Ausführungen über Topik und Syllogistik nie ganz befriedigend ausfallen, sondern immer wieder zwischen Wahrheit und Gültigkeit der Schlüsse, zwischen Satzlogik und Prädikatslogik, zwischen formaler und semantischer Analyse, zwischen Syllogismus als Satz und Syllogismus als Regel hin- und herschwanken.” 28 Compare Stump, Dialectic, 57–66 with Pinborg, 158–160.

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true generalizations and differentiae under which maximal propositions can be grouped. For example, some maximal propositions are generalizations about definitions, hence definition is a differentia. The differentiae constitute Boethius’s main instrument for finding arguments providing a third or intermediate term between two terms of a question. The third term joins the other two together in the form of a syllogism. Differentiae, then, are aids in finding arguments because they provide third terms. Boethius distinguishes twenty-eight differentiae that he regards as exhaustive. In specific cases where a differentia is used to find a third term, it may be necessary to validate the argument, and that is the function of the maximal proposition, namely as a sort of generalized rule. In categorical syllogisms, maximal propositions are general premises that guarantee the validity of the argument; in hypothetical syllogisms they validate the connection between the antecedent and consequent in the conditional premise of the argument. Hence, differentiae help us find third terms to construct arguments, and maximal propositions validate the argument discovered.29 To understand what Boethius accomplished here we must refer to a difference among Aristotle’s Greek interpreters on what Aristotle understood by a topic. Aristotle did not provide a definition of the term in Topics. When he announces a topic, he presents it as a strategy and as a principle. Theophrastus considers only the principles to be topics, whereas Alexander of Aphrodisias regards topics as both principles and strategies.30 Boethius’s distinction between maximal propositions and differentiae seems to have it both ways.31 In calling maximal propositions “topics,” Boethius is following Theophrastus, but by calling differentiae “topics” and placing emphasis on differentiae, even though they group the maximal propositions, he is also focusing attention on strategies. By organizing topics according to twenty-eight differentiae, Boethius was able to provide a clearer and more useful structure than Aristotle did by grouping them under the predicables.32 We might say that Boethius provided a scheme that was easy to memorize and apply almost automatically, whereas Aristotle’s scheme required searching

29

Stump, “Dialectic,” 133–135; eadem, Dialectic, p. 4. Stump, “Dialectic,” 131–135. 31 Stump says that he follows Theophrastus, Dialectic, 62–66. Compare Pinborg, 158–159. See also, however, the reconstruction by Ebbesen, Commentators, pp. 106– 126, and idem, “Theory of Loci.” 32 Stump, Dialectic, 48. 30

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through all four predicables to find the appropriate topic. Slomkowski counts around 300 topics in the middle books of Topica.33 Of course, it is also clear from the Topics that Aristotle expected students to become so proficient in the method by means of exercises and repetition that they would apply the skills in a habitual way. It seems that Aristotle was too optimistic inasmuch as his followers introduced schemes that were designed to be more efficient. Because of what appear to be peculiarities of the curriculum at Cracow, the discussion that follows, as already mentioned, will focus primarily on the relation between topics, consequences, and the paradoxes of implication. According to Green-Pedersen, however, thirteenth-century works on topics do not contain an incipient theory of consequences.34 The precursors of treatises on consequences, on the other hand, remain obscure. Ebbesen, following suggestions by Stump and Green-Pedersen, thinks that treatises on syncategorematic terms led commentators to investigate the validity of consequences as a way of systematizing their observations. Commentators formulated rules of consequence, and occasionally in these contexts they employ topics. The development in the fourteenth century is complicated, but the relevant point is that by the middle of the century reference to the topics disappears from treatises on consequences. That observation, however, appears to require one significant qualification. In cases where the necessary link between the antecedent and consequent of a consequence was founded in a semantic relation between one term of the antecedent and one term of the consequent, some authors adduced the topics to warrant the validity of this transition.35 Thus, in some important contexts involving consequences and paradoxes, authors did refer to dialectical topics, but such use of topics seems to have been more prevalent in treatises on syncategorematic terms and sophisms than in treatises on consequences or topics.36 The most important introductory textbook of logic after the thirteenth century was Peter of Spain’s Tractatus. Although medieval manuscripts

33

Slomkowski, pp. 9–13. See Topics A2, 101a26–30. See Green-Pedersen, Tradition, 265–299; and Ebbesen, “Theory of Loci,” 27. 35 Compare Ebbesen, “Theory of Loci,” 27–29 with Schupp, Logical Problems, 20– 28, 79–80, and 90–91. 36 Part of the story here involves the different ways in which fourteenth-century authors defined and used the distinction between formal and material consequences. See Schupp, Logical Problems, 27–30; Green-Pedersen, “Early British Treatises,” 291– 292. 34

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and early printed editions down to 1550 arranged Peter’s treatise in a variety of ways, for the sake of convenience I describe the work as it appears in the modern edition.37 The Tractatus is divided into two main parts, the first summarizing Aristotelian logic as interpreted by Boethius and the second scholastic terminism of the Middle Ages. Hence, the first part contains an introduction to categorical syllogisms, and treatises on predicables, predicaments (categories), syllogisms, topics (De locis), and fallacies. The second part includes treatises on supposition, relatives, ampliation or extensions, appellation, restriction, and distribution, all of which derive from the thirteenth-century common theories about the properties of terms.38 The division of the Tractatus into two parts is a little artificial inasmuch as the treatise on fallacies is often numbered VII while the one on suppositions is numbered VI; nevertheless, the parts do correspond to the differences between the earlier and later traditions. There is another confusion with respect to terminology that I mention for the sake of accuracy. What is referred to as logica vetus is often taken to mean the Aristotelian treatises On Interpretation and Categories, and logica nova the treatises Prior and Posterior Analytics. In fact in both Boethius’s interpretations and Peter of Spain’s Tractatus, which is based on Boethius, the so-called logica vetus is taken largely from the first part of Boethius’s introduction to categorical syllogisms. The second treatise in Peter of Spain on predicables goes back to Boethius’s exposition of Porphyry’s Isagoge, not directly to Aristotle’s On Interpretation. The treatise on categories is also dependent on Boethius’s commentary on Aristotle’s Categories. The treatise on syllogisms is not a compilation of Prior Analytics but is taken mainly 37 The copies at Cracow vary, and sometimes authors selected particular treatises for special treatment. I saw no compelling reason to prefer one ordering over another. See Peter of Spain, Tractatus. For the record, I consulted Peter of Spain, Language in Dispute, tr. Dinneen, but see Ashworth’s review in Vivarium, 30 (1992), 277–281. See, instead of Dinneen, the translation by Eleonore Stump, Cambridge Translations, 226– 245. For a brief and illuminating summary, see Spruyt, “Peter of Spain,” 3–5. Because some critics have pedantically questioned the use of language such as “inference” and “warrants” as modern ways of speaking about “premises” and “conclusions,” I cite Spruyt’s comment on Peter’s tract on topics, p. 3: “This tract starts off with an explanation of the notions argumentum and argumentatio, and then proceeds to deal with the species of argumentation: syllogism, induction, enthymeme, and example. Next, it gives a definition of locus (the Latin translation of the Greek topos): a locus is the seat of an argument (i.e., the locus is supposed to warrant the inference by bringing it under some generic rule).” 38 Stump, “Dialectic,” 128–131.

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from the second part of Boethius’s treatise on categorical syllogisms. Again, the treatise on topics is not a compilation of Aristotle’s Topica but rather comes from Boethius’s On Topical Differences.39 Dialectic in the strict sense, that is, probable argument, was also a part of logica vetus. Logica nova refers to the doctrine of the syllogism (Prior Analytics) and the doctrine of demonstration (Posterior Analytics), but in practice it also encompassed fallacies and sophistical reasoning. The expression logica modernorum refers to specifically medieval developments, especially the logic of terms. We will see, however, that in the late fifteenth century some university professors at Cracow returned directly to the Aristotelian texts so that students’ education in logic combined both the medieval teaching of logic along with a return to Aristotle.40 Because the university curriculum at Cracow devoted much attention to dialectic or probable reasoning, to the logic of consequences, and to syncategorematic terms, I summarize Peter of Spain’s treatise on topics. Peter conceived of dialectic as an art rather than as a science. “An argument,” he says, “is a reason producing belief regarding a matter that is in doubt, that is, a middle proving a conclusion that needs to be confirmed by means of an argument.”41 Peter followed Boethius in dividing a topic into what Peter calls a “maxim” (that is, a maximal proposition) and a differentia. Through Boethius he also followed Themistius in dividing topics into three subcategories: intrinsic, extrinsic, and intermediate. An intrinsic topic appears in an argument that is taken from the nature of one of the terms of the argument, extrinsic in an argument that is taken from what is external to their nature, and intermediate is one that comes partly from the nature of the term and partly from without.42 For Peter a topic confirms an argument by providing a middle term through which an enthymeme, an incomplete syllogism, can be transformed into a complete syllogism.43 Because this doctrine plays such an important role in the construction and confirmation of arguments, I will provide examples of several of

39

De Rijk, xcii–xciii. Compare de Rijk, lxxxix–xcv; Stump, “Dialectic,” 128–129; and Green-Pedersen, 14. 41 Stump, Cambridge Translations, 226. 42 Stump, Dialectic, 139. 43 Stump, Dialectic, 140–146, where William of Sherwood (or Shyreswood) makes explicit what is admittedly only implicit in Peter. 40

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the topics, especially the more important and useful ones from intrinsic, extrinsic, and intermediate topics. The intrinsicness of topics in the first subcategory does not mean that these topics produce demonstrations.44 Where they are dialectical, the syllogisms that are produced by means of intrinsic topics are probable, hence even intrinsic topics in such syllogisms are considered probable and only contingently related to a term in the conclusion. In demonstration, by contrast, intrinsic terms are always essentially and necessarily related to a term in the conclusion. As this clarification suggests, there is a metaphysical doctrine at work here. In demonstrations the middle term is a real cause of the connection between extreme terms. In dialectical arguments the middle term is a sign, not a cause, of the connections between things and the validity of an inference. As a consequence, dialectical arguments produce at best only highly reliable opinions, not knowledge.45 Peter distinguishes twenty-five differentiae, forty-three topics, and fifty-seven maxims. Under intrinsic differentiae he distinguishes between topics from substance and topics from concomitants of substance. He divides the topic from substance into the topics from definition and description and from an explanation of the name. Because a definition is a relation between the definition and the thing defined, Peter distinguishes a topic from definition from a topic from the thing defined. Here I present only the topic from definition completely, for it can be used to establish a pattern that runs throughout Peter’s account. All of the topics with examples are outlined in Appendix I. The topic from definition has four arguments and four maxims. The first argument makes the definition the subject in an affirmation; the second makes the definition a predicate in an affirmation; the third makes the definition the subject in a negation; and the fourth makes the definition the predicate in a negation. An example of the first is “A mortal rational animal is running; therefore, a man is running.” The topic is from definition, and the maxim is “Whatever is predicated of the definition is also predicated of the thing defined.” An example of the second is “Socrates is a mortal rational animal; therefore, Socrates is a man.” The topic is from definition, and the maxim is “If the definition is predicated of something, then the defined is also predicated of

44 45

Pinborg, 178. Stump, Dialectic, 155.

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it.” An example of the third is “A mortal rational animal is not running; therefore, a man is not running.” The topic is from definition, and the maxim is “Whatever is removed from the definition is also removed from the thing defined.” An example of the fourth is “A stone is not a mortal rational animal; therefore, a stone is not a man.” The topic is from definition, and the maxim is “If the definition is removed from something, then the thing defined is also removed from it.” The topic from the thing defined follows a similar pattern. One example will suffice. The first argument makes the thing defined the subject in an affirmation. For example, “A man is running; therefore, a mortal rational animal is running.” The topic is from the thing defined, and the maxim is “Whatever is predicated of the thing defined is also predicated of the definition.” A description is an expression signifying a thing’s being by way of its accidental characteristics, or it is an expression consisting of genus and peculiar property. For example, “risible animal” is a description of man. The topic is the relation of description to the thing described, and it follows the same pattern as definition and thing defined with four arguments and four maxims. In the topic from the explanation of a name, the sort of explanation relevant here is one in which the explanation and the thing explained are interchangeable or convertible. For example, “lover of wisdom” is an explanation of “philosopher.” This topic also follows the same pattern as the topic from definition and the thing defined. Under topics from concomitants of substance Peter enumerates from the whole (universal whole, a species or subjective part, integral whole, whole in quantity, whole in mode, whole in place, and temporal whole), from a cause, from generation, from destruction, from uses, and from associated accidents. Examples of the topics from an integral whole and from an efficient cause will suffice. The first is a relationship of an integral whole to its part, and it is always constructive. For example, “A house exists, therefore, a wall exists.” The topic is from integral whole, and the maxim is “If an integral whole is posited, then any one of its parts is also posited.” A cause is that from the existence of which another thing naturally follows. There are four types of cause: efficient, material, formal, and final. The topic from an efficient cause is the relation of an efficient cause to its effect. For example, “The builder is good, therefore, the house is good.” The topic is from an efficient cause, and the maxim is “If the efficient cause of a thing is good, then the thing itself is also

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good.” This topic can also be destructive, namely, “The house is not good; therefore, the builder is not good.” The topic is from an efficient cause, and the maxim is “If the thing effected is not good, then the efficient cause is not good.”46 In sum under the category of intrinsic topics, Peter distinguishes twenty-nine topics and forty-two maxims. Intrinsic topics are grouped under definition, description, explanation of a name, whole, part, cause, generation, destruction, uses, and associated accidents. Under extrinsic topics Peter enumerates from opposites, from a greater, from a lesser, from a similar, from proportion, from transumption, and from authority. He distinguishes several senses of opposition such as from contraries. As an example of an extrinsic topic, we may select from authority. This topic is a relation of an authority to that which the authority proves. For example, “An astronomer says that heaven is revolvable; therefore, the heaven is revolvable.” The topic comes from authority, and the maxim is “We should believe an expert in his field of knowledge.” In the category of extrinsic topics Peter distinguishes ten topics and twelve maxims. Intermediate topics occur in arguments that are taken from things that agree to some extent with the terms used in the question and disagree with them to some extent. Peter enumerates from conjugates, from cases, and from division. One sort of division is by negation. For example, “Socrates either is a man or is not a man; but he is not not a man; therefore, he is a man.” The topic comes from division, and the maxim is “If two things exhaustively divide something, then when one is posited, the other is removed, or when one is removed, the other is posited.” Peter enumerates altogether four intermediate topics and three maxims. That in brief is Peter’s account of topics. Topics serve a function in arguments. A conclusion is a proposition that is proved by an argument. Before it is proved, however, it is in doubt, that is, we have a question about it. From the conclusion we identify extreme terms, and the exercise is to find a term that mediates between the extreme terms in the conclusion. Topics help us to find middle terms. An argument, then, is a reason that produces belief about a matter that is in doubt. Medieval students learned these techniques to prove conclusions and in the process learned to think logically and critically.

46

Peter does not provide an example of the destructive case.

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There is one other treatise by Peter that influenced medieval masters. The Syncategoreumata was a more technical treatise than the Tractatus. Its actual influence on students is more difficult to assess, but it is this text that raises some important issues in logic relevant to one of the central problems in Copernicus’s beliefs about hypotheses in astronomy. I am referring to the paradoxes of strict implication. The Copernican context will be discussed in chapter eight. In the treatise Syncategoreumata, the problem is discussed in the context of the syncategorematic term si, that is, “if.” In other words, the problem arises in the context of inferences made up of conditional propositions. The paradoxes of strict implication are (1) From an impossible, anything follows, and (2) A necessary proposition follows from anything. In his account of conditionals, Peter maintains that the word “if ” signifies causality or antecedence rather than consecution. Even with respect to causality, it signifies causality by means of antecedence in that the antecedent is prior to and hence the cause (not in reality) of the consequent, that is, of its being consequent.47 The signification of “if ” implies consecution relatively, for one thing is said to follow from another in many ways but the only sense appropriate with respect to consequences is one in which one term follows another because they are used in a mutually relative way.48 In analyzing examples and paradoxes, Peter resorts to topics to solve the problems. In the case of the paradoxes of strict implication, Peter asks “whether from an impossible anything follows or whether an impossible is antecedent to any47 Peter of Spain, Syncategoreumata, 198–199. See also Spruyt, “Peter of Spain,” 5–9. On p. 6, Spruyt says, “The fifth chapter is about the word si, which is said to signify causality in or via antecedence. The chapter also contains discussions of the kinds of consecution or consequence, problems of inference connected with the referents of terms used in consecutive sentences, and also on how to contradict a conditional sentence. Special attention is given to the problem whether from the impossible anything follows.” On pp. 8–9, she elaborates: “A similar fusion of the domains of language and reality is found in Peter’s account of the consecutive ‘if ’, which he explains as signifying causality. Like his contemporaries he looks into the question of whether from the impossible anything follows. In his account, the notion of ‘impossibility’ can be taken in two ways, viz. impossibility as such, or absolute impossibility, which amounts to nothing, or the impossible state of affairs that is referred to when notions of things that do have a reality separately but are incompatible are combined in statements. From the latter type of impossibility, such as ‘A man is an ass’, something, but not anything can follow, e.g. ‘Therefore a man is an animal’. From impossibilities as such, e.g. ‘You know that you are a stone’, nothing can follow. The fundamental idea is that in order to be able to have something follow, the antecedent in the consecutive relationship must be a something (res) of some sort.” 48 Peter of Spain, Syncategoreumata V, 6–8: 200–201.

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thing.”49 After presenting the arguments in support, Peter responds to the contrary:50 Since a conclusion is a proposition proved by an argument or arguments, and every argument provides the rationale for inferring it according to some logical relationship or relationships [habitudines] (for an argument forms the rationale which produces faith in something doubtful, and faith in something that is doubtful can only be produced by means of a logical relationship or logical relationships), therefore it is necessary that wherever something is concluded from something else and something follows from something else, that there be some logical relationship or relationships, involved in virtue of which the one can follow from the other.

After an example, he concludes: Therefore it is not the case that from the impossible anything follows. Furthermore, in an argument from the beginning to the end it is necessary that the intermediate inferences always be confirmed by certain intrinsical, extrinsical or intermediary topics.

Among the ways in which “impossible” can be understood, anything can follow an impossible, or an impossible can follow anything only in those cases where the terms have some logical relationship [habitudinem]. For example, “If a man is an ass, a man is an animal.” The consequent follows here because the example involves the topic from a species.51 The point is that the consequent follows not because the antecedent is impossible but on account of a topical relationship.52 We may also explain these discussions from the perspective of the fallacy of affirming the consequent, which Peter discusses in the Tractatus.53 Peter divides consequences into simple and composite, and each of these further into two species. The principal source of fallacies of the consequent is the mistaken belief or assumption that a consequence is convertible.54 Aristotle, Peter says, discusses three modes of

49

Ibid. V, 39: 230–231. Ibid. V, 41: 232–233. 51 Ibid. V, 42–44: 234–237. 52 Ibid. V, 56: 245–247. The paradoxes seem to arise from standard logical rules or conditions for the validity of consequences. The type of analysis provided by Peter restricts the manipulation of propositions in proofs, which explains in part why modern mathematical logicians tend to be critical of relevance and connexivist logics. For additional literature, see Goddu, “Consequences,” esp. 146–147, footnote 35. 53 Tractatus, 169–173. 54 Tractatus VII, 169–170. 50

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this mistake.55 The first is a case of a simple consequence based on a topical relationship.56 Peter provides four examples: (1) “If it is a man, it is an animal; therefore, if it is an animal, it is a man.” (2) “If it is not an animal, it is not a man; therefore, if it is not a man, it is not an animal.” (3) “If it is honey, it is reddish; therefore, if it is reddish, it is honey, but bile is reddish; therefore, bile is honey.” (4) “If it is raining, the ground is wet; therefore if the ground is wet, it is raining.” All four exemplify the fallacy of affirming the consequent based on the false assumption that the term in the antecedent (man, not-animal, honey, and raining) is convertible with the term in the consequent (animal, not-man, reddish, wet). These examples are based on topical relationships, for example, the first is based on the topic from species.57 The second mode is also a case of simple consequence, but one that is dependent on some circumstance inherent in a person.58 For example, (5) “If he is an adulterer, he is a stylish dresser or a night wanderer; therefore, if he is a stylish dresser or a night wanderer, then he is an adulterer.” (6) “If it is a man, it is colored; therefore, if it is colored, it is a man.” (7) “If he has stolen something, then he has not earned it nor asked for it; therefore, if he neither earned it nor asked for it, he stole it.” All three illustrate the fallacy of affirming the consequent based on the false assumption that terms are convertible that are not. In example (7) suppose that the person received the item as a gift. These are examples that one often finds in rhetoric59 and in the statements of politicians.

55 56 57 58 59

Sophistical Refutations 5, 167b1–20. This is the first species of simple consequence. Tractatus VII, 170–171. This is the second species of simple consequence. Tractatus VII, 171.

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The third mode is a case of a composite consequence in which the conversion of the consequence is made on the basis of an opposition. For example, (8) “If it is made, it has a beginning; therefore, if it is not made, it has no beginning. But the world is not made, that is, generated; therefore, the world has no beginning; therefore, the world is infinite in duration and so the world is eternal.” This is the fallacy of denying or negating the antecedent and constructing a consequence that negates the consequent, so Peter calls this a fallacy of consequent citing the example, “If it is a man, it is an animal; therefore, if it is not a man, it is not an animal.”60 We may now see the significance of this discussion by focusing on the relevant example, “If is raining, then the ground is wet; therefore, if the ground is wet, it is raining.” The false conversion here rests on the unstated assumption that rain is the only cause for the wetness of the ground. The ground may become wet in some other way, and so the point is that from the wetness of the ground alone we may not infer that it is raining. This example also illustrates the point that a logical connection is not necessarily a real or causal connection. Indeed, if the paradoxes are true, the connection between antecedent and consequent need not be relevant. For example, “If my mother is wearing army boots, then it is raining.” In a truth table this would be counted a valid inference on that interpretation if the consequent were true; for the truth of a consequence all that is required is the truth of the consequent. Only from the falsity of the consequent can we infer the falsity of the antecedent. To be valid, a conditional must be true on every line of its truth-table.61 Through analysis of such inferences, we can generate the paradoxes of strict implication. During the Middle Ages we find some logicians who accept the paradoxes, some who reject them, and some who accept them only in a qualified way. Those who reject or qualify them rely on topics to justify their views, and among the criteria that they advocate are at least relevance or—a stronger claim—a real connection between the antecedent and consequent. There are representatives of all three views about the paradoxes

60 61

Tractatus VII, 171–172. Again, I owe refinements, qualifications, and corrections to Jennifer Ashworth.

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at Cracow in the late fifteenth century with which Copernicus may have been acquainted.62 Among Copernicus’s reasons for insisting on the truth of some hypotheses or antecedents in astronomy is relevance between hypotheses and the observed phenomena. With that enticing suggestion we turn to fifteenth-century Cracow. 2. The Teaching of Logic at Cracow Some professors at the university in the fifteenth century wrote commentaries on the works of Peter of Spain and Aristotle. From these we can develop an account of the sorts of issues that concerned logicians and a sense of what students learned from their lectures and exercises. In general the story of philosophical instruction at Cracow in the fifteenth century is divisible into three periods: 1400–1460, 1460–1475, and 1475–1500. The first period is characterized by the influence of John Buridan and his nominalistic terminism on masters at the university. During the second period we encounter a wave of influence from the University of Cologne that brought the works and views of Albert the Great, Thomas Aquinas, Giles of Rome, and John Versor (Johannes Versoris or Jean le Tourneur) into greater prominence. In the third we find the continuation of the previous trends along with appearance of masters writing commentaries ad mentem Scoti, that is, in accordance with the teachings of John Duns Scotus. Because none of these approaches was dominant in the last decade of the century, the views and teaching on logic are highly eclectic. In the early period up to 1460 Cracow masters characterized logic as a practical, rather than speculative, science that achieved primarily probable conclusions.63 They taught students to regard logic as a tool of argumentation by means of which they could distinguish truth from falsehood and draw sound conclusions. As a result, masters devoted more time to dialectic than to demonstration, and this is reflected in the fact that the last logical treatise that they required students to mas62 Below in this chapter I present only the views congenial to Copernicus’s analysis. For representatives of the other views at Cracow, see Goddu, “Consequences,” 164–166. As we saw above, Peter’s own view derives from a strong ontological commitment. See Spruyt, “Peter of Spain,” 6, and 8–9. 63 Markowski, Logika, 5–42. See also Markowski, “Logik und Semantik,” 73–80; idem, “Gegenstand,” 81–84.

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ter was Aristotle’s Topics. They studied the Topics just as they began work towards the master’s degree in preparation for disputations in which they were required to participate. It seems that none of the early masters at Cracow regarded these techniques as capable of arriving at the principles from which one can demonstrate necessary conclusions. The preference for probable arguments resulted from the development of dialectic, the philosophical natural sciences, and the moral sciences.64 In 1449 the faculty of arts introduced a curricular reform that was pro-humanistic to the extent that it placed greater emphasis on the works of antiquity. We have evidence of the success of the reform already in commentaries by 1456 and around 1460 in changes in formal logic. The former preference for dialectical argumentation gave way gradually to certain, necessary inferences, at first in the re-emergence of syllogistic demonstration and then around 1469 in the development of the logic of consequences.65 By the third quarter of the fifteenth century dialectic was no longer privileged with greater time and effort devoted to the Prior and Posterior Analytics. The shift is especially notable after 1473 in the works of John of Glogovia who, while not denying altogether the practical dimension of logic, nonetheless maintained, in agreement with John Versor, that logic is a theoretical science. The second shift is reflected in another reform in 1475.66 In John’s analysis we find a metaphysical doctrine at work that served to support demonstrative science and that placed real limits on the validity of consequences.67 Still, there was no violent anti-dialectical reaction but greater emphasis on the logic of consequences and demonstrative syllogism. Despite this shift, however, masters continued to quote the definitions and views of their nominalist predecessors. After all, Buridan had also written on consequences, and included a section on demonstration in his commentary on Peter of Spain.68 64

Markowski, Logika, 68–97. Markowski, Logika, 127. 66 On the reforms of 1449 and 1475, see Szujski, “Założenie,” 95–118. See Palacz, “Michael Falkener,” 33–39, esp. 34, where he relates the reforms at Cracow to recommendations by Nicholas V in the 1440s, the reform of the University of Paris by Cardinal d’Estouteville in 1452, and the anti-nominalist decree of Louis XI in 1473. See also Markowski, “Nauki wyzwolone,” 91–115. 67 The direct source would seem to be Peter of Spain’s Syncategoreumata, Tractatus V, 230–237. The doctrine could also have arrived from Cologne where it seems to have been prevalent. See Braakhuis, “School Philosophy,” 1–18, esp. 13–14. 68 I owe this clarification to Jennifer Ashworth. 65

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Michael Falkener of Wrocław is an especially prominent example of this tendency. In this regard the eclectic, harmonizing character of late fifteenth-century Cracow philosophy is the dominant motif.69 As emphasized in chapter two, the leading philosophers at Cracow in the early 1490s were John of Glogovia, Michael of Biestrzykowa, James of Gostynin, and Michael Falkener of Wrocław. John’s written commentaries were completed in the course of his lectures. His influence lasted well into the sixteenth century with the publication of his works in the early 1500s. Michael of Biestrzykowa’s extensive output was issued in print in the 1510s. He regarded logic as a theoretical science, and he emphasized the Aristotelian doctrine of the syllogism.70 James of Gostynin, like John, followed John Versor and Albert the Great, and, like Michael of Biestrzykowa, he also relied on John Duns Scotus, but he is also a good example of an author who glossed the Aristotelian texts.71 Michael Falkener wrote and later published mostly handbooks that were very influential as introductions to logic. With Michael, as indicated, we find a continuation of the changes represented by John of Glogovia and Michael of Biestrzykowa, yet he rescued dialectic while rehabilitating syllogistic as an instrument of argument and investigation of truth in speculative science. Note, however, that the contrast between dialectic and demonstrative syllogistic is not a contrast between dialectic and syllogistic pure and simple.72 While these doctrinal developments are important, what the focus on logical theory misses is instruction in the use of logic. Instruction in medieval logic had a theoretical dimension, to be sure, but the entire curriculum and exercises on works of logic were eminently practical. I have sketched the doctrine of topics, what its purpose was, and how topics were used to construct arguments. John of Glogovia and Michael of Biestrzykowa commented on Peter of Spain’s treatises, and taught the treatises in lectures and exercises. James of Gos69 Markowski, Logika, 164 and 204, nn. 71–72. On the continuation of the nominalist tradition: Logika, 184–186. 70 Markowski, Logika, 166–168, 204, n. 79. 71 Markowski, Logika, 155–156. 72 Although I rely heavily on Markowski (for no one is as familiar with these sources as he is), it seems to me that his interpretation requires some qualification. The contrast that he makes between dialectic and syllogistic overlooks the compatibility of these forms of argument, and he makes too much of the quarrel between realists and nominalists. Markowski’s own description of the actual situation in Poland in the period from around 1470 to about 1520 explicitly acknowledges the syncretistic or eclectic character of the major philosophical and logical thinkers of the period.

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tynin focused more on Aristotle’s works, but he too lectured on Peter of Spain. Michael Falkener likewise taught Peter, and he produced his own handbook intended to make logic an even handier book of argumentation.73 With respect to theoretical issues, for our purposes the relevant ones concern the relation between topics, the logic of consequences, fallacies of the consequent, and the paradoxes of strict implication. On these issues there were indeed noteworthy developments in the 1490s. We cannot prove that Copernicus was aware of them, yet the coincidence is striking. It may be that Copernicus’s view was intuitive, still his intuition in regard to the evaluation of astronomical hypotheses found some support in the discussions of his likely teachers. We may discuss developments in the logic of consequences, especially those related to the paradoxes of strict implication, and simultaneously illustrate the teaching and use of topics, for the arguments developed by Cracow philosophers rely on their interpretation and application of topics. In the literature, authors assign two functions to topics—either as premises in syllogisms or as rules mediating between propositions or steps in an argument. When an author writes an argument, it may be that the argument can be reduced to a syllogism, but most arguments turn out to be very complicated with many steps, possibly several statements containing evidence linked to conclusions by means of several warrants and further backing for the warrants. In each specialized discipline there are different conventions or rules of evidence, and what constitutes a legitimate argument in one discipline may be considered inadequate or even irrelevant in another. Now, what is of relevance to Copernicus’s education is not the rejection of paradoxical entailment rules but the reason that John develops for rejecting them. Ivan Boh, who first alerted me to this possibility, made a startling announcement in his customarily modest fashion:74 When Nicolaus Copernicus was a student at the University of Cracow at the turn of the 15th century, he may have encountered the following novel if not revolutionary passage written by Johannes Glogoviensis, one of the professors teaching logic and natural philosophy in the last

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On Michael Falkener, see Palacz, “Michael Falkener,” who, like Markowski, interprets the teaching in terms of realism versus nominalism, although he departs from Markowski on the issue of Copernicus’s dependence on nominalist views. 74 Boh, “John of Glogovia’s Rejection,” 373–383, esp. 373–374.

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chapter three quarter of the 15th century: “From what has been said, the falsity of two rules laid down by the ancients (antiqui) is evident. The first rule is From the impossible anything follows, so that every proposition is true whose antecedent is impossible; for example, ‘If Plato is a jack-ass, Plato is a stone.’ The second rule is, The necessary follows from anything. Therefore every conditional is said to be true whose consequent is necessary, regardless of what the antecedent is; for example, they said that ‘If Plato is a stone, man is an animal’ is not necessary, because for truth of a conditional it is required that the antecedent could not be true without the consequent.” This passage is surprising for at least two reasons: first, because it expresses a view that goes against the long logical tradition; and secondly, because it occurs in a book that was supposed to be a commentary on the famous Summulae of Peter of Spain. To be more precise, the passage occurs in a commentary on the parva logicalia, i.e. on the seventh treatise of the Summulae. The full title of the work from which this relevant text for the topic of my paper has been chosen is: Super omnes tractatus parvorum logicalium Petri Hispani Magistri Johannis Glogoviensis, alme florentissimeque universitatis Studii Kracouiensis, maioris Collegii artistarum, printed in Leipzig in 1500.75

Now before we follow Boh’s analysis any further, let us examine John of Glogovia’s account in the treatise on consequences. John reports that logicians have two views on the rule that from the impossible anything follows.76 Those who object to it are of the opinion that in every good consequence, the consequent is understood in the antecedent [de intellectu antecedentis], that is, the meaning of the consequent is understood as included in some fashion in the meaning of the antecedent. If the antecedent is impossible, then the consequent is either true or false. The true cannot be understood together with the impossible [de intellectu impossibilis], and an impossible consequent is not

75 There are some questions about the authorship of the passage cited by Boh, which I have considered and answered in Goddu, “Consequences,” 155. 76 Exercitium, Tractatus de consequentiis, fol. 140v. In the Strasbourg edition, see fol. 81r: “Notandum quod de isto apud logicos est duplex positio. Aliqui enim volunt dicere et tenent quod ad impossibile non sequitur quodlibet. Et arguunt primo sic. In omni consequentia bona consequens est de intellectu antecedentis, ut dicit unum principium logice. Sed consequentia in qua antecedens est impossibile in ea consequens non est de intellectu antecedentis, ergo ad impossibile non sequitur quodlibet. Maior est nota. Minor quia quando antecedens est impossibile tunc consequens erit verum aut impossibile, modo verum non est de intellectu impossibilis, similiter impossibile consequens non est de intellectu impossibilis antecedentis.”

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included in the meaning of an impossible antecedent, hence from the impossible not just anything follows.77 The second objection reported by John is that in every good consequence the antecedent and consequent are related as cause to effect. “Antecedent” derives from what goes before, and “consequent” from what follows, just as an effect follows from its cause. Between an impossible antecedent and a true or impossible consequent there cannot be a relation (ratio) of cause and effect. Between a cause and effect there is a mutual proportion, but between an impossible antecedent and a consequent, whether true or impossible, there is no mutual proportion. Between two impossible propositions there is no proportion because one of them contradicts the other. Between the impossible and the true there is no proportion because the true and the false are contradictory.78 John adds, however, that other logicians concede that from an impossible antecedent anything follows, and they support their view by citing Aristotle’s Physics I where he shows that from one inconvenient proposition many propositions follow. John summarizes the response by saying that the logicians regard the rule as valid in formal consequences, but not in material consequences, because in formal consequences the consequent should be understood in the meaning of the antecedent, which is not the case when the antecedent is impossible.79

77 In Syncategoreumata, V, 4–5: 198–201, Peter of Spain expresses these notions more clearly in terms of the signification of ‘if ’. ‘if ’ signifies antecedence, and where it signifies causality, it does so in antecedence or by means of antecedence. 78 Exercitium, fol. 140v: “Secundo arguitur sic. In omni consequentia bona antecedens et consequens habent se ut causa et effectus. ‘Antecedens’ enim dicitur ab antecedendo, ‘consequens’ a consequendo, modo effectus sequitur ad suam causam. Sed inter impossibile antecedens et consequens verum aut impossibile non potest esse ratio causae et effectus, ergo impossibile antecedens non habet se, ut causa respectu cuiuscumque consequentis. Minor patet quia inter causam et effectum est mutua proportio, sed inter impossibile antecedens et consequens, siue illud sit verum vel etiam impossibile, non est mutua proportio. Inter enim duo impossibilia non est proportio, quia quodlibet eorum repugnat alteri. Similiter inter impossibile et verum non est proportio, quia verum et falsum similiter repugnant.” 79 Ibid. “Alii autem logici in oppositum dicunt et concedunt quod ad impossibile antecedens sequitur quodlibet consequens, et fundant se in dicto Aristotelis primo physicorum, ubi ostendit quod dato uno inconvenienti, sequuntur plura. Constat autem quod impossibile est quoddam inconveniens. Breviter autem logici ad dubium respondent quod ad impossibile sequitur quodlibet non in consequentia formali sed materiali. Primum probant sic quod ad impossibile non sequitur quodlibet formaliter, quia in consequentia formali consequens debet esse de intellectu antecedentis, quod non contingit quando antecedens est impossibile . . . ”

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To the objection concerning cause and effect, John provides additional arguments, and he responds to the objections. The first begins from the assumption that the antecedent is the cause of the consequent, but since the false cannot cause anything and since the impossible is false, it follows that from the impossible not just anything follows. John responds with a distinction. A cause in reality is of the same order with its effect, but a cause in an inference is not of the same order with that of which it is the cause. The false and impossible are causes in inferences only, not in reality.80 The second argument concerns dignity. Every cause is more worthy than its effect, but an impossible antecedent is not more worthy than the true, and hence the impossible cannot be the cause of the true, and so from the impossible not just anything follows. John responds that the correct conclusion is that the impossible and false are not causes of the true in being but in inferring, and a cause in inferring is not necessarily worthier than its effect.81 So much for John’s comments in the treatise on consequences. The only restriction on the rule arises from the distinction between formal and material consequence, and this is the standard doctrine of the Middle Ages, or, at least, the standard doctrine among those who maintained that the consequent had to be understood in the antecedent for a consequence to be formally valid.82 John devised a rule for distinguishing a formal from a material consequence that appears to

80

Ibid., fol. 141v (Strasbourg, fol. 81r–v): “Arguitur quarto. Ad impossibile non potest sequi quodlibet. Probatur quia ex falso non potest sequi quodlibet, sed impossibile est falsum ergo ad impossibile non sequitur quodlibet. Maior probatur quia antecedens est causa consequentis, sed falsum non est causa alicuius. Probatur quia falsum est nonens ut dicitur primo posteriorum, sed nonens non est causa alicuius. Minor est nota quia omne impossibile est falsum. Dico verum argumentum concludit quod causa in essendo est eiusdem ordinis cum suo effectu, sed causa in inferendo non est eiusdem ordinis cum illo cuius est, modo falsum et impossibile est causa in inferendo tantum et non in essendo, et sic argumentum non concludit.” 81 Ibid., fols. 141v–142r: “Arguitur quinto. Ad impossibile non sequitur quodlibet, ergo probatur impossibile non est causa aliorum, ergo probatur antecedens omnis causa est dignior suo effectu, sed impossibile non est dignius vero, ergo impossibile non est causa veri, et sic ad impossibile non sequitur quodlibet. Maior est nota, quia causa dat esse effectui, et effectus recipit esse modo dans esse est perfectius recipienti esse. Minor, quia falsum non est dignius vero, immo falsum est privatio veri, privatio autem deficit a dignitate sui habitus ut dicitur in post predicamentis. Dico verum argumentum concludit quod impossibile et falsum non est causa veri in essendo sed bene in inferendo, et causam in inferendo non oportet esse digniorem suo effectu.” 82 Boh, 376–377. For the authoritative account, see Ashworth, Language and Logic, 133–136.

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be complicated, but it amounts to the following: If a consequence that appears valid has an instance or example that is invalid, then the first consequence was material. For example, “if a man runs, then an animal runs” is material because the instance “a man runs, hence an ass runs” is false even though it has the same form. Hence, the rule about impossible antecedents is valid for formal consequences, which is to say for consequences that have no false instances.83 The restriction, then, does not appear to be very significant for the logic of consequences and does not require rejection of the paradoxical entailment rules. Nevertheless, it is significant that the objections are raised, and arguments provided. In earlier summaries of John’s treatise on consequences, I emphasized the introductory or intermediate character of the text, which was very likely used as lectures to or exercises for students preparing for the bachelor’s degree.84 As argued there, the text’s definitions and descriptions are very similar to John’s commentary on the first and fourth treatises of Peter of Spain, and which have survived in one manuscript at Cracow, Biblioteca Jagiellonica, MS 25. To my knowledge this is the only extant manuscript of John’s logical works containing this particular treatise. On fol. 17r–v, John provides the following definition and divisions of hypothetical propositions:85

83 Exercitium, Tractatus, fol. 134r (Strasbourg, fol. 79r): “Ad cognoscendum autem quae consequentia sit formalis et quae materialis est regula attendenda. Si aliquis vult cognoscere si aliquae consequentia est materialis vel formalis debet formare orationem ad modum consequentie cum illa consequentia quam vult cognoscere esse materialem vel formalem. Hoc est quod antecedens et consequens illius orationis ad modum consequentie formate sint eiusdem quantitatis et qualitatis cum priori consequentia, et quod termini in eis accipiantur eodem modo sicut in priori consequentia quo ad ampliationem, appellationem, restrictionem, et quod in tali oratione ad modum consequentie formate ponantur tot termini specifice distincti sicut in consequentia bona, et eodem modo quo ad subiectum et predicatum, et si tunc talis oratio ad modum consequentie formata fuerit bona consequentia, signum est quod prior consequentia fuerit formalis, eo quod non habet instantiam simili forma retenta. Si autem non fuerit bona, signum est quod prior consequentia fuit materialis, eo quod ipsa habet instantiam, ut patet de ista consequentia, ‘homo currit, ergo animal currit’, quae est materialis quia habet instantiam per istam, ‘homo currit, igitur asinus currit’, quae est mala consequentia, et tamen est similis forma.” 84 In Goddu, “Consequences,” 158–159. 85 Ioannes de Glogovia, Quaestiones in I et IV tractatum, fols. 1r–26v. For a description of the manuscript, see Catalogus codicus . . . in Bibliotheca Jagellonica Cracoviae I: 18–22, description by Zwiercan: “Lat. XV ex. (1493–1495), chart. cm. 31 × 21, f. 175 + VI.” For the date, see fol. 60v: “Anno Domini M 493 [1493].” See Lohr, Commentaires XXVI, 1970, 199, nr. 1. fol. 72v: “Finit lepide 1495.” The text of the Elenchi, fol. 73r–99r, is also in codex Bibl. Univ. Wratislaviensis IVQ 14, a. 1485 exarato, fol. 287r–356v: “Explicit exercicium Elenchorum . . . per venerabilem virum magistrum Iohannem de

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chapter three A hypothetical proposition contains at least two categorical propositions joined together by a conjunction such as “while,” “if,” or “because,” or, more generally, by a conjunction that is a copulative, a disjunctive, or a conditional. Hence, there are three species of hypothetical proposition: conditional, copulative, and disjunctive.

Now, no objections at all are raised in this text because it is a straightforward summary and commentary on Peter of Spain and not a commentary on the treatise on consequences. Nevertheless, characteristic features of John’s teaching are clearly present, features that are repeated in the treatise on consequences thus suggesting its appropriateness for an introductory or intermediate-level account of the logic of consequences. Especially significant is the characterization of consequence in terms of a habitudo, a characterization that is fundamental for the more advanced analysis of 1500.86 Our brief account of the history of treatises on consequences (based on Schupp, Green-Pedersen, and Ebbesen) suggests, in addition, that John’s discussion here was typical of many authors in the fourteenth and fifteenth century. As described by Boh, the greater part of John’s book is a concise commentary on parva logicalia, topics that John considered to be part of logica vetus (i.e., Porphyry’s Isagoge with Aristotle’s Predicaments and Perihermenias). The book also contains commentaries on three other treatises, on consequences, on obligations, and on insolubles or sophismata that constitute developments later than Peter of Spain, a fact explicitly mentioned by John. The book concludes with a separate treatise characterized near its conclusion as De syncategorematibus.87 The text from John quoted by Boh and cited above occurs in this last treatise in a section of De syncategorematibus labeled “De modo syllogisandi.”

Glogovia, . . . 1485 in Studio Cracoviensi.” Hence, John held this view as early as 1485 and taught it. The commentary on Posterior Analytics (f. 100r–155v) is found in cod. Bibl. Capituli Metrop. Pragensis 1282, f. 299r–310r, a. 1488; the commentary on the Prior Analytics, f. 159v–175v, concludes: “Amen. 1495.” Also cf. Wisłocki, Katalog rękopisów I: 9; and Markowski and Włodek, Repertorium commentatorium medii aevi in Aristotelem, 10. 86 A more detailed analysis of the logical issues and of Boh’s study is in Goddu, “Consequences,” 152–165. 87 This is the treatise referred to by Boh as “on insolubles or sophismata,” but there is also a separate, albeit very short, section between De consequentiis and De syncategorematibus on insolubles. See Goddu, “Consequences,” 153–155, for a description of the text.

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Let us return at this point to Boh’s analysis. As he indicates, the important idea behind John’s rejection of the paradoxes in De syncategorematibus is the claim that the truth or falsity of a consequence is independent of the truth or falsity of its component statements, but is rather dependent on a connection between antecedent and consequent.88 As interpreted by Boh, John maintained that the connection between antecedent and consequent is “based on the intentions (meanings, concepts) whose relationships are recognized by topical maxims”—and the topics mentioned by John are essential superior to inferior, whole to essential part, integral whole to part, cause and effect, cause of following, correlative, inclusion, and containing and contained.89 In positing the relationship of the antecedent to the consequent as a condition of validity, rejection of the consequence requires either the denial that the consequent follows from the antecedent or negation of the entire consequence.90 As we saw earlier in Syncategoreumata, Peter of Spain had already rejected the paradoxes on the basis of the relationship (habitudo) between antecedents and consequents, implying relevance as a condition for validity. In earlier accounts I had suggested that Boh exaggerated John’s originality with his claim about “a view that goes against the long logical tradition.”91 But, if all that Boh meant was the fourteenth and fifteenth centuries, then he was right. I had previously referred to the influx of works from the University of Cologne between 1460 and 1475. There were several authors who regarded the paradoxes as materially, but not formally valid. This fits with John’s first account of conditional propositions, and he did so in all likelihood while Copernicus was a student at Cracow. But there were also later commentaries

88 Boh, “John,” 381. It seems that the connection between antecedent and consequent is thought to remain in force regardless of the conditions at any given moment. 89 John of Glogovia, Super omnes tractatus, fol. cciiiv: “Quare omnis conditionalis vera est necessaria et omnis falsa est impossibilis, quia fundatur supra intentiones universales ut sunt totum, pars, genus, et huiusmodi que sunt semper necessarie vel impossibilis. Ulterius sequitur quod ex impossibili non sequitur quodlibet. Ratio quia in omni consequente antecedens se habet ut causa consequentis vel ut causa essendi vel ad minus ut causa consequendi respectu alterius, nisi ad ipsum habeat habitudinem includentis vel continentis.” 90 Boh, “John,” 381. See John of Glogovia, BJ, Inc. 2596, fol. cciiir: “Ex quo patet ad dandum contradictionem alicuius conditionalis oportet negare consequens ut sequitur ex antecedente vel proponendo toti conditionali negationem.” See Goddu, “Consequences,” 175–182. 91 Boh, 373–374; Goddu, “Consequences,” 153; idem, “Logic,” 28–68, esp. 39–42.

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from Cologne that distinguished between contradictory propositions taken absolutely and those taken suppositionally, and it is possible that John knew these later commentaries.92 According to this later interpretation, an impossible proposition could be stipulated as true for the sake of argument as, for example, at the beginning of a disputation or in the analysis of an insoluble or paradox. This is evidently the sort of circumstance that John has in mind in his later analysis when he asserts that one mode of impossible proposition is conceded in an enunciation or argumentation, in which case a conclusion follows by virtue of the form of arguing and not because of the impossibility of the premises.93 John’s comment and the fact that the 1500 edition of his commentary on syncategorematic terms comes after commentaries on obligations and insolubles suggest that his interpretation of the paradoxes was related to sophisms.94 Markowski’s comment about the relative unimportance of sophistic at Cracow does not mean that the sophistical literature was completely neglected. Copernicus was probably unfamiliar with John’s treatise from 1500, but he might have heard discussions at Cracow in the early 1490s that questioned the standard view on consequences, hypothetical propositions, and paradoxes. At least one other teacher at Cracow in the 1490s made a distinction that emphasizes the relation between antecedent and consequent. Michael of Biestrzykowa taught at the university from 1487 to 1504. In one of his discussions of consequences Michael distinguishes between simple and composite consequences. A simple consequence has only

92 Read, “Formal and Material Consequence,” 233–259, esp. 251–259. See also Ashworth, “Theory of Consequence,” 289–315, esp. pp. 293–300; eadem, “Essay Review,” 297–300, esp. 300–303. 93 John of Glogovia, BJ, Inc. 2596, fol. ccvv–ccvir: “Compositio impossibilis potest tripliciter considerari. Uno modo inquantum impossibilis. Alio modo ut compositio est. Tertio modo ut est corruptio rerum que disponuntur in enuntiatione vel in argumentatione. Duobus primis modis ex impossibili nihil sequitur penitus quia illo modo non possunt habere respectum ad habitudinem continentis. Sed tertio modo ex impossibili aliquid sequitur, quandoque preter habitudinem rerum ex quibus fit compositio impossibilis, ut ‘Si lapis est homo, est animal’, quandoque vero preter dispositionem forme arguendo, ut ‘omnis lapis est animal, arbor est lapis, ergo arbor est animal’. Sequitur conclusio ratione forme arguendi, et non propter impossibilitatem premissarum. Et per idem habetur quod necessarium non sequitur ad quodlibet eo quod necessarium non potest habere habitudinem contenti respectu cuiuslibet consequentis alicuius.” See Goddu, “Consequences,” 161–162. 94 On the significance of this context, see Read, “Formal and Material Consequence,” 254–259.

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one hypothetical proposition, which is further divided into natural and accidental: A natural consequence is one in which the consequence is included in the antecedent, as that which holds through the relation [habitudo] of some intrinsic locus. But accidental is one in which the consequent is not included in the antecedent, but holds only by means of the relation of some extrinsic locus.95

What is important and relevant here is Michael’s emphasis on the natural connection between antecedent and consequent and his reference to the use of an intrinsic locus as the ground for a natural consequence. What John of Glogovia and Michael of Biestrzykowa mean by a topical maxim and an intrinsic locus we can derive from Peter of Spain’s summary of logic, specifically Treatise V on topics.96 Let me draw your attention by way of example once again to the intrinsic topics from an integral whole and from an integral part. Peter of Spain says of these types: An integral whole is what is composed of parts having quantity, and one of its parts is called integral. The topic from integral whole is the relation of a thing itself to its part. It is always constructive, for example: ‘a house exists; therefore a wall exists’. Where does the topic come from? From an integral whole. The maxim: when an integral whole is posited, any part of it is also posited. The topic from integral part is the relation of a thing itself to its whole. It is always destructive. For example, ‘a wall does not exist; therefore a house does not exist’. Where does the topic come from? From an integral part. The maxim: when a part is destroyed, then its whole is also destroyed.97

95 Michael of Biestrzykowa, Quaestiones, fol. 72v. The distinction between consequences that are natural and not natural can be traced back to William of Shyreswood. See Jacobi, “Drei Theorien,” 385–397, esp. 387–389. 96 Peter of Spain, Tractatus, Tractatus quintus: De locis, 54–78. As we reported above, the treatise derives from the thirteenth century, but it went through many modifications including additions not written by Peter himself. 97 Peter of Spain, Tractatus, 64: “Totum integrale est quod est compositum ex partibus habentibus quantitatem et pars eius dicitur integralis. Locus a toto integrali est habitudo ipsius ad suam partem. Et est semper constructivus. Ut ‘domus est; ergo paries est’. Unde locus? A toto integrali. Maxima: posito toto integrali, ponitur quelibet eius pars. Locus a parte integrali est habitudo ipsius ad suum totum. Et est semper destructivus. Ut ‘paries non est; ergo domus non est’. Unde locus? A parte integrali. Maxima: destructa parte integrali, destruitur et suum totum.” For the sake of completeness, I note here that Peter’s analysis of part/whole relations simplifies the logic of such relations, and, in general the area of philosophy known as mereology. As we shall see in Chapter 8, Copernicus was completely unaware of the technical issues, and follows the sort of simplified version that we find in Peter of Spain. For a brief,

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When John of Glogovia and Michael of Biestrzykowa applied this doctrine to the logic of consequences, they tried to develop rules that ground the assertion of a connection between antecedent and consequent, a connection on which depends the truth or falsity of the consequence. As Boh is at pains to emphasize, causality is only one intrinsic relation mentioned by John of Glogovia. The significance of the point cannot be overemphasized. According to John’s view, a relation much weaker than causality can be used as an intrinsic ground for the relation between antecedent and consequent. The additional (and weaker) grounds that he enumerates are inclusion and containment: It follows further that from the impossible not just anything follows. The reason is that with respect to every consequence the antecedent is related to the consequent as the cause of the consequent, or as the cause of being, or at least as the cause of following with respect to another, unless it has to it the relation of inclusion or containment.98 [Emphasis added.]

In sum, there were professors at Cracow in the 1490s who were in agreement about restricting the paradoxical entailment rules, and who did so by emphasizing the connection or natural relationship between antecedent and consequent governed by intrinsic topics.99 Among the criteria for a sound consequence they enumerated the following minimal condition: what is signified by the consequent must be included in, contained by, or relevant to what is signified by the antecedent. Conversely, a good consequence admits nothing extraneous or irrelevant. The relevant points for the teaching that Copernicus may have received at Cracow are the following: (1) The connection between antecedent and consequent is based on intentions (meanings, concepts). (2) The relationships of intentions are recognized by topical maxims. (3) Topical maxims provide the ground justifying the belief that if the antecedent relates to the consequent as contained to containing, for example, then it is impossible for the antecedent to be true and not

useful survey, see Burkhardt and Dufour, “Part/Whole I: History,” 663–673; Goddu, “Copernicus’s Mereological Vision,” 331–339. 98 Boh, “John,” 381, n. 14: “Ulterius sequitur quod ex impossibili non sequitur quodlibet. Ratio quia in omni consequente antecedens se habet ut causa consequentis vel ut causa essendi vel ad minus ut causa consequendi respectu alterius, nisi ad ipsum habeat habitudinem includentis vel continentis.” 99 Cf. Ashworth, Language, 120–171. The standard fourteenth-century view on the paradoxes of strict implication was also represented at Cracow, as can be seen in the work of another influential professor, Michael Falkener of Wratislava, Congestum logicum, fol. sig. L1v–M5v.

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include the truth of the consequent. (4) Rejection of the consequence requires denial that the consequent follows from the antecedent or negation of the entire consequence. In sum, topical maxims provide reasons for emphasizing certain connections between antecedents and consequents and for accepting certain antecedents as probably true. The concreteness of John’s analysis is impressive. Even if he does not generate a general, formal objection to the paradoxes, the one exception that he allows makes it clear that the following of the consequent or of the conclusion of the argument is not because of the impossibility of the antecedent or the premises but because of the inseparability of the truth of one part (antecedent or premises) from the truth of the other part (consequent or conclusion). In this chapter I have focused on issues as reflected in the teaching at Cracow and that relate to one of Copernicus’s most controversial statements in De revolutionibus. Copernicus says:100 Hence in the process of demonstration or “method”, as it is called, those who employed eccentrics are found either to have omitted something essential or to have admitted something extraneous and wholly irrelevant. This would not have happened to them, had they followed sound principles. For if the hypotheses assumed by them were not false, everything [that] follows from their hypotheses would be confirmed beyond any doubt. Even though what I am now saying may be obscure, it will nevertheless become clearer in the proper place.

We will examine Copernicus’s statement more fully in chapter eight and return to the issue in the conclusion. It bears emphasis at this point, however, that my approach assumes that Copernicus meant a relationship between antecedent and consequent that is weaker than a causal one, and that he was content to stipulate mere relevance as an adequate reason for rejecting the standard interpretation of astronomical hypotheses. According to that interpretation, hypotheses or antecedents need not be true so long as they “save the phenomena.”

100 Copernicus, On the Revolutions, Preface, 4, a text written in 1542, some fifty years after his education at Cracow. Cf. De revolutionibus, Gesamtausgabe 2: 4, ll. 21–26: “Itaque in processu demonstrationis quam μέθοδον vocant, vel praeteriisse aliquid necessariorum vel alienum quid, et ad rem minime pertinens, admisisse inveniuntur. Id quod illis minime accidisset, si certa principia secuti essent. Nam si assumptae illorum hypotheses non essent fallaces, omnia quae ex illis sequuntur, verificarentur procul dubio. Obscura autem licet haec sint, quae nunc dico, tamen suo loco fient apertiora.”

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It should be clear, however, that Cracow logicians in concert with medieval logicians and Aristotelian scholastics took it for granted that where the relationship between the premises and a conclusion of a syllogism or between the antecedent and consequent of a consequence or hypothetical proposition is a causal one, then a true consequent can follow only from a true antecedent. Although I have found no special emphasis in commentaries on Prior Analytics, it is clear that Cracow philosophers knew the doctrine.101 As emphasized in chapter two, John of Glogovia probably influenced the teaching of James of Gostynin, who, in turn, relied less on scholastic commentaries and more on interpreting the texts of Aristotle in Latin translation directly. The relevant texts that discuss the relation between premises and conclusions are from Nicomachean Ethics I, 7–8, 1098b2–12 and Prior Analytics II, 2–4. In the Ethics, Aristotle says, in one standard and authoritative translation:102 Now of first principles we see some by induction, some by perception, some by a certain habituation, and others in other ways. But each set of principles we must try to investigate in the natural way, and we must take pains to state them definitely, since they have a great influence on what follows. For the beginning is thought to be more than half of the whole, and many of the questions we ask are cleared up by it. We must consider it, however, in the light not only of our conclusion and our premisses, but also of what is commonly said about it; for with a true view all the data harmonize, but with a false one the facts soon clash. [Emphasis added.]

Robert Grosseteste’s Latin translation of the emphasized passage follows: Vero quidem enim omnia consonant existencia, falso autem cito dissonat verum.103 The text became a scholastic formula: Omnia vera vero consonant.104 In the Latin Averroes (1562 edition) it appears thus: Cum vero enim consonant omnia, quae in re insunt; a falso autem cito dissonant ac discrepant.105 In the supplement to that edition, Antoniusmarcus Zimara gave it yet another formulation: Verum vero consonat ex omni parte, falsum autem statim dissonat vero.106

101 In discussions of method, the emphasis tends to be on Posterior Analytics. See Markowski, Methodologia nauk, passim. 102 Ethica Nicomachea, tr. Ross, 943–944. 103 Aristoteles Latinus, XXVI, 1–3, 152. 104 Hamesse, Auctoritates Aristotelis, 233, (15). 105 Aristotelis opera cum Averrois commentariis, 3: fol. 10ra. 106 Marcantonio Zimara, Tabula dilucidationum, fol. 390vb.

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Copernicus could have known Marcantonio Zimara’s version (though not in the Giuntina edition of 1562), and he might well have seen or heard one or all of the others, including some earlier Latin version of Averroes.107 The idea expressed by Aristotle in Ethics is broadly consistent with his comments in Prior Analytics II, 2–4, where he discusses those cases in which a true conclusion can follow from false premises. Consider II, 2, 53b4–10:108 The premises of a syllogism may be both true, both false or one true and one false. The conclusion is necessarily either true or false. True premises cannot give a false conclusion; false premises may give a true conclusion, but only of the fact, not of the reason. We shall see later why the reason cannot be inferred from false premises.

The last comment refers presumably to II, 4, 57a37–b4:109 Thus if the conclusion is false, one or both premises must be false; but if the conclusion is true, neither both premises nor even one need be true. Even if neither is true the conclusion may be true, but its truth is not necessitated by the premises. The reason is that when two things are so related that if one exists the other must, if the second does not exist neither will the first, but if the second exists the first need not; while on the other hand the existence of one thing cannot be necessitated both by the existence and by the non-existence of another.

In standard Latin versions, the passages read as follows:110 DE SYLLOGISMIS EX FALSIS.—Est ergo sic se habere ut verae sint propositiones per quas fit syllogismus, est autem ut falsae, est vero ut haec quidem vera, illa autem falsa ex necessitate. Ex veris ergo non est falsum syllogizare, ex falsis autem est verum, tamen non propter quid, sed quoniam; nam eius quod propter quid non est ex falsis syllogismus; ob quam autem causam in sequentibus dicetur. Manifestum igitur quoniam, si sit conclusio falsa, necesse est, ex quibus est oratio, falsa esse aut omnia aut aliqua; quando autem vera, non necesse est vera esse neque quid neque omnia, sed est cum nullum sit verum eorum quae sunt in syllogismo conclusionem similiter esse veram, non tamen ex necessitate. Causa autem quoniam quando duo sic

107 Ibid. fol. 390vb. Lohr, Latin Aristotle Commentaries, 2: 507, No. 3, cites an edition from 1537. Copernicus wrote his remark in the Preface in 1542, although he probably adopted this view much earlier. 108 Aristotle, Prior and Posterior Analytics, tr. Warrington, 113. 109 Ibid. 123. 110 Aristoteles Latinus III, 1–4, Analytica priora, Translatio Boethii, 94 and 104.

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There is one more relevant Aristotelian text about which we will have more to say in chapter eight. In Metaphysics I minor, 993b26–27, a very brief passage, Aristotle says, “That which causes derivative truths to be true is most true.” A Latin version follows: Verissimum est id, quod posterioribus, ut vera sint, causa est.111 It is possible that Copernicus had the stronger doctrine about causal relations in mind. For reasons that I will address in chapter eight, it seems likelier that he adopted the weaker view for which relevance between hypothesis and conclusion suffices as a criterion. The interpretation hinges on what he understood by “causes” and “explanation,” for if he believed that the natural explanation of an observation offered a complete causal account, then he was either claiming too much and committing a fallacy or he was engaging in a sleight of hand. Neither of those conclusions, in my view, corresponds to his understanding of cosmology and the role of geometrical models in mathematical astronomy. We will return to these questions specifically in chapter eight, treat the cosmological and mathematical issues in chapters nine and ten, and revisit them in the general conclusion. We may conclude that students at Cracow in the 1490s received instruction on the construction of arguments, consequences, and hypothetical propositions. Through exercises they learned how to use topics to construct arguments. Students may not have understood, let alone retained, the theory in any precise way. It is likely, however, that they developed habits of thinking, arguing, and writing on which they could have drawn for the remainder of their lives. Exercises on topics would have reinforced intuitions about connections between antecedents and consequents or hypotheses and results, especially as applied to the natural sciences. Copernicus was not a scholastic logician, but he was trained in the use of topics and in logical forms of argumentation as his treatises reveal when his arguments are examined for their logic.

111 This is the version found in Rheticus, Narratio prima, Nikolaus Copernicus Gesamtausgabe, 8/1: 22. Or consult Narratio prima, Sc, 20: 58.

CHAPTER FOUR

NATURAL PHILOSOPHY 1. General Orientation1 After logic the next most important topic in the medieval curriculum for the bachelor’s degree in arts was natural philosophy. Because Aristotle’s texts in natural philosophy entered western Latin consciousness later than logic, the tradition in the Latin West is significantly different. Aristotle’s texts in natural philosophy were first translated into Latin from Arabic sources, and Arabic commentaries exercised a major influence on scholastic natural philosophy well into the sixteenth century. Issues that emerged in thirteenth-century universities, in part as a result of translations directly from the Greek and in part because of their relation to theological doctrines, remained issues for centuries.2 In several cases, commentators developed their own view on a topic independently of Aristotle’s account and then subsequently applied their view to the interpretation of Aristotle’s analysis.3 Similarly, relatively independent developments in the fourteenth century,

1 Goddu, “Sources of Natural Philosophy,” 85–114; idem, “Teaching of Natural Philosophy,” 37–81. 2 The principal secondary sources for this chapter are the following: Markowski, Filozofia przyrody; Świeżawski, “Quelques aspects,” 699–709; Palacz, “Nicole Copernic,” 27–40; idem, “Streit,” 97–108; Seńko, “Philosophie médiévale,” 5–21; Kuksewicz, “Einflüsse,” 287–298; Włodek, “Note sur le problème,” 730–734; Zwiercan, “‘Quaestiones’,” 86–92. See also Markowski, “Albert und der Albertismus,” 177–192; idem, “Die wissenschaftlichen Verbindungen,” 274–286; idem, Burydanizm w Polsce. Finally, important articles from a conference at the Catholic University of Lublin provide a dialectical inquiry into the relation between natural philosophy and astronomy at Cracow in the fifteenth century. Mikołaj Kopernik: Markowski, “Doktrynalne,” 13–31; Rosińska, “Mikołaj Kopernik,” 33–56; and Kurdziałek, “Średniowieczne stanowiska,” 57–100. I summarize Markowski’s analysis, Filozofia przyrody, in “Teaching,” partly extracted below in subsection 2. Cf. A. Maier, Studien: Trifogli, Oxford Physics; Lang, Order of Nature; eadem, “Inclination, Impetus,” 221–260; eadem, Aristotle’s Physics; Solmsen, Aristotle’s System; and Weisheipl, “Interpretation,” 521–536. For an excellent brief review, see Lohr, “Latin Aristotelianism,” 369–380, esp. 369–373. 3 Trifogli, Oxford Physics, 37.

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as in logic, led to new interpretations that influenced the curricula of many universities. Cracow was no exception. There are several important discussions of the relation between Aristotle and Aristotelianism, and they all recognize a serious problem that we cannot avoid without misleading readers. Charles Schmitt proposed the adoption of Wittgenstein’s notion of “family resemblances.”4 Edward Grant has advocated the “population approach.”5 Hans Thijssen has argued for a “typological approach” combined with a model that distinguishes between a “hard core” surrounded by a “protective belt” that absorbs all of the criticisms and undergoes adjustment, leaving the “hard core” intact until the theory is decisively overthrown.6 Finally, Luca Bianchi and Eugenio Randi have adopted the felicitous expression “dissonant truths” to characterize the varieties of Aristotelianism.7 All of these proposals have strengths and weaknesses. In my view they all serve to explain continuity and transformation within the Aristotelian tradition. Above all they document the ways in which commentators believed themselves to be “interpreting” Aristotelian texts and “preserving” Aristotelian doctrine while advancing “truth” or “true philosophy” as they saw it. I am sympathetic to these proposals insofar as they help us to understand “Aristotelianism” or the “Aristotelian tradition.” On the other hand, these accounts do not absolve us of the responsibility (thankless though it be) of identifying genuine doctrines of Aristotle and taking a stance on the interpretations and

4 Schmitt, Aristotle and the Renaissance, esp. 111–112. Cf. Wittgenstein, Philosophical Investigations, 31–32. 5 Grant, “Ways to Interpret,” 335–358, esp. 347–353. 6 Grant initially proposed this model in an essentialist way, “Ways,” 345–347, and discarded it. Thijssen modified the model by interpreting it as a comprehensive framework of shared beliefs restated according to the model developed by Lakatos that provides a heuristic rescuing of the typological approach from the question-begging that is fatal to Grant’s version of the typological model. Cf. Lakatos, Methodology, esp. 4–7, where Newton’s three laws of mechanics and the law of gravitation are said to constitute the ‘hard core’ of the Newtonian program. A ‘protective belt’ of auxiliary hypotheses surrounds the ‘hard core’, and the research program has a ‘heuristic’ characterized as a ‘powerful problem-solving machinery’. Progressive research programs lead to the discovery of hitherto unknown novel facts. Degenerating research programs fabricate theories only to accommodate known facts. The former lead to novel facts. The latter lag behind them and ‘cook up’ auxiliary hypotheses to protect the theory from the facts. Thijssen reviews the population and typological approaches in “Some Reflections,” 503–528. 7 Bianchi and Randi, Verità dissonanti.

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revisions. We can explain how and why authors regarded their interpretations of Aristotle as genuinely Aristotelian, but we must make a judgment about the legitimacy and significance of the revisions. In my view, we must wonder how receptive Aristotle would have been to interpretations that reject or modify the following fundamental doctrines. 1) Nature is everywhere a cause of order that is sufficient to explain the order of the universe and the motion and rest of bodies that move according to nature. 2) The world is eternal. 3) The infinite exists only potentially. 4) The cosmos is a unique, finite, complete, and perfect whole. 5) Matter cannot exist apart from form. 6) Terrestrial matter and celestial matter are entirely distinct. 7) Mathematics is subordinate to natural philosophy. Finally, 8) Aristotle’s account of violent (projectile) motion is subsidiary to his account of natural motion, hence it is of little interest to him because it is at best peripheral to his project.8 Against such “hard-core” Aristotelian doctrines, some scholastic philosophers and their followers in Cracow held one or more of the following. 1) God created and sustains the order of the universe. 2) The world is not eternal. 3) Extracosmic void space is actually infinite, and 4) it can serve as a receptacle for bodies. 5) Matter in individual things is really distinct from, and it can exist apart from, form. 6) Celestial matter and terrestrial matter are essentially the same or, at

8

In an earlier version I also asserted as a fundamental Aristotelian doctrine the view that prime matter is pure potentiality. Expert interpreters now challenge that assertion. See Aristotle, Physics I and II, Charlton tr. and commentary, 129–145: “Did Aristotle Believe in Prime Matter?” I confess that the traditional view still seems correct to me. Aristotle often uses the composition of artifacts to illustrate his doctrine. When he speaks of a bed as composed of the form of a bed and the matter of wood, what would correspond to the “matter” of the wood itself? The matter of the wood is what traditional interpretations thought of as first matter or primary matter, and that it is pure potentiality. Some scholastics also interpreted Aristotle in this way, but other scholastics interpreted primary matter as having some determinateness. See also Aristotle, Metaphysics, Z and H, Bostwick tr. and commentary, 72–85, esp. 73 where he says: “There are some who have claimed that Aristotle was not committed to the existence of this ultimate matter, or anyway that he did not accept the commitment. Since it seems to me quite clear that he was committed to it and did accept it, I shall not discuss the issue here.” He goes on to list all of the modern doubters and their critics. Suffice it to say here that commentators are divided, and that the disagreements expose ambiguities in Aristotle’s accounts. I owe the references and caution about pure potentiality to Dilwyn Knox. Similar qualifications about terrestrial and celestial matter are appropriate. As readers will see below and in chapter nine, I owe a great deal more to Knox.

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least, belong to the same genus.9 7) Mathematics is not always subordinate to natural philosophy. 8) Projectile motion is explained by assuming the transmission of a force, impetus, either to the projectile, or to both the projectile and air, or just to the air surrounding the projectile. Such explanations give violent motion a prominence that Aristotle had denied of it. We can try to explain deviations from Aristotle away, but we do so at the risk of making Aristotle’s philosophy of nature incoherent. For these reasons I have focused in this study on the “Aristotelian tradition.” The tradition, however, revised Aristotle’s doctrines in ways that, while possibly coherent in their own terms, were inconsistent with Aristotle’s deeply held beliefs about the order and structure of the cosmos. My study is not about Copernicus’s relation to Aristotle but Copernicus’s relation to the tradition. My thesis is that Copernicus was so impressed by the different interpretations and revisions of Aristotelian principles and doctrines that he believed himself to fit in the tradition, regardless of the shocking revisions that he was proposing. The evidence for my interpretation is contained mostly in Part Three—Copernicus’s own assertions and arguments. We can appreciate the force of the arguments, however, only against the background of the Aristotelian philosophy that Copernicus encountered in Cracow. His view of Aristotle was formed by 1495, and his reading or re-reading, as he says in the Preface to De revolutionibus written in 1542, of other ancient authors probably between 1495 and 1510 modified his view. By 1510 Copernicus had developed his own philosophy. We may quibble over whether his philosophy was broadly Aristotelian and scholastic or non-Aristotelian and non-scholastic. In

9 The identity of terrestrial and celestial matter does not imply that terrestrial elements will be found in the heavens. Even medieval philosophers who argued for identity maintained that terrestrial and celestial forms are different. John Philoponus’s view of the identity of terrestrial and celestial form was rejected by the medievals. See Grant, “Celestial Matter,” 157–186. Other ancient Platonists adopted the unity of all matter as a metaphysical doctrine. This was certainly the case for Proclus. See Siorvanes, Proclus, 183–189, 235–244, and 273–278. The relevant Aristotelian texts taken together are ambiguous, and they cannot be reconciled completely with Ptolemaic astronomical models. Medieval thinkers exploited these ambiguities and combined them with Neoplatonic conceptions. Robert Grosseteste asserted that the stars were composed of the four terrestrial elements, but his later account and those of others, in fact, remain nuanced, unclear, and ambiguous, regardless of how suggestive they may appear to modern readers. See Dales, “De-animation,” 531–550. I owe the above qualifications and references to Dilwyn Knox.

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fact, his cosmology was decidedly and clearly non-Aristotelian and non-scholastic, but he subordinated his arguments to rhetorical and dialectical strategies intended to persuade Aristotelians and scholastics to adapt Aristotelian principles as modified by other ancient and medieval commentators to a heliocentric and geokinetic cosmology. It was also about 1510 that he came to the conclusion that he would devote the rest of his life, to the extent that his duties permitted, to carrying out a fundamental reform of astronomy. He recognized some of the problems with ancient-medieval astronomy and learned the basics by 1495, developed a mastery of the technical issues by 1503, began to consider a variety of approaches and solutions between 1503 and 1510, and came to his earliest conclusions around 1508. By 1512 he recognized problems with his first effort, and defined the project that would occupy him on and off for, as it turned out, the next thirty years. In this chapter, then, I focus on the Aristotelian philosophy of nature that Copernicus learned in Cracow. As in the previous chapter, the curriculum in natural philosophy at Cracow follows the same general pattern. There was relative dominance by followers of John Buridan in the first half of the fifteenth century, followed by an influx of ideas from Cologne and Paris, through which earlier medieval traditions influenced commentaries and teaching. As with logic, the teaching of natural philosophy in the 1490s was highly eclectic. Likewise, we find a variety of interpretations of Aristotle’s philosophy of nature, some of which appear very early. Whatever the “correct” interpretation of Aristotle may be, teachers at Cracow presented all of the major medieval traditions to their students.10

10 Some interpretations of Aristotelian philosophy of nature are more widely accepted than others, yet I am partial to one (controversial and severely criticized by some) that, it seems to me, makes the best historical sense of the varieties of Aristotelianism and deviations from fundamental Aristotelian principles. I am referring principally to articles and books by Helen S. Lang, but I also rely on some articles by James Weisheipl—and that despite my reservations about Weisheipl’s interpretation of fourteenth-century developments. Cf. Goddu, Physics, 194. Perhaps the most neutral way to express the problem with Aristotle’s philosophy of nature is to say that after him problems, questions, and agenda appear that were of secondary interest to Aristotle or of little or no relevance to his main projects. Yet, later writers believed themselves to be Aristotelians carrying out Aristotelian projects adapted to their own purposes. See also Maier, Vorläufer Galileis, 53–78: “Ursachen und Kräfte.” For strikingly different reviews of Lang’s Order of Nature, cf. van Luchene, 421–426; Sharples, 359–360; and Johnson, 687–688.

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Most modern and sympathetic accounts of Aristotelian natural philosophy make excuses for Aristotle’s errors and erroneous conclusions. Unsympathetic readers dismiss him and leave us puzzled as to why anyone would have taken obviously erroneous assumptions and conclusions seriously. In what follows I aim to understand why Aristotle’s philosophy maintained such a hold on his successors that he influenced even Copernicus in a fundamental way on his vision of the cosmos. Aristotle’s philosophy of nature comprises all of the texts related to the study of nature, the metaphysical principles of nature, change and motion, earth, the heavens, his studies in biology, and the shorter treatises on the senses and perception, culminating in his major work on the soul. In the Middle Ages, the interpretation of Aristotle’s natural philosophy continued the classical tradition of interpretation in the context of Peripatetic, Neoplatonic, Stoic, Christian, Islamic, and other agendas. In medieval natural philosophy we find philosophical discussions of texts, typically of Peter Lombard’s Sentences, Aristotle’s Physics, and of the other treatises by Aristotle as well as the commentaries by Averroes. From a modern perspective what stands out about Aristotle’s natural philosophy is its qualitative character, subordinating even quantitative considerations to qualitative principles.11 Because my focus is ultimately on Copernicus and on the relation between physics and astronomy, we are in danger of distorting not only Aristotelian natural philosophy but also late medieval commentaries. We cannot do justice to all of the complex issues. We must be selective and focus on the issues emphasized by fifteenth-century philosophers in Cracow, all in turn surbordinated to what a student like Copernicus would have learned about Aristotle and natural philosophy from his teachers.12

11

McMullin, “Medieval and Modern Science,” 103–129. Such readings are challenged, but the challenges seem hardly plausible when one compares Aristotle’s applications of mathematics with early modern approaches. See Hussey, “Aristotle and Mathematics,” 217–229. Aristotle’s conclusions about the simple natural motions of simple elemental bodies depends on his assumptions about the qualitative characteristics of simple elemental bodies and his premature search for a causal explanation, not a quantitative empirical analysis of actual motions. I return to these issues in chapter nine. 12 The most relevant of these studies is by Markowski, Filozofia przyrody. Polish scholars have written the most authoritative studies of fifteenth-century philosophy in Poland, and comparatively little of it has been translated into any western European language. Exceptions are Świeżawski, L’univers; A. Birkenmajer, Études; and

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In the second article cited in the first note of this chapter, I followed the main outline of Markowski’s monograph on natural philosophy at Cracow in the second half of the fifteenth century.13 There I registered one objection, namely, to his unfortunate reliance on “Aristotelianism” and other “-isms” as catalogues of doctrines. In fact, I regarded it as more consistent with Markowski’s own examples to refer to “schools” or “sects,” because these terms suggest communities made up of relations between teachers and students and a tradition of common texts. Indeed, the history that Markowski traces is a history of “schools” in which commentators became full participants in the construction of natural philosophy. All of the commentators learned from Aristotle a powerful set of terminologies and principles by means of which they tried to understand the natural world. But it is only in such ways and not as adherents of some defining content that we should understand the Aristotelian tradition and those who were formed within it. Followers of the tradition belonged to “schools,” and it is in that way that I understand Copernicus’s relation to the Aristotelian tradition, namely, as a relation of Copernicus to his teachers and of his teachers to the “schools” and texts on which they drew for their interpretations of natural philosophy.14 With respect to John Versor (d. ca. 1485), Markowski notes that his influence in the 1460s was short-lived. But around 1488 his works appeared in print and became available in Cracow. Unlike copies of the printed works of Albert the Great at Cracow, John’s commentaries on De caelo et mundo, De generatione et corruptione, and Meteorologica of Aristotle do contain some annotations. The Jagiellonian Library possesses two copies of the 1489 edition of John’s commentaries on Aristotle’s works in natural philosophy published in Lyon. Both contain annotations from the end of the fifteenth and first quarter of the sixteenth century. Indeed, BJ, Inc. 208 contains extensive glosses on the commentaries on Physics, De caelo, De generatione et corruptione, and Meteorologica, although it is difficult to determine whether the

Kokowski, Copernicus’s Originality. Otherwise, only short articles and brief summaries in French, German, or English are available, which often reduce nuanced and subtle arguments to exaggerated claims. 13 To my knowledge, Markowski’s monograph has been completely neglected outside of Poland. Only in Markowski do we find the broad context and exhaustive evidence. For expression of caution about identifying ‘schools’ and their followers, see Seńko, “Philosophie médiévale,” 5. 14 My view here is very much dependent on Jordan, “Aquinas Reading,” 229–249.

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annotations are of Cracow provenience. The Jagiellonian Library possesses another 1489 edition apparently published in Cologne, however, and some of them have extensive annotations though mainly on the works of Aristotle and few on Versor’s commentaries. Some of the annotations cite the views of Albert the Great and Giles of Rome. John’s questions on De generatione et corruptione (BJ, MS 511) were copied in 1476 and were the subject of lectures by Paul of Zackliczew in winter semester 1494.15 The conclusion to which Markowski comes is that Versor’s commentaries were viewed as a compromise fusion of Albertism with Thomism, and, as such, influenced the interpretations of the 1490s. But when the published versions became available, the professors focused more on the text of Aristotle than on Versor’s commentary, suggesting that around 1495 Versor’s influence declined with a correspondingly greater interest in Aristotle’s texts. And that brings us to the last characteristic distinguished by Markowski. In Cracow, the introductory texts written by Michael Falkener of Wrocław, though revealing his familiarity with and preference for particular medieval traditions by the selections he made, do not cite by name any ancient and medieval author. This is an approach that Michael developed already in the 1490s while or shortly after Copernicus was a student at the university.16 The summary presented in the article mentioned above is superficial to the extent that “schools” and “representatives” were identified by explicit references. The references do not inform us directly of how the views were received or, indeed, if they were rejected. Markowski saved internal content that supported his distinctions for the remainder of his monograph. I refer briefly to typical examples rather than providing a thorough summary, for my focus is on the sorts of questions and problems of relevance to Copernicus’s education in natural philosophy and cosmology. The Aristotelian natural philosophy in which Copernicus was educated was based on the texts of Aristotle that reflected the first efforts at Cracow to interpret the texts historically but still under the influence of the major traditions of the Middle Ages. The effort towards a more authentic Aristotle, we may suppose, influenced Copernicus positively and encouraged him while he studied at Cracow to pursue his interest in astronomy in a broadly Aristotelian context. 15 16

Markowski, 34–36; Karliński, Żywot Kopernika, Appendix III, Table 7. Markowski, 46–47.

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2. Markowski’s Most Important and Relevant Conclusions Markowski thinks that discussions at Cracow on the nature of celestial matter constitute a transition to the modern conception of a homogeneous matter, and that they influenced or encouraged Copernicus to take the next step towards the modern understanding of celestial mechanics.17 We will examine this question with texts in detail below and in chapter nine. We may point out at once, however, that no scholastic suggested from an identity in genus that Earth is a heavenly body, and none concluded that terrestrial elements exist in the heavens. We will also see, however, that Copernicus’s position is nuanced and more complicated than the standard interpretations claim, especially with respect to the nature of celestial spheres. There is little doubt as well that Platonic or Stoic views on the elements encouraged Copernicus to attribute some terrestrial properties to celestial bodies.18 Of some relevance here is how Cracow philosophers regarded the views of Plato. In cases where they followed scholastic authors dependent on Augustine, Cracow philosophers did not always seem to be aware of adherence to Neoplatonic modifications of Aristotelian doctrine except in cases where the motive was to preserve Christian doctrine. On the other hand, in cases where they identified or detected a clearly distinctive Platonic view, they explicitly rejected the Platonic view and affirmed the truth of Aristotelian doctrine. We do not know what Copernicus’s reaction to such conclusions was in the early 1490s, but by 1503 at the latest he was familiar with more positive conclusions about Plato, with interpreters who admired both Plato and Aristotle, and others who attempted to harmonize their doctrines. Cracow philosophers followed those scholastic traditions that distinguish between void conceived from a natural or supernatural point of view. The discussions almost inevitably led philosophers to mechanical issues that departed dramatically from authentic Aristotelian conceptions. Cracow philosophers adopted a variety of solutions, some more in conformity with Aristotle or Thomas Aquinas than others. We may nevertheless imagine that students were impressed by the variety of

17 Markowski, 152 and 170, n. 190. See also John of Glogovia, Komentarz do Metafizyki VIII, [q. 50], 93–101. Cf. Grant, “Celestial Matter,” 171–172 on the view defended by Ockham. 18 I owe part of this observation to Dilwyn Knox; however, I am not as convinced as he is about how far Copernicus meant his suggestions to be taken.

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views and by some efforts to harmonize contrasting opinions by combining the Aristotelian conception of place with the Platonic view that admitted space as potential place. Extracosmic space, actually void but a potential receptacle of body, could be infinite regardless of the impossibility of confirmation because it is impossible to imagine what could limit it. Some Cracow philosophers reported the opinion that void is a place in which there is no body but in which there can be bodies, and added that Aristotle proved that there is no such place.19 There is no doubt that one of the major philosophical motivations for the belief in the uniform motions of celestial bodies was the Aristotelian-scholastic conception that the pre-eminent measure of time is the uniform motion of the highest celestial sphere. Some expressed this conclusion in the strongest terms—were there no celestial motion, there would be no time, however dependent the measurement of time is on the existence of an intellectual soul. The view was represented at Cracow along with more subjective views and compromises between them.20 In his account of Cracow philosophers on motion, Markowski shows that the doctrine of impetus and its application to the explanation of celestial motion were well known in Cracow circles in the 1490s. Such an impetus, regarded as indefatigable, led some to dispense with the doctrine of separate intelligences or of souls as the moving cause of celestial spheres. As Markowski’s account makes clear, however, as with the plurality of schools on other issues represented at Cracow, so is it the case on the question of impetus. By the late 1450s we find explicit efforts to reconcile the theory of impetus with the Aristotelian account. Indeed, the Aristotelian doctrine was interpreted as compatible with impetus regarded as transmitted to the medium, acting at least as an instrumental aid to the medium, rather than to the body in motion.21

19

Markowski, 178, cites Michael Falkener by way of example. Markowski, 179–181. For an explanation how such notions become transformed into the later classical conception of infinite void space, see Grant, Much Ado About Nothing, xi, 106–120 and 135–149. 21 Markowski, 182. See also Markowski, “Philosophical Foundations,” 213–223, esp. 217. In Oresme’s version, once impetus is imparted to the body, the body becomes a self-mover. See Maier, Studien, Vol. 5, on Peter John Olivi and Blasius of Parma. Maier finds the versions in Olivi and Blasius the closest to the modern notions of impetus and inertia. 20

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In his general conclusion Markowski draws together the main results of his investigation. Natural philosophers at Cracow in the second half of the fifteenth century manifested Aristotelian and anti-Aristotelian solutions to problems relating to the intrinsic and extrinsic properties of material bodies. Some authors departed from the Aristotelian definition and conception of place. They adopted at least partly nonAristotelian views about the place of the universe and about void, sometimes motivated by theological doctrines. Several adopted the theory of impetus as formulated by John Buridan or they reinterpreted the Aristotelian account to accommodate the doctrine of impetus. The keynote is a doctrinal pluralism that deviated from genuine Aristotelianism. Yet it did so in a way that expressed the confidence of Cracow natural philosophers in their ability to adapt Aristotelianism to the conclusions that they regarded as more probable and more in conformity with reason, experience, and the truths of Christianity. Markowski concludes that the teaching of natural philosophy along with the impact of printing and Renaissance humanism at Cracow influenced Copernicus and to that extent contributed to the emergence of a truer image of the cosmos than that held by his teachers.22 I conclude from Markowski’s history of natural philosophy in fifteenth-century Cracow that professors were Aristotelians in the following sense. They followed a number of schools of Aristotelian commentators, and they shared a tradition of texts, both of which served them to construct the natural philosophy that they taught Copernicus. For his part Copernicus left Cracow as a participant in the Aristotelian tradition as modified by other ancient traditions and scholastic commentators, prepared to add his voice to the construction of natural philosophy. 3. The Quaestiones cracovienses on the Physics of Aristotle In this section and in the six subsections I select and summarize the most relevant conclusions from the most important introductory books on natural philosophy at the University of Cracow in the 1490s.

22

I have perhaps expressed Markowski’s conclusions in a somewhat more modest way than he does, but my summary can be taken in that case as representing Markowski’s interpretation read moderately. As readers will see, I adopt an even more cautious interpretation of Copernicus’s dependence on his education at Cracow.

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The most important fifteenth-century “commentary” on Aristotle’s Physics in the form of questions was an anonymous collection dubbed by later scholars Quaestiones cracovienses super I–VIII libros Physicorum Aristotelis.23 The formulation of the questions was unquestionably influenced by John Versor, but the text also displayed a decidedly more Thomistic orientation.24 Markowski takes this shift as a signal characterizing the period that he identifies—1464 to 1474—as a period of Cracow Thomism.25 During this period the Quaestiones cracovienses became the most popular text in natural philosophy. As with other periods, however, Markowski is careful to note references in one manuscript to Albert the Great and Giles of Rome as well as to several other authors including Averroes, Avicenna, “even Albert of Saxony and some Scotists.”26 In other words, the Thomism of the period is not completely authentic, but this is typical of philosophy at Cracow. The Quaestiones were not only popular but became the official handbook on natural philosophy in lectures and exercises at the university. I take these texts and, in some selective cases, John of Glogovia’s version of them as representing the teaching at the university and, hence, what students would have learned about the topics selected. The Quaestiones cracovienses contain hundreds of questions on the major books of Aristotle—Physics, De caelo, De generatione et corruptione, and Meteorologica. In the following six subsections I summarize the principal conclusions reached by Cracow philosophers on nature and natural place, the infinite, celestial spheres and celestial matter, mathematics and natural philosophy, impetus and the void, and dialectical topics specific to natural philosophy.27

23 Markowski, 17. See the edition by Palacz (1969). We will select some of these questions as the basis for a summary of teaching in natural philosophy below. See also the article by Palacz, “Les ‘Quaestiones’.” 24 John Versor has received little attention. Cf. Geyer, Patristische und scholastische Philosophie, 627. Versor is generally regarded as having constructed a compromise between the views of Thomas Aquinas and Albert the Great. 25 Markowski, 17–19. 26 Markowski, 18. He is referring to Biblioteca Jagellonica, MS 2007. This is the version published by Jan Haller in 1510 in Cracow as Exercitium ‘Physicorum’ exercitari solitum per facultatis artium decanum studii cracoviensis pro baccalauriandorum et magistrandorum in artibus completione. One copy in Cracow carries the shelf number BJ, Cim. 4098. 27 For the complete summary with texts, see Goddu, “Teaching,” 52–76.

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3.1. Nature and Natural Place Already in late antiquity Aristotle’s doctrines were transformed in subtle but nonetheless decisive and dramatic ways.28 From a source of being moved and being at rest, some commentators interpret nature as an intrinsic mover, and also describe inclination as an intrinsic mover of the elements. Such accounts tend to identify nature with form to the extent that they exclude matter from any role in nature, leading to redefinitions of physics and mathematics. In interpretations of form and matter embedded in discussions of motion, on the other hand, the accounts transform form into an extrinsic agent that excludes an intrinsic relation of matter to form. They accordingly transform inclination of natural place into a principle whereby place is a receptacle for body. That is to say that the “power” or potentiality of place lies not in determining the order of the cosmos and explaining why the cosmos is inherently directional but in receiving the body moved into it by inclination. The account requires an extrinsic mover because there is no intrinsic orientation, merely receptivity. Bodies are not actively oriented toward form, rather bodies are passive, governed by an inclination to which bodies are not intrinsically related.29 The revised accounts, perhaps coherent in their own terms, were not consistent with the principles laid out by Aristotle, yet they were presented as interpretations of Aristotle’s doctrines. In the Quaestiones cracovienses we find the results as transmitted by teachers at the university. Nature is described as a source and cause of being moved and being at rest because natural things have in themselves their principle of being moved and being at rest. With respect to the motion of the heavens, nature does not seem to be a principle of being moved, for the intelligences move the heavens as a sailor moves a ship. Their natural principle of motion, then, is passive.30 The

28 I have borrowed extensively in my use and interpretation of the terms from Lang, “Inclination.” Compare Weisheipl, “Interpretation,” 523–527. 29 Lang, “Inclination,” esp. 224–251. See also Lang, Order, 28–32. For examples from medieval philosophy, see Goddu, “Avicenna.” 30 Quaestiones cracovienses, Q. 34, 65–67. Q. 35, 67–69: “Per hoc ad rationes: . . . “Ad secundam dicitur, quod, licet caelum in se non habeat principium activum, habet tamen in se principium passivum. Unde intelligentia non inhaeret caelo, sed assistit ei sicut nauta navi. Similiter dicitur de corruptione, quae habet principium passivum intrinsecum, et hoc est pro ultima conclusione.” Compare Aristotle, Physics II, 1, 192b8–32. The text is reproduced more fully in Appendix II, text 1. The sailor/ship analogy is ultimately of Platonic origin (Plato, Republic I, 332e and 342d–e), although

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solution combines the idea of nature as a principle of motion with the idea that nature is an internal cause of motion and functions as a mover, even if passively. The Quaestiones, however, also preserve the distinction between the actual and potential, although in the account of celestial motion, the celestial motor is extrinsic leaving matter as the internal passive principle of motion. Natural place is characterized as a wonderful power attributed to place itself as an appetite or inclination of simple bodies that makes all things naturally tend to and seek their proper place as their being. In place is a natural immobile power that saves or preserves the bodies placed.31 The language of natural place while retaining the notion of inclination also suggests that place is a receptacle where elements of the same kind are better preserved. The text also implies that the inclination is a power or force (virtus) implanted in things by God.

scholastic philosophers may have relied on Averroes or Averroist interpretations for this metaphor. 31 Quaestiones cracovienses, Q. 74 pp. 127–128: “Per hoc ad rationes: Ad primam dicitur, quod quantitas etiam consideratur a physico sub esse naturali. In loco autem est virtus naturalis immobilis salvativa sui locati. Unde, quia posteriora non abstrahunt a prioribus, licet econverso, physicus, qui est posterior artifex, etiam considerat entia mathematicalia, minus tamen abstracte. . . .” Compare Aristotle, Categories 6, 5a1–15; Physics IV, 1, 208a27–32; IV, 4, 212a20–21. The expression salvativa sui locati is difficult to translate, but the idea is that in its natural place an element is conserved, saved, or preserved. Compare Aristotle, Physics IV, 1, 209a4–18. See Appendix II, text 2, for a more complete text. See also Sarnowsky, Aristotelisch-scholastische Theorie, 191. Dilwyn Knox kindly led me to the following sources. See Cicero, De finibus bonorum et malorum IV, vii 16: “Omnis natura vult esse conservatrix sui, ut et salva sit et in genere conservetur suo.” In this and other like comments, Cicero is repeating Cato’s defense of Stoic ethics, but the contexts are restricted to natural organisms, and only by extension to the whole of nature. The scholastics may have derived their conception from Stoic philosophy. See Thomas Aquinas, Opera omnia, De natura loci, 635, col. b: “Locus autem naturalis non nominat solum aliquid continens, sed continens et conservans et formans locata, propter quod unumquodque corpus naturaliter movetur ad locum suum tamquam ad conservativum esse sui.” Also Albert of Saxony, Questiones in libros de celo et mundo III, q. 7, fol. sig. H4vb: “Tertia conclusio: locus naturalis est causa agens respectu locati non per motum producentis ipsum, sed per motum conservantis quando locatum iam fuerit in eo. Nam locus conservat locatum, tam per virtutem elementarem, quia secum convenit in una qualitate elementari, quam per virtutem a celo influxam. Quarta conclusio: locus deorsum potest dici causa finalis gravis. Et similiter motus eiusdem, ratione illius virtutis conservative. Quia propter hoc grave naturaliter appetit et intendit esse deorsum, scilicet, ut ibi naturaliter conservetur. Quinta conclusio: si locus accipiatur non pro loco continente, nec pro superficie eius, sed pro ista virtute conservativa quam celum ad talem distantiam influit, tunc locus potest dici causa formalis ipsius locati sibi inherens, quando locatum est in suo loco naturali.”

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John of Glogovia minimizes the mechanical features of the account, preferring to express the more rapid motion of a heavy body downwards as a function of being joined to its perfection. That is to say, the stress here is on the relation of potentiality to actuality, matter to form. Similarly in the discussion of celestial motion, he prefers to express the motion in intellectual and volitional terms, reinterpreting succession in terms of its effect on lower spheres.32 3.2. The Infinite Aristotle denied an actual infinite, admitting infinity only potentially. One of the problems with which medieval philosophers struggled was the sense in which the last heaven is in place. The Quaestiones reports all of the alternatives, citing several authors of the ancient and medieval traditions, including the view favored by Averroes, Albert the Great, and Giles of Rome, namely, that the heaven is in place accidentally by virtue of the fact that the center of the universe is in place essentially.33 The Quaestiones settles for the solution attributed to Aristotle, Themistius, and Thomas Aquinas, namely, that the heaven is in place accidentally limited by the parts in the circle, which contain one another.34

32 I cite Johannes de Glogovia, Quaestiones in octo libros Physicorum Aristotelis, BJ, MS 2017. John renumbered the questions from the Quaestiones cracovienses by combining several questions into one. For example, John’s q. 43 corresponds to qq. 74–76, and his qq. 45–48 to qq. 80–87. When I compare the numbers between the two texts, I use the abbreviation QC for Quaestiones cracovienses. See Appendix II, text 3. 33 Q. 81, pp. 138–139: “Utrum ultima sphaera sit in loco. “Arguitur, quod non, quia locus est ultimum corporis continentis; sed ultima sphaera continetur; igitur etc. “Secundo: Caelum omnia continet et est circulare, et ergo a nullo continetur, et per consequens sequitur, quod non est in loco. . . . “Ex conclusionibus sequitur correlarie, quod caelum per accidens est in loco, quia per partes, in quibus est; partes autem per se sunt in loco in potentia. Secundo ponitur, quod motus caeli est actualissimus, quia tantum variat locum in potentia, et hoc est rationale, quia in primo caelo est minima diversitas, unde plurimum habet de entitate et unitate, et minimum de deformitate. . . . “Dicit enim textus: ‘Alia secundum accidens in loco sunt, ut anima et caelum; per partes enim in loco quodammodo sunt omnes, in eo enim, quod circulariter sunt, continent alia aliam.’ “Ad rationes dicitur, quod sunt pro prima conclusione.” For a more complete version of the text, see Appendix I, text 5. Compare Aristotle, Physics IV, 5, 212b18–22; Thomas Aquinas Physicorum Expositio IV, 7, 475 (4)–480(9). On Averroes’s solution as falling under the “accidental,” see Trifogli, Oxford Physics, 192. For further background, see Trifogli, “Place of the Last Sphere,” 342–350; eadem, “Egidio Romano,” 217–238. 34 Quaestiones cracovienses, Q. 16, 31–32. See Appendix II, texts 4 and 5. For background, see Świeżawski, L’univers, 53–61.

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On the question of the last celestial sphere, the Quaestiones considers the objection that beyond the last celestial sphere, we apprehend an infinite space. Every body is limited both extrinsically and intrinsically, but the last heaven, however, has no extrinsic limit, only an intrinsic limit. Our ability to imagine an infinite space is not an apprehension, for our intellect apprehends that beyond heaven there is nothing.35 Even more controversial fourteenth-century authors like Albert of Saxony concluded that space is not infinite.36 In John of Glogovia’s version of the question we find a discussion that sets out the various options and standard solutions, yet, as in many other questions, he ends his analysis with objections and doubts. He evidently preferred the philosophical conclusion that heaven is not in place, but John often adds theological considerations, as he does in this case. Perhaps, then, his intention was to leave the question for students to ponder.37

35 Q. 66, 114–116: “Utrum aliquod corpus sit infinitum. . . . “Quarto: Omne corpus particulare finitur, ut terra ad aquam, aqua ad aerem; igitur etc.; ergo non datur ultimum corpus, quin illud non fineretur ad alterum. “Quinto, quia res correspondet apprehensionibus nostris; sed nos apprehendimus extra caelum spatium infinitum; ergo ibi est infinitum. . . . “Ad quartam, cum dicitur: ‘omne corpus est finitum,’ dicitur, quod corpus finitur termino extrinseco et intrinseco, sed ultimum caelum finitur solum termino intrinseco et non extrinseco. “Ad quintam, cum dicitur de imaginatione, respondet Aristoteles, quod imaginationi non est credendum. Et causa est, quia imaginatio habet organum continuum, ideo iudicat continua; intellectus autem existens prohibet extraneum, tertio De anima, sed intellectus, quia non habet organum continuum, ideo apprehendit extra caelum nihil esse etc.” Compare Aristotle, Physics III, 5, 205b24–31. On the notion of an infinite void, see Furley, “Aristotle and the Atomists,” 85–96, esp. 92–94; Grant, “Medieval Doctrine of Place,” 59–64. Compare also Aristotle, Physics IV, 5, 212b18–22; Thomas Aquinas Physicorum Expositio IV, 7, 475 (4)–480(9). 36 Albertus de Saxonia, Expositio et Quaestiones in Aristotelis Physicam, 2: III, q. 13, 580: “Ad tertiam dico quod extra caelum non est aliquod spatium; et si Deus extra caelum crearet unam fabam, tunc etiam crearet spatium extra caelum tantum quantum est illa faba, et illud spatium esset illa met faba. Et ulterius dico quod, si Deus moveret illam fabam a caelo, non propter hoc faba distaret a caelo, recte sicut dicebatur de lapide moto ab uno latere caeli ad aliud, omni annihilato quod esset infra latera caeli.” See also Sarnowsky, Aristotelisch-scholastische Theorie, 164–186 and 456–457. 37 Johannes de Glogovia, Quaestiones, [Q. 45], f. 155v: “Conclusio secunda. Ultima sphera est in loco non per se sed per accidens et non ratione partium ergo centri. Patet conclusio quod ultima sphera non est in loco per se. Illud quod est in loco per se continetur ab aliquo, sed ultima sphera a nullo continetur. . . . Sequitur corrolarie secundo quod consequendo positionem theologorum de localitate ultime sphere, ultimum caelum est per se in loco. Patet quia ipsi ponunt quod primum caelum sive

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3.3. Celestial Spheres and Celestial Matter Medieval theologians could not concede to Aristotle the eternity of celestial matter; instead they proposed three solutions to questions about corruptibility and incorruptibility. Some held that celestial matter is different in both genus and species and that while naturally incorruptible, it is supernaturally generable and corruptible. Others maintained that celestial and terrestrial matter are of the same genus but of a different species. They further concluded that even celestial matter has potency to place, although in a way different from terrestrial matter. And still others argued for the essential identity between celestial and terrestrial matter while acknowledging actual differences in fact. In all of the fifteenth-century sources no one at Cracow argued that celestial and terrestrial matter are of the same species, and they all rejected or modified the doctrines advanced by Aristotle and Averroes. The Quaestiones elaborated all of the connotations of matter, concluding that whatever has actual being has it from the form. Matter does not have actual being, only potential being.38 The Quaestiones adopted the view that celestial and terrestrial matter belong to the same genus but differ in species because their natural motions differ.39 On the question of perpetual circular motion, the author displays familiarity with basic facts of astronomy and also explicitly rejects Aristotelian doctrine as contrary to the Catholic faith.40 The Christian

ultimam spheram continetur a caelo quoddam immobili ut a caelo empireo in quo est sedes dei et sanctorum. Et sic primum caelum vel ultima sphera quia continetur a caelo immobili empyreo per se est in loco eo quod continetur ab ipso. Sed caelum empyreum nullo modo est in loco quia sed quiescit quia ordinatur ad quietem limitarum. Locus enim debet coaptari locato et ideo philosophi non noscentes illam latitudinem ponunt esse caelum mobile.” 38 Quaestiones cracovienses, Q. 22, pp. 44–45: “Utrum materia sit aliquid positivum in natura. . . . “Secundo sciendum: Materia habet quaedam nomina propria et quaedam nomina ei attributa per metaphoram. Nomina propria sunt haec: hyle, materia, massa, subiectum, origo et elementum. Hyle nominat substantiam materiae et est proprium suum nomen. Dicitur materia, ut ex ea tamquam ex matre exeunt formae. Dicitur massa, quia ei primo convenit corpulentia. Dicitur subiectum, in quantum suscipit formam. Dicitur origo, quia praecedit compositum. Dicitur elementum, quia manet in composito facto ex ipsa, quia elementum est, ex quo fit aliquid, cum insit. . . .” The answer is that whatever has actual being has it from the form. Matter does not have actual being, but it does have potential being. Compare Aristotle: Physics II, 2, 194a. See also Świeżawski, L’univers, 149–241. 39 See Appendix II, text 6. 40 See Appendix II, texts 7–9.

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belief in creation falsifies the Aristotelian doctrine of the eternity of the world.41 John of Glogovia preferred to solve the question about celestial and terrestrial matter by siding with the view of Thomas Aquinas that there is celestial matter but it is of a nature different from that of terrestrial matter.42 In dealing with questions about eternity and creation,

41 Q. 136, 241–243: “Utrum in omni motu necesse sit mobile in puncto reflexionis quiescere. . . . “Sed diceres, quod in circulo motus ab oriente non impedit eum, qui est ab occidente, ut patet in sphaeris planetarum, quae duplici motu moventur. Dicendum, quod illi motus non sunt super eosdem polos facti, sed super diversos; omnes enim planetae moventur ab oriente in occidens super polos mundi et omnes moventur ab occidente in oriens super polos zodiaci.” See Appendix II, text 9. Compare Thomas Aquinas, Physicorum Expositio VIII, 18, 1123 (1); VIII, 19, 1134 (6). Q. 137, pp. 244–245: “Utrum motus circularis possit esse continuus et perpetuus . . . “Secunda conclusio Aristotelis est, quod motus circularis est continuus et perpetuus. Patet, quia motus localis est perpetuus et non rectus, ut iam probatum est in praecedenti quaestione, ergo circularis. Tenet consequentia ex sufficienti divisione. Verum tamen est, quod ista conclusio non est catholica, immo falsa. Dicimus enim et firmiter credimus, quod motus caeli incepit determinato principio temporis; sed hoc non habemus per philosophiam, sed per prophetiam. Prima vero conclusio simpliciter conceditur . . .” See Appendix II, text 9. Compare Aristotle, Physics VIII, 9, 265a13–15. 42 Johannes de Glogovia, [q. 19], f. 70v–75v. See Markowski, Filozofia, 166–167, nn. 139–143, for the following texts, which I have corrected from BJ, MS 2017: ff. 71r–73r: “Notandum secundo, secunda questio partialis querit, utrum omnium corporalium rerum, ut inferiorum et corporum celestium, sit una materia. De materia presentis questionis varie inveniuntur opiniones. Una est positio Commentatoris, quod in celo nulla sit materia et quod celum non sit compositum ex materia et forma . . . Egidio autem et doctor Sanctus et generaliter omnes philosophi huius oppositum determinant ponentes in celo esse materiam et dicunt hoc esse de mente et intentione Aristotelis. Dicit enim Aristoteles primo Celi: Cum dico ‘celum’ dico formam tantum, sed cum dico ‘hoc celum’, dico formam in materia. Constat autem quod illud, quod habet materiam, est compositum. Forma enim et materia rem naturalem compositam efficiunt, ut primo Physicorum . . . Licet Egidium et Thomas ambo concedunt materiam in celo, tamen diversificati sunt. Thomas enim dixit, quod materia istorum inferiorum et celi non esset eiusdem rationis. Egidius vero tenet, quod materia celi est eiusdem rationis cum materia inferiorum . . . Egidius autem econverso rationibus plurimi ostendit, quod eadem sit materia celi et inferiorum. Et dicit, quod hoc est de mente precipuorum doctorum et maxime katolicorum . . . concludit ergo Egidius, quod materia inferiorum et celi est eadem per essentiam. Quia ergo iste positiones Commentatoris et Egidii non sunt communes in philosophia, sed positio doctoris Thome communiter approbatur, ideo probabiliter ponitur conclusio quo ad hanc questionem partialem ista. Conclusio responsalis: Materia celi et istorum inferiorum non est una, sed materia istorum inferiorum est alterius rationis a materia corporum celestium.” See also John of Glogovia, Komentarz, VIII, [q. 50], 94–108, where he cites Gabriel of Verona. The relevant difference between the views of Giles of Rome and Thomas is that Thomas allows no mixture of celestial matter with privation. In celestial matter,

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John repeatedly cites Albert the Great in pointing out the differences between Aristotle and Moses. He attempts to rescue the Aristotelian view by relativizing the notion of the eternity of the world as coeval with the creation of time.43 3.4. Mathematics and Natural Philosophy There were many developments during the Middle Ages related to the role of mathematics in philosophy and theology.44 There is almost no evidence in Cracow of these developments. The increased use of mathematics in the fourteenth century as a language useful for finding the mathematical principles by means of which we may prove known or accepted conclusions in astronomy is far from saying that mathematical form exhausts the matter of each specifically different body, that is, Sun, Moon, and the other planets. On Gabriel of Verona, see Włodek, Filozofia bytu, 17, 28 (n. 54), 32 (n. 84), 43, 54 (nn. 54–55), 74, 90 (n. 65), 122, and 152 (n. 175). Włodek refers to Gabriel as Gabriel Zerbus of Verona, and maintains that he attempted to reconcile the doctrines of Thomas Aquinas with those of John Duns Scotus. The Jagiellonian Library possesses one copy of his commentary on the Metaphysics, a text published in Bologna in 1482, BJ, Inc. 1049. Finally, in a more recent study, Baldner, “Thomas Aquinas on Celestial Matter,” 431–467, argues that Thomas did not hold that there are two kinds of prime matter, but he too acknowledges the problems related to hylomorphism and the incorruptibility of the heavens. For a summary of Buridan’s account and his reading of Thomas Aquinas and Giles of Rome on celestial matter, see Ghisalberti, Giovanni Buridano, 169–176. I owe this reference to Dilwyn Knox. 43 Ibid. [Q. 78] = QC, q. 126; f. 219r–221r. John makes the same distinction between time and motion on the one hand and eternity and creation on the other. Aristotle is right, but time was created with the world. This is also the view adopted by Michael Falkener, suggesting that Albert the Great is the source. [Q. 79] = QC, q. 126; f. 221r: “Utrum mundus sit eternus, ut Aristoteles docuit vel a Deo in certo tempore creatus, ut Propheta Moyses scripsit.” Albert is cited throughout as the primary authority, for example, f. 223v: “Immo dico quod Aristotelis non consuevit dicere in philosophia nisi physica que rationibus physicis possunt probari. Sed inceptio mundi per creatorem nec physice potest probari, et ideo hanc viam Aristotelis creditur tacuisse in philosophia. Tamen tangit eam expresse in libro De natura deorum quem ipse edidit hic Albertus. Iste scilicet est haec conclusio responsalis fidelis et katholica. Mundus secundum veritatem non est eternus. Patet, illud quod incepit non est eternus, sed mundus incepit, igitur mundus non est eternus.” 44 Goddu, “Teaching,” 62–69, summarizes these developments with bibliography. When Copernicus proposed his new theory, he was following fifteenth-century trends that go back at least to Regiomontanus. He may have been influenced by a more Platonic view about the power and utility of mathematics, but there is no evidence that he adopted a Pythagorean or Platonic metaphysical interpretation of mathematics. In fact, he seems to have been completely unaware that he was violating an Aristotelian prohibition. On the contrary, he regarded his move as compatible with examples approved by Aristotle himself. Even Copernicus’s comparisons of “natural” with “health” and “unnatural” with “sick” have an Aristotelian basis that goes back to legitimate examples of metábasis. But more on these subjects in chapters nine and ten.

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principles may be used to prove conclusions in natural philosophy that are contrary to widely accepted conclusions. In other words, the scope of natural philosophy as superior to mathematics remained intact. With those qualifications in mind, we may note and emphasize the role of dialectical topics in evaluating and constructing arguments. In Cracow, as we saw, dialectical techniques served to emphasize relevance in the evaluation of consequences. The author of the Quaestiones frames such questions in a conventional way according to the standard Aristotelian distinction between the order of nature and the order of knowledge. Metaphysics is prior to mathematics which, in turn, is prior to physics in the order of nature, but the priority is reversed in the order of cognition.45 Even when the question is put in terms of physical science, the three are distinguised according to their proper subjects. Physics considers movable bodies, mathematics considers magnitudes and shapes as attributes of the movable bodies, and metaphysics considers separate substances as causes and principles of motions. As we saw above, the analysis of the infinite is subordinated to metaphysical issues, which tends to discourage the development of mathematics as a tool of conceptual analysis. For example, in the discussion of magnitudes and divisibles, the mathematical analysis is clearly subordinated to the physical.46 The

45 Quaestiones cracovienses, Q. 1, 1–3: “Utrum inter tres scientias speculativas reales naturalis philosophia ordine doctrinae sit prima, mathematica secunda, metaphysica tertia . . . “Istis notatis sit prima conclusio: Ordine rei quaesitae et scibilis metaphysica est prima, mathematica secunda, physica ultima, quia ea, quae considerat metaphysica, sunt maxime abstracta et per consequens secundum naturam prima; similiter ea, quae considerat mathematica, sunt magis abstracta quam ea, quae considerat physica, et per consequens ordine rei scibilis prima est prior naturali philosophiae, quae est de magis concretis. “Secunda conclusio: Ordine doctrinae et quo ad nos physica est prior, deinde mathematica, postremo metaphysica. Probatur, quia propter reflexionem intellectus nostri ad sensum omnis nostra cognitio inchoari habet via sensus; ergo quae sunt sensibilia, imaginabilia et intelligibilia, maxime sunt proportionata modo nostrae cognitionis, sicut sunt physica. Patet ex alio: modus nostrae cognitionis est de potentia ad actum procedere; cum ergo entia physica sunt propinquiora aliis, quia minus abstracta, ergo ab eis inchoabitur nostra cognitio.” Compare Physics I, 1, 184a 24–184b26. 46 Q. 17, pp. 33–35: “Utrum entia naturalia sint determinata ad maximum et minimum . . . “Secundo sciendum, quod magnitudo consideratur dupliciter. Uno modo physice, et sic capitur magnitudo, ut est dimensio materiae, in qua est forma physica. Alio modo capitur mathematice, et sic abstrahit a materia physica. Unde capiendo materiam mathematice, non datur minima, immo quacumque data ipsa est divisibilis in minorem, cum semper quantitatis divisibilis sit. Etiam non repugnat ei, quantum est

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specific question about the relation between physics and mathematics follows the Aristotelian analysis.47 John of Glogovia followed Albert the Great in regarding movable body as the proper subject of natural philosophy. John also adopted the solution that the priority of metaphysics, mathematics, and physics depends on the distinction between the order of nature and the order of cognition.48 On the relation between mathematics and natural philosophy, John tended to see them as in agreement, arriving at the same conclusions but by different means. The physicist demonstrates the sphericity of Earth by means of the natural motion of heavy bodies in a straight line towards the center. Astronomers base their proof on

ex parte quantitatis, nec etiam quantumcumque augeri. Est ergo quaestio hic solum de entibus naturalibus. Unde ens naturale dicitur, quod est compositum ex materia et forma physicis, modo omnia talia habent quantitatem. Ex quo sequitur, quod hic non est facienda quaestio de terminis, quibus terminantur potentiae naturales, ut qualiter terminatur potentia portativa etc., sed solum quaestio est de entibus naturalibus compositis ex materia et forma physicis. Sed qualiter potentiae terminantur, habet videri primo Caeli. “Istis praemissis est prima conclusio: Entia naturalia sunt terminata ad maximum et ad minimum. Probatur conclusio: quia entia naturalia non principiant operationes naturales nisi per magnitudinem, sed omne instrumentum operis terminatur versus excellentiam et versus defectum. . . . “Conclusio secunda: Magnitudo mathematice accepta nec terminatur ad maximum nec ad minimum. Patet ex ultimo notabili. Sed accepta secundum esse, quod habet in re naturali, terminatur ad maximum, et ad minimum, quia datur maxima magnitudo, sub qua potest stare forma Socratis. Similiter datur minima. Et fundamentum huius et praecedentis conclusionis est, quia forma finit materiam et materia formam. Ex hoc sequitur, quod nullum potest esse corpus naturale infinitum.” 47 Q. 38, 72–73: “Utrum physicus differat a mathematico. . . . “Secunda conclusio: mathematicus et physicus semper differunt ratione. Patet, quia physicus considerat entia, ut sunt materiae coniuncta, ut quantitatem considerat, ut est terminus materiae; sed mathematicus considerat abstracta a materia sensibili. Hoc etiam patet inductive in singulis, quae considerat physicus et mathematicus. Nam simul considerat physicus et concipit materiam in eius definitione, quia simitas definitur per nasum; est enim simitas nasi curvitas. Mathematicus vero considerat curvum, quod abstrahit a materia secundum definitionem; definitur enim sic: curvum est, cuius medium exit ab extremis. Et sic patet, quod physicus necessario differet a mathematico, quia formalis ratio subiecti physici et subiecti mathematici differunt, quia in ratione subiecti physici ponitur materia, non autem in ratione subiecti mathematici. “Sed diceres: Astronomus est mathematicus et considerat corpora mota, cum ergo motus non abstrahit a materia, mathematicus non abstrahit a materia. “Respondetur secundum Averroem secundo Metaphysicae, quod astrologus considerat corpora mota, non ut sunt mota, sed considerat de figura et situ corporum caelestium motorum secundum quantitatem motus, quia secundum alium et alium motum corpora coelestia faciunt aliam et aliam figuram inter se et alium et alium situm.” Compare Aristotle, Physics II, 2, 193b22–24. 48 Johannes de Glogovia, [qq. 1–4], ff. 2r–13r.

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the shape of eclipses, the rising and setting of stars, and on the shadow of Earth on the Moon in a lunar eclipse.49 3.5. Impetus and the Void Among the most innovative revisions of Aristotle in the Middle Ages was the doctrine of impetus. Characteristic of medieval scholastics, they tried to present the doctrine as an improvement on the Aristotelian account and essentially in conformity with it. By the last quarter of the fifteenth century, however, Cracow philosophers report the theory but often without adopting it.50 The Quaestiones does not adopt the principle of impetus in its fourteenth-century forms to account for projectile motions, nor do the texts apply the principle to explain heavenly motions. 51 Impetus is not transmitted directly from the projector to the projectile. The text attri49 Ibid. f. 101v–104v [Q. 28] = QC, q. 38. [Q. 28], f. 103v (427): “. . . propter magnam convenienciam astronomie cum phisica tunc astrologia et phisica demonstrant eandem conclusionem, ut quod terra est sperica. Naturalis enim phisicus demonstrat hanc conclusionem per medium naturale, ut quod [terra] est gravissimum corpus et per consequens eius partes equaliter concurrunt ad medium. Astrologus autem probat [illam] conclusionem ex figura eclipsis, ex ortu et occasu stellarum et umbra in eclipsi lune incidente in lunam.” Compare Thomas Aquinas, Summa theologiae IIaIIae, q. 1, a. 1. 50 Goddu, “Teaching.” I discuss this question and Copernicus’s acquaintance with the concept of impetus in detail in chapter nine. See Appendix II, text 10. 51 Q. 122, 215: “Utrum omne movens sit simul cum suo motu sive cum re, quae ab ipso movetur. “Arguitur primo, quod non, quia movens et mobile sunt duo corpora; sed, ut patet ex dictis in quinto, duo corpora non sunt simul; ergo nullum movens est simul cum mobili. . . . “In oppositum est Aristoteles. “Pro responsione sciendum: Illa vere sunt simul, quae in eodem loco primo sunt, et tamen aliquando in analogia ad istum modum corpora dicuntur simul, inter quae non mediat aliquod corpus, et sic accipitur in proposito. “Secundo sciendum, quod tres sunt species motus, scilicet motus localis, alteratio et motus ad quantitatem; motus vero localis dividitur in naturalem, qui fit a principio intrinseco, et violentum, qui fit a principio extrinseco. Motus autem violentus dividitur in quattuor species, quae sunt pulsio, tractio, vectio et vertigo. Quarum sufficientia sic sumitur: Nam omnis motus violentus vel est per se, vel per accidens. Si per accidens, sic est vectio, nam illud vehitur, quod movetur motu alterius. Si sit motus per se, hoc dupliciter aut est compositus, aut est simplex. Si sit simplex, hoc dupliciter: vel movens extrinsecum movet ad se, sic est tractio, vel a se, sic est pulsio. Si vero sit compositus, sic est vertigo: componitur enim motus vertiginis ex pulsu et tractu, qualis est motus mobile fabri. “Ex istis patet, quod motus vectionis dividitur in quattuor species, quia illud, quod vehitur, movetur motu alterius, illud ergo movetur naturaliter vel violenter, et hoc contingit tribus motibus per se violentis. Secundo patet, quod omnis motus localis

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butes to Aristotle the view that the projector condenses the air next to it and impresses its power or force onto the air, which again rarifying itself condenses the air next to it, and so on until the force dissipates. It is not necessary for the motion of the projector to be in continuous contact with the projectile, because diverse motors move the projectile, namely, the diverse parts of the air. Nor is it necessary for everything to be moved, for even though the air yields to the projectile, it does so by means of condensation. Impetus, then, participates in the motion of the projectile for the impetus is in the air. This is clearly a compromise solution that combines the theory of impetus with Aristotle’s account, and it does so in a way that makes it look compatible with the Aristotelian account.52 The fourteenth-century Parisian views about impetus were also known at Cracow. Albert of Saxony adopted impetus, described as a motive power and quality, to account for projectile motion, explaining that the greater distance achieved by one body over another is due to

violentus reducitur ad duas species, scilicet pulsum et tractum, quia vectio reducitur ad illas tres et vertigo redicitur [sic] ad illas duas sicut compositum ad simplicia . . .” 52 Q. 141, 250–252: “Alia opinio est Aristotelis, quod proiecta moveantur a proiciente, qui condensat aerem iuxta se, ei impremendo suam virtutem, qui se iterum rarefaciens condensat alium aerem, et sic consequenter quousque cessat violentia . . . Moderni autem ab Aristotele differunt, quia ponunt impetum in ipso proiecto, sed Aristoteles ponit proiectum ab aere motum moveri. Ex istis sequitur, quod motus proiectorum non est continuus, quia proiecta moventur a diversis motoribus, scilicet a diversis partibus aeris, ut dictum est. Secundo patet ex dictis, quod non oportet omnia moveri, tenendo, positionem Aristotelis; licet enim aer cedat lapidi proiecto, tamen hoc est per condensationem. Tertio, patet ex dictis, quod impetus concurrit in motu proiectorum, est enim in aere.” Of course, the interpretation seems to be supported by Aristotle himself in De caelo III, 2, 301b20–30. Aristotle’s comments are vague, encouraging elaboration and thereby supporting the combination of the two theories. Modern translations have had to resort to interpretations that also represent Aristotle’s view in terms of a transmission of force to the air. What all agree on is that Aristotle attributes an instrumental role to air, and I suggest that one way to understand the transmission is directionally. That is to say, the force determines the instrumentality of air as light and hence upwards or heavy and so downwards, thus explaining the direction of the continued motion, not the cause of the motion itself. See Lang, “Inclination,” 251–260. Cracow philosophers followed a variety of commentators (Albert the Great, John of Jandun, Lawrence of Lindores, Andrew of Kokorzyna, John Versor, or a Leipzig commentary) in their rejection of impetus and for their compromise view. Versor rejected impetus altogether. See Palacz, “Streit,” 103–107. One source for the compromise as adopted at Cracow was Lawrence of Lindores. See Markowski, Burydanizm, 119–120 and 152–153; and Seńko, “Philosophie médiévale en Pologne,” 16. On Andrew of Kokorzyna, see Markowski, Burydanizm, 121–122, and Markowski’s summary, 534–535. On impetus, see Maier, Zwei Grundprobleme, Studien, 2: 113–314: “Impetustheorie.”

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its greater mass or density. Likewise, a falling body accelerates because as it moves, it acquires a certain ability or aptitude with its heaviness that causes it to move more rapidly. The reference to ability shows that he adopted this explanation from Nicole Oresme. Finally, he also resorted to impetus to replace the theory of intelligences with a motive force imparted by God at creation to the celestial spheres.53 John of Glogovia tends to follow the Quaestiones cracovienses, sometimes settling questions that are left open. For example, on succession with respect to heavenly motions, he prefers the solution that relies on the relation between the intelligences as movers and their end, the generation of inferior substances.54 John provides the same answers on questions about the mover and moved and on the analysis of natural and violent motions.55 John also mentions the theory of impetus and follows the interpretation that transfers the impetus to the air, representing it as an interpretation of Aristotle’s account.56

53 Albert of Saxony, Quaestiones, VIII, q. 13, 1074–1075: “Alia opinio est quam pro nunc reputo veriorem. Et est quod proiiciens imprimit proiecto quandam virtutem motivam quae est quaedam qualitas quae innata est movere, nisi fiat impedimentum aliunde ad eandem differentiam positionis ad quam proiiciens proiicit. Et secundum istam opinionem possunt reddi causae quarundam experientiarum. Primo: quare lapis proiicitur remotius quam pluma? Breviter huius causa est ista: quia, ex quo lapis habet plus de materia et est magis densus quam pluma, plus recipit de illa virtute motiva et diutius eam retinet quam pluma, et sic diutius movetur post remotionem eius a proiiciente quam pluma; et etiam fortius percutit, propter hoc quod habet plus de illa virtute motiva sibi impressa. . . . Et ex consimili modo potest reddi ratio quare motus naturalis velocitatur in fine: nam mobile, quando movetur naturaliter, acquirit sibi quandam habilitatem ex tali motu, quae quidem habilitas sibi acquisita unacum gravitate eius movet ipsum velocius. Iuxta istam opinionem posset dici quod non est necesse ponere tot intelligentias quot sunt orbes. Unde diceretur quod Prima Causa, cum creavit orbes caelestes, cuilibet eorum impressit unam talem qualitatem motivam quae illum orbem taliter movet, nec illa virtus motiva ibi corrumpitur, propter hoc quod talis orbis non est inclinatus ad motum oppositum.” See also Sarnowsky, Aristotelisch-scholastische Theorie, 58–64, 253–254, and 320–321. 54 Johannes de Glogovia, [Q. 47] = QC, q. 86; f. 159v–161v. See, for example: f. 161v : “Dubitatur primo unde proveniat successio in motu celesti. Dicendum quod tenendo, quod intelligencia moveat celum naturaliter, tunc successio provenit ex resistencia mobilis, quia ut corpus celeste est in uno situ quodam modo resistit moventi, ut est in alio situ, sed tenendo, quod intelligencia celum movet intellectualiter et libere, ut dicit Albertus. Dicendum quod successio provenit ex parte finis, intelligencia enim movet celum tanta velocitate quanta exigit finis motus celestis, qui est generacio istorum inferiorum, que requirit successionem.” Compare John of Glogovia, Komentarz, XII, [q. 67], 183–189. 55 Ibid. [Qq. 80–81], ff. 225v–228r. For example, f. 225v: “Conclusio secunda. Omne quod movetur ab alio movetur et habet motorem ab ipso distinctum.” 56 Ibid. [Q. 88], ff. 239r–240v. The text has been published by Markowski, Burydanizm, 177–181, and I have corrected it from the manuscript in Appendix II, text

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3.6. Dialectical Topics Specific to Natural Philosophy The principal logical topics applied to physical examples are species of from the cause. These are conventional applications. Of somewhat greater interest are the examples of from the whole and from the part. These often involve as well the interpretation of the containing and the contained. The principles are relevant to settling the question about the place of the last heaven or the entire universe. Those who hold that the parts of the last heaven are in place by relation to the center contrast this with the view that the last heaven is in place accidentally. The idea here is that the center is in place essentially, hence the parts are in place by relation to the center. On the other hand, those who hold that the parts are in place accidentally maintain that the part containing

11. The question begins: “Utrum proiecta cessante proiciente moveatur a medio, per quod ferunter, ab ipso proiciente? . . . “Et ideo Philosophus ponit unam aliam solutionem et est: Proiciens movet aerem proximum circa se et ille aer movet alium aerem proximum circa se et ille aer movet alium aerem et sic ulterius donec cessat virtus proicientis in aere et illa virtute deficiente deficit motus. Et est simile de inclinationibus, quia parte mota ista movet aliam partem et ulterius ista pars movet aliam, donec cessat virtus primi moventis, sic etiam est in aere, quamvis non ita manifeste apparet ad sensum. Sequitur corrolarie, quod positio Platonis, que dixit proiecta moveri per antiparistasim et per partium positionem, scilicet quod cum proiectum dividit aerem quo aere terminato proiectum se veniret impetuose et impelleret sic impetuose proiectum. Sic etiam sequeretur, quod moto lapide celum moveretur. Lapis enim motus movet aerem et aer iterum alium, cui alter cedit et sic uno motu omnia moverentur. Unde et ipse dixit, quod sicut navis mota cum decursu procellarum deferuntur per impetum, qui est in procellis, ita etiam moveretur proiectum ab aere, in quo est virtus proicientis et tertio Celi loquens de hac opinione dixit, quod aer est organum et instrumentum in motu gravium et levium. [Cf. Aristotle, De caelo III, 2, 301b16–25.] “Notandum quarto, quod proiecta moventur a pluribus consequenter se habentibus, cuius rationem assignat Aristoteles in textu istam, quia quanto aliqua virtus est fortior, tanto distantius se diffundit in operationem, sic tamen, quod semper proximum movens simul sit cum proximo motu. Cum ergo virtus proiectiva sit, que virtus ergo diffundit se primo in proximo mobili, quod est aer et ille aer movet alium aerem proximum et etiam proiectum. Ille autem aer proximus ultimus movet remotiorem aerem et hoc fit donec cessat virtus proicientis et tunc etiam cessat motus et sic semper proximum movens est simul cum moto, quia ille aer, qui est immediate circa proiectum est proximum movens, ut declaratum est in declarationibus ipsius aque, in quibus una pars aque movet aliam. Sequitur corrolarie, quod in motu proiectorum est tria assignare: Primum quod est motum tantum et hoc est proiectum. Secundum quod est movens et motum simul et hoc est aer medium, quia talis aer movetur a virtute /f. 240r/ proicientis et movet ulterius ipsum proiectum. Tertium est movens tantum et proiciens. Sequitur corrolarie secundo, quod proiecta moventur a pluribus moventibus consequenter se habentibus, quia a partibus aeris consequenter se habentis. Una enim pars aeris movet aliam, donec cessat virtus proicientis.”

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is only potentially separated from the part contained.57 Likewise, the Quaestiones elaborates on the proper application of part and whole to physical cases.58 Such examples are especially relevant to Aristotle’s view about the motions of whole and part being identical. The Earth cannot have a circular motion, for if it did, each of its parts would have the same motion, but we always observe heavy bodies to move in a straight line towards the middle. It follows, then, that the Earth cannot rotate or otherwise move in a circular fashion.59 4. Aristotle’s De caelo, De generatione, Meteorologica, and Metaphysics With the last type of example, we may briefly turn to the other books of Aristotle summarized in the standard commentaries on De caelo, De generatione et corruptione, and Meteorologica. These are discussions in other contexts that discuss the following questions. Is figure or form a cause? What is the order and motion of the spheres? What is the significance of the distinction between medium mundi and medium terrae? Again these are subjects on which teachers at Cracow expressed opinions in the context of Aristotle’s other works and also in their commentaries on the Tractatus de sphaera. There is some overlap between the issues discussed here and the teaching of astronomy to be discussed in chapter five, but the discussion here is limited to a few important themes from De caelo as contained in standard commentaries used at Cracow. From De caelo, I begin with a brief survey of major themes in Aristotle that are relevant to Copernicus’s arguments. We may then focus on a few texts that influenced professors at Cracow and that represent the teaching at the university. The curriculum for the M.A. at Cracow was exceptional in paying attention to De caelo, De generatione et corruptione, Meteorologica, and the shorter physical treatises. Unlike other universities, the statutes at Cracow required students to devote four months each to De caelo and Meteorologica, the same amount as

57 Quaestiones cracovienses, Q. 81, 138–139. See Appendix II, text 5. Compare Aristotle, Physics IV, 5, 212b18–22; Thomas Aquinas, Physicorum Expositio IV, 7, 475 (4)–480(9). 58 Q. 97, 165–166. See Appendix II, text 12. Compare Aristotle, Physics V, 1, 224a23–26. 59 Aristotle, De caelo II, 14, 296a24–296b25.

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for De anima, ten weeks to De generatione et corruptione, and fourteen weeks to the Parva naturalia.60 For Aristotle the cosmos is a complete, synthetic whole, constituted of parts that are separate bodies. The universe is a perfect, single, allencompassing, three-dimensional, spherical body that is not part of a larger whole.61 Although Aristotle delays discussion of the question whether the universe is finite or infinite, he raises the question early to help the reader anticipate that the universe must be finite. He turns his attention to the formal parts or the elements, and the first apparent facts observable in their local motions. It is almost breathtaking to follow Aristotle in his reasoning. Simple motions correspond to simple magnitudes, and just as bodies are completed by the number “three,” so also are the motions of the simple elements—circular and straight (up and down). Compound bodies have the motion according to the prevailing element in their composition. From three assumptions—that there is simple motion, that circular motion is simple, and that simple motion is the motion of a simple body—he concludes that there must be a simple body that moves in a circle according to its own nature. Furthermore, circular motion has no contrary and must be primary, for that which is complete is prior to what is incomplete. The circle is a complete entity, but no straight line is. In equally rapid succession Aristotle draws the assumptions together—motion that is prior to another is the motion of a body that is prior in nature, circular is prior to rectilinear motion, and rectilinear is the motion of the simple bodies that move that way. From these assumptions he concludes that circular motion must be the motion of some simple body and it must be natural. If circular motion were unnatural, it would be exceptional, because in the rest of nature what is unnatural exhausts its motion rapidly. There exists, then, a physical substance that is a body different from those found about us, and it is more noble than those around us in proportion to its distance from our world.62

60 Statuta, XIII. On the comparative neglect of books other than Physics and De anima at most universities, see Weisheipl, “Interpretation,” 522–523. 61 De caelo I, 1, 268a1–b13. 62 Ibid. I, 2, 268b14–269b17. We should observe here that while the argument seems to be leading to the complete separation between the supralunar and sublunar realms, Aristotle’s language is comparative, and the argument proceeds by analogy with our experience of motion in the sublunar realm. Furthermore, as we shall see, the heavens influence sublunar motions!

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If the simple body has only one natural motion and the whole and part move together, then it is a body with its own distinct nature. If bodies that move toward the center are “heavy,” those that move away “light,” then the body that moves in a circle cannot be heavy or light. There is no motion opposite to the circular, nor can the primary body have an opposite, so it cannot have the kind of matter that is subject to generation and destruction, growth and diminution. Some of the ancients called the primary body “ether.” No one has ever recorded a change in it. Ether is not subject to alteration, is eternal, suffers no growth or diminution, and it is ageless, unalterable, and impassive. There is no contrary to circular motion. If there were a contrary to motion in a circle, it would be to no purpose, but God and nature do nothing in vain.63 At this juncture Aristotle returns to the question whether the cosmos is infinite. Aristotle recognizes how fateful the correct answer to this question is. The answer makes all the difference in our search for the truth. The wrong answer is the source of all subsequent contradictions in natural science, for a small error at the beginning is multiplied ten-thousandfold as the argument proceeds.64 The body that moves in a circle must be finite. We observe the heavens to revolve in a circle, an infinite body cannot revolve in a circle, a figure cannot be unlimited; therefore, the body that revolves in a circle must have a limit.65 That which moves towards the center and that which moves away from the center cannot be infinite, for they move towards opposite places. If one is determinate (the center), then so must be the other. The center is determined—it is that towards which all downward moving bodies tend. The upper place, then, must be determined; therefore, the bodies themselves must be limited. It follows that there cannot be an infinite body.66 All bodies move naturally and by constraint. Their natural motion is to that place where they rest without constraint. Individual bodies with the same form move towards one and the same place, one center and one circumference. There cannot be more than one world. There can be no bodies outside of or beyond heaven. The 63

Ibid. I, 3–4. We will see in chapter nine the relevance of this motif to Copernicus’s criticism of geocentrism. See also Thomas Aquinas, De ente et essentia at the beginning. Cf. Hamesse, Auctoritates Aristotelis, 161: (19) Parvus error in principio, maximus erit in fine. 65 De caelo I, 5. 66 Ibid. I, 6–7. 64

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world is made up of all of the available matter, that is, perceptible body. The world is one, unique, and complete. There cannot be place, void,67 or time beyond heaven, because there is not and cannot be body beyond heaven.68 The world is ungenerated and indestructible.69 In Book II of De caelo, Aristotle considers other characteristics that the ancients attributed to the world and the heavenly sphere, working his way eventually down to the Earth. Because the heavenly sphere is an animate and moving thing, for it contains within itself a principle of motion, it must have top and bottom, right and left, and front and back. The poles define top and bottom,70 the stars rising in the East define right, and similarly their forward and backward motion define front and back. Why the planets, Sun, and Moon have different circular motions from the fixed stars leads Aristotle to anticipate Earth at rest at the center with fire as its contrary along with the intermediate elements arranged in circles around Earth. The existence of the four elements made up of contrary qualities introduce change, generation, and destruction, which are caused by the oblique motions of the planets and especially the Sun producing day and night and the changes in the seasons. The first heaven or sphere of the universe in which the fixed stars are located is perfect, that is, spherical and uniform in motion.71 The stars consist of ether and because they are fixed in relation to each other move as a result of being carried around by the sphere or circles in which or to which they are fixed.72 Why does the primary motion include so many stars, whereas the other spheres have only one? In answering this question, Aristotle asserts that whatever is in the best possible state has no need of action.73 It is its own end. Action occurs when there is an end not yet

67

Even if void be supposed as that which can contain body. De caelo I, 8–9. 69 Ibid. I, 10–12. 70 Aristotle says that the pole above us is the lower part, and the one which is invisible is the uppermost (II, 2, 285b15–28), although he seems to adopt the contrary view with respect to the planets in the text just below (285b28–286a2). 71 Ibid. II, 1–6. 72 Ibid. I, 7–8. 73 Copernicus will use this principle in a modified form to explain the rectilinear motions of heavy bodies towards the center of a rotating Earth. He may have relied on Physics VIII, 4, 255a1–b24 to explain why heavy bodies outside of their natural place move with a rectilinear motion, although the idea was so commonplace that a supposed reliance on Aristotle here may be superfluous, as Dilwyn Knox pointed out to me. 68

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attained and a means to achieve it. This principle provides yet another reason why Earth rests for it does not arrive at the highest, whereas the first heaven attains it immediately by one motion. It follows too that the outermost revolution is the swiftest, and because it counteracts the revolutions below it, the star nearest to it takes the longest time and the star that is farthest in the shortest time. After attention to other characteristics of the stars,74 Aristotle finally turns to Earth. Aristotle summarily dismisses predecessors’ reasons for locating Earth anywhere but at the center as well as the reasons held by those who did place it at the center. For example, he dismisses a Pythagorean theory about the revolution of Earth around a central fire, because their system is based on a priori notions about fire as the most noble and therefore at the center. Aristotle had settled the question to his satisfaction about the natural motion of earth. That answer leads him to conclude that earth tends towards the center from all sides, and so Earth is spherical and rests at the center of the cosmos, for where any part of it moves, so too must the whole. In other words, a part should have the same motion as the whole.75 In the last chapter of Book II, he provides all of the positive and constructive reasons for placing Earth at rest in the center and in the shape of a sphere. The motion of earth is invariably in a straight line towards the center. The same stars always rise and set at the same regions of the Earth, which we would not observe if the Earth had its own proper motion in the plane of the ecliptic. The natural motion of Earth as a whole and of the parts is towards the center of the universe, and for that reason Earth lies at the center. The motions of whole and part are identical, for the whole should have the same motion as the part. The part cannot move naturally from the center; therefore, Earth as a whole cannot move. It is natural for the whole to be in the place towards which the part has a natural motion and for it to have the same motion if it could move. Because there is no force capable of moving it, the Earth must rest at the center. Finally, the Earth is a sphere and it is also very small in comparison to the sphere of the fixed stars. Books III and IV consider the four sublunar bodies and the heavy and light or weight and lightness. De caelo III, 1 is largely taken up with the relation between mathematics and physics and the refutation 74 75

De caelo II, 9–12. Ibid. II, 13.

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of Plato’s account in the Timaeus. De caelo III, 2 (already treated in the context of the Physics) discusses natural and forced motion and once again returns to the doctrine of natural place. The remainder of Book III is on the number and generation of the elements. Book IV on weight and lightness begins with the usual dialectical inquiry. After considering and rejecting all previous theories, Aristotle concludes that weight and lightness are tendencies in bodies to move downwards or upwards respectively. The motion of each thing towards its proper place is motion towards its proper form, and from potentiality to actuality. Heavy bodies that move to their proper place where other heavy bodies are located may be taken to mean that motion towards its own place is motion towards its like. But to say that like moves to like is not true in every sense. If the Earth were where the Moon is now, separate parts of it would move to the place where the Earth is now, that is, the center of the universe.76 After considering the relative properties of the elements, Aristotle turns to the role of shape in accounting for motion. Shape is not the cause of motion but of making the motion faster or slower. In this context Aristotle does consider the resistance of media, but because air among continuous bodies is more easily divided than water and earth, the analysis remains qualitative requiring only the condition that the force exerted by the weight exceed the resistance of the medium.77 And so concludes De caelo. As for De generatione et corruptione and Meteorologica we may restrict the summary to themes arising from the discussion in De caelo. Aristotle explains the changes, generation, and destruction of the elements as an effect of planetary, solar, and lunar revolutions. The clearest and least controversial claim is that the diurnal motion of the Sun and its proper motion on the ecliptic account for changes of day and night and of the seasons, affecting the relations of the four sublunar elements. After a discussion of coming-to-be and passing away and distinguishing them from alteration and growth and diminution, Aristotle shows that the elements that come to be are formed of material constituents by their combination. Combination involves action and passion, which involve contact.78

76 77 78

Ibid. IV, 3. Ibid. IV, 6. De generatione et corruptione I.

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In Book II he turns to the elements of bodies. Each of the four elements arises from a combination of two of the four elementary qualities, and they change into one another in various ways. Earth and water form that which moves towards the center.79 After examining the material, formal, and final causes of generation and corruption, he turns to the efficient cause, which is the Sun’s annual motion on the ecliptic. Generation is necessary because absolute necessity is characteristic of events that are cyclical. In the Meteorologica Aristotle deals with a number of topics that today fall under many separate disciplines including astronomy, meteorology proper, oceanography, optics, geology, seismology, chemistry, and geography. In this text Aristotle enters into somewhat more detail about the relations between the celestial sphere and what lies immediately beneath it. Here he allows for variety in the purity of ether, which by its circular motion sets on fire that part of the region beneath it and generates heat. The substance beneath the celestial sphere is potentially hot, cold, wet, and dry, acquiring these in actuality from motion and rest caused by the motion of the Sun on the ecliptic. The mass of air contiguous with fire moves in a circle because the motion of the heavens carries it around. The Sun’s motion is sufficient to produce warmth and heat. The Earth when heated by the Sun gives off two kinds of exhalations, one hot and one dry.80 Aristotle considers comets to be sublunar phenomena caused by the motion of the celestial sphere and a hot dry exhalation of the terrestrial sphere.81 In explaining various changes on Earth, Aristotle prefers to refer to local conditions than explain them by changes in the universe as a whole, for the mass and size of Earth are as nothing in comparison to the mass and size of the universe.82 Book IV, thought in the Middle Ages to be inauthentic at least in part, returns to the elements to examine the processes whereby the metals and other substances are formed.83 As can be seen from this sketchy reference to its contents, Meteorologica is largely natural history. Copernicus relied to a great extent

79

Ibid. II, 3–4. Meteorologica I, 3. 81 Ibid. I, 4–7. 82 Ibid. I, 14. 83 Scholarly consensus has evidently shifted to the view that Meteorologica IV is authentic. See Martin, Review of Aristoteles chemicus, 44–46. 80

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on Pliny’s Natural History for such information, not on Aristotle’s Meteorologica. Finally, for the sake of completeness, we may mention some texs from Aristotle’s Metaphysics. We know that Copernicus was familiar with it; there is even some evidence that he cited it from memory, so we will have occasion to refer to it in chapter nine. Metaphysics I, 3 discusses the ancient doctrine of the elements in the context of the four causes. In III, 4–5, Aristotle treats ancient theories of mathematical entities and their relation to substances and bodies. In VII, 2, he affirms that the stars, Sun, and Moon are substances. In VII, 7, Aristotle provides an important analogy for the understanding of how some things are generated and why they undergo change or motion. Although a thing comes from both its privation and material substratum, it is said to come rather from its privation. For example, what becomes healthy is both an invalid and a man, but, speaking more properly, we say that the healthy subject is produced from an invalid rather than from a man. A healthy subject is not said to be an invalid. It is from the condition of sickness, or the privation of health, that the healthy subject is produced.84 In a very abstract analysis of the actual and potential, Aristotle asserts that some things are only actually, some potentially, and some potentially and actually what they are.85 Because there is a distinction in each class of things between the potential and completely real, Aristotle calls the actuality of the potential as such, “movement.” It is hard to grasp what movement is, for we are inclined to classify it under privation or potency or absolute actuality, but all of these are impossible. The only alternative, then, is to think of movement as actual, not qua itself, but qua movable. Movement is in the movable, for while a thing is capable of causing movement because it can do it, it is a mover because it is active, and it is on the movable that it is capable of acting. The actuality of both is one, just as the mover and moved are one or together. If there is something that is capable of moving things or acting on them but does not actually do so, then there will not necessarily be movement. That which has a potency need not exercise it, and that which is potentially may possibly not be. Everything that acts can act,

84 85

Metaphysica VII, 7, 1033a5–22. Ibid. XI, 9, 1065b5–1066a33.

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but not everything that is able to act does so.86 After explaining the necessity for an unmoved mover, Aristotle turns to the motions of the celestial spheres—the famous text in which he elaborates on the systems of Eudoxus and Callippus. Aristotle’s contribution is that he interprets the system in material and mechanical terms.87 5. Johannes Versoris We may now turn to themes from De caelo as contained in standard commentaries used at Cracow and relevant to Copernicus’s heliostatic system.88 Such discussions evidently impressed Copernicus as evidence that questions were still open. On questions of direct relevance to his views, I select the last from De caelo, about figure or shape as a cause of motion.89 The context of the question is the atomist explanation of the motion of bodies. The solution is to attribute the cause of motion to heaviness and lightness and to admit that figure can be a cause of acceleration or deceleration. As representative of the views adopted at Cracow I cite John Versor’s conclusion to this question as it appears in the 1488 edition of his Quaestiones from BJ, Inc. 597.90 Versor affirms the association of one simple motion with one simple body. He recognizes, however, that the natural motion of an element can be affected by the motion of another body, and also by virtue of 86

Ibid. XII, 6, 1071b3–25. Ibid. XII, 8, 1073a–1074a32. 88 From my brief examination of the manuscripts of the Quaestiones cracovienses on De caelo, I concluded tentatively that these works were treated cursorily, but only a thorough study will settle the matter conclusively. A more complete summary of Versor’s commentary is in Goddu, “Sources.” I have retained only that part of the text here that contains opinions that Copernicus knew in a form similar to Versor’s comments. I do not mean to suggest, however, that Copernicus knew Versor’s commentary directly or that he cited it. Rather, Versor’s commentary represents interpretations that were typical or representative of the late fifteenth and early sixteenth centuries. Copernicus was, I believe, familiar with typical and representative versions, but identification of a single source I also believe to be elusive and difficult to establish because Copernicus’s comments seldom lead us to a unique source. The same holds for his acquaintance with Sacrobosco’s Sphaera and the various commentaries on it. More on this claim in chapters 5–7 and 9–10. 89 Compare Copernicus, De revolutionibus I, 4, on the relation between spherical shape and circular motion, a text to be discussed in detail in chapter nine. 90 The BJ codex contains Inc. 596 and Inc. 597. See Appendix III for a full description of the contents of Inc. 596 and Inc. 597. See also Markowsky, “Philosophical Foundations,” 219–221. 87

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its being ordered to the good and to the conservation of the whole universe, it is moved according to its common nature. Fire is moved rectilinearly according to its proper motion, but the circular motion of heaven can cause fire to move in a circle, and it can descend to fill a void according to its common nature.91 This argument represents a typical pattern for a scholastic commentary. Natural motions are, of course, simple, but the motions of elemental bodies are in fact more complicated as a result of external or extrinsic conditions, whether they be the actions of other bodies or the orderliness of the universe as a whole. Such qualifications were not lost on Copernicus. It became clear to many scholastics that perfectly homocentric, geocentric models of the universe did not work. The observational facts suggested the following inconvenient consequences. First, there is no unique center of heavenly motions. Second, there is no unique place downwards, but diverse centers. Third, the motion of a body on an epicycle would result in the penetration of dimensions or spheres, requiring them to posit the existence of void.92 Versor accepts the models of Ptolemaic astronomy as necessary to save the appearances. Aristotle, of course, made no mention of these models because he was unaware of them. Versor appeals, then, to John of Sacrobosco’s De sphaera, and the standard system of orbs to explain why the nearest spheres rotate more rapidly than the most remote spheres and also to save the Aristotelian conception of the unique center of the universe.

91 BJ, Inc. 597, De caelo, I, [q. 9]: f. 3ra: “Dubitatur primo, utrum unius corporis simplicis sit tantum unus motus simplex secundam naturam ut ex procedentibus habetur. Respondetur quod sic quia unius corporis simplicis est tantum una forma propria simplex. Et motus consequitur formam quia est effectus nature, et forma principalior est quam materia, ergo etc. Et dicitur notanter secundum naturam propriam, quia idem corpus simplex bene movetur diversis motibus uno secundum naturam propriam et alio secundum naturam alterius, ut ignis movetur motu recto sursum secundum naturam propriam et motu circulari secundum motum ipsius celi et potest descendere ad replendum vacuum secundum naturam communem. Et si queratur an sit eadem natura propria et communis. Respondetur quod in eodem eadem secundum rem sed differens secundum rationem, quia inquantum natura rei ordinatur ad proprium esse rei et ad conservationem unius rei dicitur natura una propria. Sed inquantum ordinatur ad bonum et ad conservationem totius universi cuius est pars dicitur natura communis.” 92 One solution is to embed the entire epicycle inside an orb. I address these problems below and in chapter ten.

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The diversity of circles in the heavens accounts for the observed irregularities in the following way. The farther a planet is on its epicycle, the slower it appears to move, and the closer it is, the more rapid it appears to move. In fact the motion on its circle is uniform and direct, and the motion of the orb is also uniform and direct, so retrograde motion is merely an appearance generated by the direct motion of a planet on its epicycle as the orb moves uniformly and directly. The effect, of course, is that the planet appears to move backwards. As for the diverse motions, all heavenly bodies share in the diurnal motion of the prime mobile. In addition, each orb has its proper motion, and the planet in the orb also has its proper motion that is distinct from the motion of the total orb or sphere. The total sphere is centered on the middle of the universe, but the center of the orb is eccentric. Consequently, when Aristotelians speak of the unique center as the unique natural place of all heavy bodies, they are referring to the order of the heavens and the total spheres, not the particular orbs or circles that they contain.93 Why are the spheres ordered according to their speeds around the middle, that is, the nearer are faster and the farther are slower? In other words, Versor reports what seems to have been a commonly held view, namely, the distance-period principle of spheres’ rotations from the center. In interpreting Aristotle here, commentators read the text in De caelo as ordering the spheres relative to the center.94 Versor points out that one complete circular motion of the ecliptic circle

93 Ibid. II, [q. 9], f. 17vb: “Conclusio prima. Ad salvandum primam diversitatem motus planetarum necesse est ponere circulos eccentricos in quibus moveantur planete . . . . Conclusio secunda. Ad salvandum secundam diversitatem necesse est ponere circulos epyciclos.” For the complete text, see Goddu, “Sources,” Appendix, text 2. 94 See Goldstein, “Copernicus and the Origin,” 219–235, esp. 220–231. Goldstein offers a new reconstruction of Copernicus’s discovery, the details of which we will examine in chapter seven. Goldstein, citing Copernicus’s mention of “ancient philosophers” in De revolutionibus I, 10, thinks that Copernicus had Aristotle’s De caelo II, 10 in mind with the interpretation of Averroes, an interpretation that perhaps derives from Simplicius. Goldstein also adds that Vitruvius gives the clearest statement of the distance-period relationship. As Versor’s comments indicate, however, the idea seems to have been a commonplace in the fifteenth century. I think it likelier that Copernicus encountered the idea in Cracow from teachers who were following the tradition as represented in Versor’s commentary. As Goldstein points out, Copernicus encountered it again in Italy where he may have concluded that the distance-period principle is incompatible with Ptolemy’s hypothesis about nesting spheres. See Goddu, “Reflections,” 1–17; and correct the typographical error in footnote 36. Change Inc. 596 to Inc. 597. BJ, Inc. 597 is bound together in the same codex with Inc. 596.

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(referring to precession) takes 36,000 years. The sphere of Saturn takes thirty years through the zodiac (sidereal period); Jupiter twelve; Mars two; and the Sun, Venus, and Mercury as if uniformly in one year (zodiacal year); and the Moon in one month. According to Versor, the reason given by Aristotle is that the closer a sphere is to the prime mobile, the slower its proper motion, which is in the direction opposite to diurnal motion. Some object to this argument on the grounds that because he places the spheres of Venus and Mercury above the Sun, they should move more slowly than the Sun. The more common opinion, however, is that the spheres of Mercury and Venus are below the Sun.95 As noted earlier, the Quaestiones cracovienses on De caelo posed the question whether the orbs nearer to Earth move more rapidly than those farther away, indicating that the period of an orb is related to its distance from Earth. Citing Thomas Aquinas, Versor argues further that heavenly bodies are midway between the perfect substances and generable and corruptible substances of earthly bodies. As such, the planetary spheres have two motions. One, the diurnal motion from east to west, is the cause of sempiternal permanence, duration, and uniformity. The second, the motion relative to the Sun on the ecliptic from west to east, is the cause of generation, corruption, and the other transmutations of inferior bodies. The closer a planetary sphere is to the prime motion, the more it has of the prime motion and the less it has of the second motion. Accordingly, the sphere of Saturn moves the slowest. The closer a planetary sphere is to generable and corruptible bodies, the more it has of the second motion and the more quickly it moves. The speeds of these motions are not proportional to their distances, however, because the celestial motions are not altogether natural but are also voluntary and directed to a desired end. To the extent that they are natural to that extent their speeds are proportional, namely, the farther are slower and the nearer are more rapid. Bound as they are to the motion of the Sun, the spheres of Mercury and Venus are moved uniformly with the Sun.96

95 Because they are always near the Sun, the phenomenon of bounded elongation, they move with the Sun and hence their zodiacal periods are one year. 96 BJ, Inc. 597, De caelo, II, [q. 14], f. 21rb: “Conclusio tertia et responsiva ad quesitum quanto orbes sunt propinquiores supremo orbi tanto motu diurno velocius moventur et motu proprio tardius prima pars patet quia propinquiores primo celo equali tempore motu primi mobilis describunt maiores circulos ergo velocius moventur.

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As one may surmise from the above explanation, the ordering of the planetary spheres and the speeds of their proper motions were problems that provoked different opinions and solutions. Similarly, explaining variations in the distances of the planets from Earth and from each other required astronomers to construct eccentric-epicycle models and to embed the models in orbs. Such revisions were necessitated by the success of the Ptolemaic models. Even so, some disagreements remained about the order of the spheres, disagreements that Copernicus would exploit to his advantage. Finally, from Versor’s questions on De caelo we come to the question whether the shape or figure of a body is the cause of its motion. With regard to spheres, as we saw, the explanation is that the celestial bodies are constituted of ether, the nature of which is to move in a circle. Not all spheres move, so it is not figure or shape that is the cause of the motion of a sphere. In this context, however, Versor is addressing the shapes of simple heavy and light bodies and their motions downwards and upwards respectively. The causes of their motions are heaviness and lightness, not their shapes. Shape is a partial cause of the quickness and slowness of the motions of heavy and light bodies. The relevant condition is the capacity of a shape to move or cut through a given medium.97 So much for Versor’s questions on De caelo. From the questions on Aristotle’s Meteorologica, Versor’s comments are consistent with his reading of De caelo. It bears emphasizing that the quantitative discontinuity between the celestial and terrestrial spheres does not mean that they are absolutely or simply discontinuous. There is, after all, only one, finite cosmos,

“Secunda pars patet quia ut dictum est celum stellatum motu proprio solum facit unam circulationem in triginta sex milibus annorum; Saturnus in triginta annis; Jupiter in duodecim annis; Mars in duobus annis; Sol, Venus, et Mercurius quasi uniformiter in uno anno; et luna in una mense.” For the complete text, see Goddu, “Sources,” Appendix, text 3. 97 Ibid. IV, [q. 5]: f. 27va: “Queritur ultimo. Utrum figure corporum gravium et levium simplicium sint causae motuum sursum et deorsum. Arguitur primo quod sic . . . In oppositum est Philosophus . . . f. 27vb: “Conclusio responsiva ad quesitum quod figure gravium et levium corporum simplicium non sunt cause suorum motuum, sunt tamen concause velocitatis et tarditatis motuum eorundem. . . . “Et hec de questionibus magistri Johannis Versoris super libros de celo et mundo Arestotilis dicta sufficiant.”

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and all of its parts belong to the whole. The parts must be at least contiguous from the lowest to the highest, and the superior exercise influence on the inferior, which are subject to the superior. Aristotle dealt with these sorts of questions about the relation between the heavenly and terrestrial realms in De generatione et corruptione. As the title suggests, the treatise is concerned with the four elements, their motions, and transformations. Influenced as they are by the motion of the heavenly spheres, the four elements are not confined to their proper and natural spheres but are in fact mixed. The Sun, its motion on the ecliptic, and the motions of the planetary spheres influence or even cause the transformations of the four elements, their generation and corruption, and ultimately account for all physical change in the terrestrial realm. The most important and relevant questions from De generatione et corruptione are those that deal with the transformations of the elements and with the relation between the celestial and earthly realms. In Book II, chapter 6, Aristotle engages in a dialectical critique of Empedocles’s denial of transmutation. Aristotle points out that Empedocles makes a comparison between air and water, maintaining that the ratio of air to water is as 10 to 1. Aristotle argues that if the elements are comparable in this way, then they are transmutable. It seems that some scholastics attributed this comparison to Aristotle, and then extended it to the relation between water and earth, arguing for a like 10 to 1 ratio. I have not yet found a source at Cracow that contains this view.98

98 In De revolutionibus I, 3, Copernicus chastises some peripatetics for claiming that the ratio of water to earth is as 10 to 1. Rosen, “Commentary,” 345 (to P. 9:27) cites one example, Ristoro d’Arezzo of 1282, but he does not claim that this was Copernicus’s source. In his questions on De generatione, John Versor does not make this claim, nor is it found in the versions of Thomas Aquinas’s commentary completed in the Leonine edition or in the version by Thomas of Sutton. For Versor, see BJ, Inc. 597, Questiones super De generatione et corruptione, II, ff. 15–18. For Thomas Aquinas, see Opera omnia, XLI–XLIII. See also the continuation by Thomas of Sutton in Expositionis D. Thomae Aquinatis in libros Aristotelis, De generatione et corruptione, 156–159. A likelier source for Copernicus’s comment, perhaps, is Henry of Langenstein, also known as Henry of Hesse. Unfortunately, Henry’s treatise Lecturae super Genesim was available only in manuscript in the fifteenth century, and I have not yet found a reference to it by any of the professors teaching at Cracow in the 1490s. It is likely that Regiomontanus knew of it, but I have not found a reference to it in any of his works known to Copernicus. See Steneck, Science and Creation, 80.

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By summarizing the views of John Versor we have shown that even a conservative follower of one of the standard scholastic interpretations of Aristotle confronted questions that required some modification or reinterpretation of Aristotelian doctrine. Many of these discussions do have the appearance of verbal gymnastics, but they also serve to exemplify the dialectical nature of the discussions and the ability of scholastics to apply principles creatively. Late fifteenth-century discussions at Cracow were not all as conservative as Versor’s, however, as Albert of Saxony’s questions on De caelo show.99 Albert’s questions were well known in Cracow.100 Because he often presents the views of John Buridan and Nicole Oresme, he provides evidence of the survival of somewhat more controversial views, even though Albert tends in the end to adopt a more conservative view than those of his predecessors. This summary is very selective, for I have treated these views elsewhere.101 As with so many scholastic predecessors, Albert examined problems about the number and order of celestial spheres. Albert settles on ten spheres or orbs and no more as sufficient to save the appearances. He reports the three alternative ways of ordering the Sun, Venus, Mercury, and the Moon. He prefers the view that places the last three below the Sun because of the symmetry in having the Sun in the middle between the three planetary spheres above (Mars, Jupiter, and Saturn) and the three below. Albert also adopted the threeorb solution that preserves both the eccentric-epicycle model with the aggregate of the orbs concentric to the Earth.102

99 On the acquaintance of fifteenth-century Cracow philosophers with the views of Albert of Saxony, see Markowski, Burydanism, 116–118, 130–135, and 182–185. On 503, Markowski cites six manuscript copies of Albert’s commentary on De caelo in the Jagiellonian Library. In the English summary on 535, he says the following: “Just as Buridan’s Subtilissimae quaestiones super octo Physicorum libros Aristotelis served as the foundation of the Polish commentaries to Aristotle’s Physics, the principal source of the Polish 15th-century commentaries to De coelo et mundo were the Quaestiones subtilissimae in libros De coelo et mundo Aristotelis by Albert of Saxony.” 100 Aside from the six manuscript copies of Albert’s questions-commentary on De caelo, the incunabula editions of 1492 and 1497 were also available in Cracow. See Berger, “Albert von Sachsen,” columns 39–56, esp. 45–46. 101 Goddu, “Sources.” 102 Albertus de Saxonia, Questiones, De celo II, qq. 6–7; ff. E2vb–3vb. “Confirmatur quod plures sint orbes celestes quam novem, nam pro solo motu solis assignantur tres orbes, unus quidem scilicet inferior concentricus mundo quo ad concavum ecentricus quo ad convexum, secundus qui vocatur deferens ecentricus mundo tam quo

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With respect to models of the Sun, Albert maintains that it is not necessary to posit one model (eccentric or epicycle) as the only solution to the problem of the Sun’s annual motion on the ecliptic, but concludes that one must be adopted to save the appearances. Eccentrics and epicycles must be adopted to save the appearances of planetary motions as well. In adopting traditional views, Albert points out that although the heavenly diurnal motion from east to west is regular, the motion is not uniform because the circumference rotates more rapidly than the axis. He rejects the hypothesis of Earth’s axial rotation for the usual reasons related to resistance caused by the motion of air, projectile motion, the observation of birds in flight, and the case of an object thrown into the air. In effect, the objection amounts to the claim that Earth constitutes an open system and behaves as an open system behaves; consequently, it is at rest at the center of the universe.103 On the question why bodies accelerate as they approach the end of their natural motions, a fact confirmed by the greater injury suffered by a body that has fallen farther, Albert rejects hypotheses proposing a decrease in the resistance of the medium or a conatus or desire. He rejects the first because an accelerated body heats air and thereby rarefies it, and, therefore, its lesser resistance is an effect of acceleration, not its cause. He rejects conatus because the “desire” for the body should be greater the farther it is from its end, and so should move more swiftly at the beginning than near the end. Following his Parisian colleagues on this question, Albert posits impetus or accidental gravity in addition to the heaviness of a body as the likeliest explanation for acceleration. The body gains momentum as it falls. He also resorts to impetus to account for the diurnal motion of the celestial orbs, rejecting the superfluous hypothesis of intelligences as the explanation in this case.104 ad concavum quam quo ad convexum, tertius autem qui est ecentricus mundo quo ad concavum et concentricus quo ad convexum, et ita pro quolibet alio planetarum oportet assignare plures orbes, propter quod videntur esse plures quam novem orbes seu spere celestes. . . . Alia est opinio quam inter ceteras magis approbo, quod decem sunt orbes, et non plures.” 103 Ibid. II, qq. 7–8, ff. E4rb–F2rb. 104 As with the previous texts, the arguments are similar to those already encountered in his questions on the Physics, but occasionally he adds an interesting detail such as the empirical confirmation of acceleration. See De celo II, q. 14, ff. F2vb–3vb: “Grave descendens in fine fortius ledit quam in principio quod non esset nisi in fine velocius moveretur quam in principio. Assumptum patet, nam si aliquis lapis descenderet

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Questions about the proper rates of rotation of the celestial orbs were difficult to reduce to one principle. In general, the farther or greater the orb, the slower the motion. Yet, the orbs of Mercury and Venus have the same period as the orb of the Sun. Here Albert is forced to concede the existence and role of intelligences as the causes of the proper motions of the orbs. The perfection of an intelligence is proportionate to the size of the orb, allowing for both the general solution with respect to the superior orbs and the special case of the orbs of the Sun, Venus, and Mercury.105 We may note here that differences about the order of the spheres, the rates of rotation of the celestial spheres, and the variations in the distances of celestial bodies from Earth played a significant role in leading Copernicus to reconsider the proper ordering of the spheres. On the relation of a celestial body to its orb, Albert maintains that the body (stella) is a certain part of the orb to which it is attached or fixed (infixa).106 As for their motions, it is not necessary for every spherical body to have a proper motion around its center! It suffices for many spherical bodies to be moved in a circle with respect to the motion of the bodies to which they are attached, and so is it for planets that are moved with respect to the motions of the orbs by which they are carried (the deferent orb). Note that this is Albert’s response to the Aristotelian objection that spheres should move in circles around their proper centers.107 It is clear that such distinctions permitted Aristote-

de alto, et aliquis reciperet illum lapidem prope initium casus non lederet recipientem, sed si reciperet talem lapidem per magnam distantiam ab initio casus illius lapidis multum lederet recipientem, quod non esset nisi talis lapis in descendendo continue intenderet suum motum.” 105 De celo II, q. 17. Because the centers of the epicycles of Mercury and Venus are always on the line between Earth and the mean Sun, their zodiacal periods are also one year. A more technically correct description of the models should include mention of the equant point, which modifies the description thus: The line from the equant point to the epicycle’s center remains parallel to the line from Earth to the mean Sun. See Evans, History, 358 (figs. 7.34 and 7.35) and 411. 106 De celo II, q. 20, f. G1ra. 107 Ibid. II, q. 20, f. G1rb: “Ad quintam dico quod non oportet omne corpus spericum habere motum proprium circa centrum suum. Sed sufficit multis corporibus spericis moveri circulariter ad motum corporum quibus sunt infixa, et sic est de stellis quae moventur circulariter ad motum orbium quibus deferuntur. Et hoc sufficit eis absque hoc quod ultra hoc habeant speciales motus circa centro propria.” Albert makes no mention of an equant point or model, but the passage could be read as support for such a model. On the other hand, he may merely intend the argument as support for the three-orb model with eccentric and epicycle. It is a response to an Aristotelian objection, f. F6vb: “Quinto, nam secundum Aristotelem quelibet stella est

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lians to accept a Ptolemaic device such as an equant model without concluding that it violated a fundamental axiom. Albert discusses proposals in support of a moving Earth, reporting hypotheses regarding Earth’s center of gravity and diurnal axial rotation. Persuasive arguments for such hypotheses are presented. Of course, Albert refutes the arguments and rejects all of these conclusions. In the discussion Albert mentions that one of his teachers argued that the question about the motion of Earth or the motion of the heavens cannot be settled demonstratively. Albert responds that in no way can the supposed motion of Earth (evidently meaning its axial rotation or the motion around the poles of the ecliptic) save the oppositions and conjunctions of the planets, nor solar and lunar eclipses.108 On the application of the principle of economy, Albert responds that the heavenly bodies do not possess terrestrial qualities. Consequently, they are entirely suited for the rapid motions that we observe them to have. It is the property of some spheres to move naturally in a circle, but it is also a property of some spheres to rest naturally with respect to their centers. In other words, if a body moves in a circle, it is suitable that it be spherical. If it rests around or at the center of the world, it is also suitable for it to be spherical or approximately spherical because on average all of its heavy parts tend to the center. Because Earth consists of heavy parts, all of them together fix Earth at the center. The only conceivable motion, then, would be slight rectilinear motions or shifts that make Earth’s center of gravity coincide with the center of the world.109 In discussing the motions of heavy and light bodies and the doctrine of natural place, Albert again reports a variety of opinions. Albert uses Aristotelian principles for the most part, but he adopts a view of natural place that reflects late medieval discussions of final cause as a conserving cause. He relies on the analogy between natural place and health to illustrate his point. Health is related to the curable and to healing. Health is the end to which healing tends and is the formal

sperica. Modo motus spericus debet esse spericus circa centrum proprium, sicut patet de motibus orbium celestium.” 108 The reference here is probably to Nicole Oresme who considered the axial rotation but not the orbital motion of Earth, and who concluded that no demonstration could settle the question. See Oresme, Livre, 519–539. 109 Goddu, “Teaching,” 74. Although some astronomers were persuaded by Copernicus’s arguments based on the principle of economy, Aristotelians used such distinctions effectively in response.

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perfection of that healing when it is acquired. Likewise, natural place is the agent cause with respect to that which is in place as a conserving cause. Natural place can also be considered the formal cause of the placed inhering in it when the placed is in its natural place.110 As we noted, Albert preferred the theory of impetus to account for projectile motion, accelerated natural motions, and the motions of the celestial spheres. In his version, there is a clear relation between the amount of material in a body and the greater effect of an impressed impetus. Although Albert relegates questions about the nature of impetus to metaphysics, his view seems to be that it is a quality. He acknowledges that after transfer to a body, impetus is intrinsic. He denies that it is natural, however, because it is violent, the result of a force impressed on the body from the outside, and because the impetus supplies an inclination contrary to the natural inclination of a mobile. It is not surprising that he tried to avoid the metaphysical issue. As a quality intrinsic to the projectile, impetus could serve as part of a theory alternative to natural motion altogether. That is clearly a consequence that Albert wanted to resist.111 The last relevant question concerns the shapes of the elements. Here Albert reports the Platonic account of five geometrical solids and their shapes, rejecting Plato’s view for the Aristotelian conclusion that the elements are spherical in shape.112 Finally on views known and represented at Cracow and probably known to Copernicus, we add John of Glogovia’s discussion of the 110 De celo III, q. 7, f. H4v: “Secundo, auctoritate Aristotelis dicentis esse simile in proposito de motu augmentationis et de motu alterationis et de istis motibus localibus. Nam videtur velle quod sicut sanitas se habet ad sanabile et sanationem, et perfecta magnitudo ad augmentabile et ad augmentationem. Ista locus deorsum se habet ad grave, et ad motum eius. Sed sanitas est finis ad quem tendit sanatio et est perfectio formalis ipsius sanabilis cum acquisita fuerit. Et sic etiam est de perfecta magnitudine ad augmentationem et augmentabile, ergo a simili debet concedi de loco deorsum quantum ad ipsum grave et a motum eius.” Following the analogy, we may imagine a comparison between a body removed from its natural place as sick and the same body in its natural place as healthy. 111 See De celo III, q. 12, f. I1rb-va. See also Sarnowsky, Aristotelisch-scholastische Theorie, 253–254 and 381–407. Note that Copernicus will also retain the notion of natural motion and resist the implication that his proposed motions of Earth are violent. 112 De celo III, q. 13. Note that Copernicus also concludes that the elements tend naturally to a spherical shape, and, of course, he will retain the spherical shape of celestial spheres. As Dilwyn Knox pointed out, however, Copernicus (De revolutionibus I, 1), following Pliny, will also argue that the Sun, Moon, and planets are spherical because they desire to be bounded, just like spherical drops of water or other liquids, an argument that Albert rejects.

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relation between the Sun and the planets in his Commentary on Aristotle’s Metaphysics. In this text John cites some commonplace doctrines that Copernicus almost certainly encountered as a student in Cracow. John maintains that the Sun is in the middle of the stars and planets as a king in his kingdom. The Sun is the cause of light and illumination of all of the other stars; all receive their splendor from the Sun. Familiar as he was with Ptolemy, John points out that according to Ptolemy all of the motions of the planets are linked to the motion of the Sun.113 *

*

*

Throughout this chapter I have focused on doctrines reported or held by Cracow philosophers when Copernicus attended the university. In several instances I have pointed out parallels with Copernicus’s views. My emphasis, however, was rather on the way in which scholastic philosophers revised and reinterpreted Aristotelian doctrines to bring them into conformity with revelation, improved astronomical models, and more sophisticated physical examinations of accelerated natural motions, projectile motions, and the motions of celestial spheres. Not all Cracow philosophers supported all of these revisions, but they reported all of them and adopted some of them. It is virtually impossible that Copernicus could have been ignorant of these discussions. In light of his later statements and arguments, we have suggested that what he learned above all from his teachers was how to adapt Aristotelian principles to ideas different from those held explicitly by Aristotle.

113 Komentarz XII, [q. 68], 193–195: “Arguitur quarto: Numerus substantiarum separatarum non accipitur penes ordinem mobilium caelestium, igitur. Probatur: quia si sic, sequeretur, quod intelligentia orbis Solis non esset dignior quam intelligentia orbis Saturni, quod tamen est contra communem determinationem astronomorum, qui dicunt orbem Solis et Solem esse dignissimam planetarum et Solem esse in medio stellarum et planetarum tamquam regem in medio regni. . . . Arguitur sexto: Sol est planeta dignior quam Saturnus, igitur et intelligentia Solis est nobilior intelligentia Saturni. Antecedens probatur: Corpus illud est nobilius, quod est causa lucis illuminationis omnium aliarum stellarum; sed corpus Solis est huiusmodi; igitur. . . . Minor est Aristotelis secundo “Caeli,” ubi ostendit, quod Sol illuminat omnis astra et omnia recipiunt ab ipso splendorem. . . . Arguitur octavo: Sol est dignissimus planetum, . . . Ille planes est dignior, qui omnium planetum motum regit et dirigit et mensurat; sed Sol est huiusmodi; igitur. . . . Minorem declarat Ptolomaeus in sapientiis “Almagesti,” qui ostendit, quod omnes motus planetum mensurantur et inventi sunt per motum Solis.” Of course, in Ptolemy’s models the line from the equant point to the centers of the epicycles of Mercury and Venus is parallel to the line between Earth and the mean Sun to account for bounded elongation. Likewise, the line from the center of its epicycle to a superior planet is always parallel to the line from Earth to the mean Sun to account for retrograde motion at opposition.

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Copernicus was familiar with Aristotle’s Metaphysics. We have discussed some texts above, but we may return briefly to two issues as we conclude this chapter. There are passages in De revolutionibus that demonstrate his acquaintance with texts that he seems to have adapted in some instances from memory.114 One of his closest friends later in Varmia, Tiedemann Giese, had written a commentary in 1497 on Aristotle’s Metaphysics. The commentary is in the form of extensive glosses on an early printed edition of Metaphysics.115 There are no annotations by Copernicus in the codex, so we have no way of knowing whether he ever read Giese’s commentary or used this codex for his knowledge of Aristotle’s Metaphysics. We should keep in mind, however, the possibility that much later than his years in Cracow and northern Italy Copernicus discussed philosophical questions with his friend, and perhaps relied on him for his understanding of Aristotelianism.116 The most relevant issues for our purposes concern interpretations of Aristotle’s view on the relation between mathematics and natural philosophy and cosmology, and on the relation between homocentric spheres and the Ptolemaic eccentric-epicycle models. We will have occasion to discuss these issues again in the next chapter. Here we may briefly mention the fact that Averroes’s critique of Ptolemaic astronomy as he states it in his commentary on Metaphysics, Book XII, was well known in Cracow. The Averroistic critique, in fact, provides a summary of both problems at once. Averroes was not impressed with the mathematical solutions. Mathematics is subordinate to natural philosophy, and he regarded the mathematical solutions as irreconcilable with geocentric cosmology. Scholastic philosophers and astronomers adopted three strategies in response to this critique. Some agreed

114

A. Birkenmajer, Études, 615–619. Today the book is located at Uppsala University Library, Inc. 31:164. The codex contains Johannes Versoris, Quaestiones super Metaphysicam Aristotelis cum textu eiusdem, Collijn 1484, Hain *16051; Versor’s commentary on De ente et essentia of Thomas Aquinas, Collijn 1477; Thomas’s treatise De ente et essentia with commentary by Gerard de Monte; and copies of Aristotle’s works on politics and economics with commentaries by Johannes Versoris, Collijn 161 and 156 respectively. Giese owned the codex, and deposited it in the collection at Frombork. See Collijn, Katalog, p. 478. The codex has been annotated in several hands, but Giese’s predominates in the text of the Metaphysics. None of the other annotations in the codex is in Copernicus’s hand. 116 On Giese, see Pociecha, „Giese Tiedeman Bartłomiej,” PSB, 7: 454–456. We will discuss the comment made by Copernicus in the general conclusion, but suffice it here to say that his comment does not reflect either the text in this edition or the comments of Giese on it. 115

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with Averroes and insisted on a true homocentric astronomy. Most accepted the models as necessary to save the phenomena by combining eccentric-epicycle models adapted to geocentric spheres. Among these, however, some regarded the models as real while others interpreted them as fictions.117 If some of the models are real (the equant model, for example), they violate the cosmological principle about uniform, circular motion, so they cannot be real. If they are not real, however, then we must suppose that the “vital force” moving the celestial body and its sphere must regulate it, but that entails the conclusion that the motion is not uniform.118 It seems as if the cosmological goals cannot be achieved in a satisfactory way by means of the mathematical models. Aristotle maintained that the truth is consonant with the truth, implying that the true cannot follow from what is false. Of course, Aristotle was referring to a demonstration propter quid, not quia.119 For centuries, however, astronomers derived the appearances from several alternative geometrical models. Some astronomers maintained that one of them must be true, but others concluded that none of them is true. Copernicus acquired his first glimpse of such questions and problems as a student at Cracow. One last issue deserves comment. What view did Cracow philosophers have of Plato on questions in natural philosophy and cosmology? Their respect for Plato as a “theologian” did not inspire them to defend him from Aristotle’s criticisms. On the other hand, we have seen several instances where scholastic philosophers modified Aristotelian doctrine under the influence of Platonically inspired arguments or questions. In such cases, commentators in Cracow relying on their medieval scholastic predecessors seem to have genuinely believed that their interpretation could be squared with Aristotle’s principles. One example will suffice. The speculation about an infinite void space that could serve as the receptacle for bodies complicated the Aristotelian conception of a finite cosmos. The technical distinctions are philosophically

117 The outstanding example in Cracow of such a fictionalist interpretation of eccentric-epicycle models was Albert of Brudzewo. See Commentariolum, 22–30. Cf. Averroes, Aristotelis Metaphiscorum libri XIII, Opera, 8: XII, text 45, f. 329G-M: “Ecentricum enim aut epicyclum dicere est extra naturam: epicyclus authem impossibile est ut sit omnino . . . . Astrologia enim huius temporis nihil est in esse, sed est conveniens computationi, non esse.” 118 Pedersen, Survey, 391–397, suggests this solution. 119 See chapter three, conclusion. In Aristotle, see Nicomachean Ethics I, 8, 1098b10; and Prior Analytics II, 2–4.

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respectable, but it is hardly surprising to find authors who were undecided about the existence of an actually infinite universe. They committed themselves to a finite picture of the universe, leaving the possibility of its infinite extent in some sense open. Such openness, I suggest, left Copernicus in some quandary about how to address philosophical opinions about the infinity of the world.

CHAPTER FIVE

HUMANISM AND ASTRONOMY 1. Introduction This chapter focuses on the teaching of astronomy at Cracow in the fifteenth century. Universities in the late Middle Ages were not particularly innovative in astronomy, but the University of Cracow developed a reputation for training scholars in the theory and practice of astronomy and astrology.1 Early in the fifteenth century a chair for astronomy was established at the university. The circumstances touch on the expansion of the Polish kingdom, the rise of the gentry, the increasing commercial importance of towns like Cracow, and the influence of Renaissance humanism on Cracow University circles in the fifteenth century. The two outstanding political and social developments in the fourteenth and fifteenth centuries were the rise of the middle class and its transformation into newer landed gentry.2 By 1500 merchant patricians, geographically and linguistically mixed, gained control over the political and economic fortunes of cities like Cracow, Gdańsk, and Toruń. The Polish monarchy remained an important player in regional politics as well as a vehicle for cultural developments, but as its need for administrative power grew, it became ever more dependent on literate and educated lawyers to staff its bureaucracy. Some of these individuals were secular and nationalistic in their goals, and saw their participation in royal administration as a way of achieving them. The new landed gentry gradually replaced the older nobility, producing

1 Excellent starting-points for this chapter are the following papers collected in The Polish Renaissance: Wróblewski, “Cracovian Background,” 147–160; Rosen, “What Copernicus Owed,” 161–173; Knoll, “University Context,” 189–212; and Ulewicz, “Polish Humanism,” 21–235. Indispensable for its study of the sources and its bibliography is Zinner, Entstehung. 2 Knoll, “World,” 19–51, esp. 19–21. Many of the references cited in this chapter come from Knoll. Compare with the much earlier but still useful chapters in Cambridge History of Poland, chapters 11–13.

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changes in medieval society that benefited the University of Cracow in the fifteenth century.3 Italians were active at the university since the fourteenth century, and the plan for the first foundation was supposedly modeled on Bologna and Naples, as the emphasis on law testifies.4 Polish students attended foreign universities to advance their education especially in law, and establish professional relationships with Roman officials. The first official contacts with Italian humanism occurred early in the fifteenth century at the Church councils in Constance and Basel. There, Italian humanists influenced Polish representatives, who, when they returned, brought humanistic works back with them to Poland. Italian humanists also visited Poland, but aside from direct Italian influence and the study and work of Poles abroad, Hungary served also as a conduit for humanistic inspiration and works.5 The first evidence for a Polish Renaissance is from the fifteenth century. Zbigniew Oleśnicki, Jan Długosz, Gregory of Sanok, Jan of Dąbrówka, Jan of Ludzisko, and Jan Ostroróg are the main representatives. Cardinal Oleśnicki entered the University of Cracow in 1406, became bishop in 1423, served as chancellor of the university for thirty-two years, and founded the Jerusalem hostel to support promising students. He corresponded with Aeneas Sylvius Piccolomini and patronized humanistic learning. Długosz (1415–1480) is best known as a medieval chronicler whose literary style has been disparaged, but more recent scholarship has shown the extent to which he modeled himself on Livy in particular as well as on other classical authors.6 Some scholars begin their account of the Renaissance in Poland with Gregory of Sanok (ca. 1406–1477). The origins of his humanist 3 Mikulski, Przesteń. I cited Mikulski previously about Toruń in the fifteenth century, but the pattern is similar to the following extent. The old patriciate educated children either to arrange marriages with nobility and/or for land or to prepare them for administrative careers in the church where they aspired to benefices and bishoprics. After 1466 the old patriciate tended to retreat to their land holdings, often selling some of their land to the new patriciate that earned its wealth in the grain trade. For the effect of political and economic changes on the university, see Koczy, University of Cracow Documents, 9–25. 4 Knoll, “World,” 27–29. On the influence of Naples, see Koczy, 1. Moraw, 181– 206, questions the historicity of the foundation in 1364. 5 Halecki, “Renaissance in Poland,” 273–274. 6 Knoll, “World,” 27–34. On Oleśnicki, see Morawski, Histoire, 2: Book 2. On Długosz, see Madyda, “Johannes Longinus Długosz,” 185–191. See also Filozofia i myśl społeczna, 502–516. On Jan Ostroróg, see Filozofia, 237–261; on Jan of Dąmbrówka, ibid. 344–352; on Jan of Ludzisko, ibid. 353–380.

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leanings are unknown, suggesting that he might represent at least in part an indigenous Polish humanism, as has recently been argued for Vienna.7 On the other hand, we know that Gregory traveled extensively as a young man, spent considerable time in German-speaking lands, and visited Italy. He returned to Poland in 1428, attended Cracow University, received a master’s degree, began to tutor the children of prominent individuals, and served as one of the king’s secretaries in Cracow. When a church office became available in Wieliczka, he traveled to Rome to receive papal confirmation. He met Pope Eugenius IV, returned to Poland, eventually became an archbishop and supported humanist education and poetry. Nothing of his own poetry has survived so that his supposed influence on the development of Renaissance humanism in Poland along with the origins of his humanism remains legendary. Still, it appears that Gregory’s adoption of humanism arose in part from dissatisfaction with scholastic style and from his contacts with Italian merchants and humanists probably in the 1420s.8 The next phase of Renaissance humanism in Poland occurred at the University of Cracow in the 1430s. The influences here definitely derive from Italian humanism, and they were deepened over the next decade as a result of Polish ecclesiastical participation in the conciliar movement. This period lasts to 1480 from which time Italian humanism became strongly entrenched in Cracow until 1500. In the last period, 1500–1540, appear the growth of private libraries and also the introduction of biblical humanism to Cracow. Despite evidence of some hostility from scholastics towards humanism, the libraries of university professors at Cracow support claims about the strong reception of humanism and the Italian Renaissance. From the first half of the fifteenth century, twenty classical-humanist codices are preserved in the collection of the Jagiellonian Library.9 In the second half of the

7

Shank, “Classical Scientific Tradition,” 115–136, provokes some reconsideration of the sources for the Renaissance in Vienna, but a figure who seems to stand out as an influence in central and eastern Europe is Aeneas Sylvius Piccolomini, who influenced Peurbach, who in turn influenced Regiomontanus. Still, there is reason to consider the influence of the proto-humanism of the thirteenth century on Vienna, and in this regard the sources are sometimes late medieval as well as non-Italian. 8 On Gregory, see Segel, Renaissance Culture, 1–35. 9 Szelińska, Biblioteki profesorów, 44–94, refers to manuscripts and codices with works of Petrarch, Poggio, and Leonardo Bruni. These representatives pale in comparison to the number of medieval works, but they testify to the presence of Italian humanist works at Cracow from 1430 to 1480. In this regard see Segel, 5–8; and Knoll, “World,” 28.

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fifteenth century, the codices with works of humanist scholars belonged to primarily university professors. Albert of Swolszowice, for example, owned commentaries on the classics written by Angelo Poliziano, Marcus Sabellius, Philip Beroaldus, Ermolao Barbaro, and Laurenzo Valla. Michael of Oleśnica, a figure who takes us through the first half of the sixteenth century, owned works of Cicero in humanist editions and works by Codro Urceo.10 Jan Ostroróg earned his law degree at Bologna, learned Greek, and returned to Poland in 1461 where he served royal interests in defense of Polish nationalism and secularism. These individuals represent a beginning. The curriculum of the university remained scholastic, to be sure, but already from the 1420s we find a greater interest in antiquity for its own sake and for more humane studies. It was by and large students returning from several years of study in Italy who advocated these changes and recommended curricular reform. The process was gradual but successful already by 1449 when the Collegium minus, a faculty specifically appointed to provide instruction in the studia humaniora, was founded as a new arts curriculum, parallel to that taught by the Collegium maius. We can see from the classes offered later in the century that the two programs in arts were fully integrated in the lectures and exercises offered to students.11 There is no evidence that Greek was formally taught at the university prior to the sixteenth century. Nevertheless, when Copernicus entered the university in 1491, there was a humanistic circle in Cracow that consisted of a few scholars and teachers and to which some of even the more scholastically trained faculty belonged.12 Among the outstanding figures to be mentioned in the humanistic context are Lawrence Corvinus, Philip Callimachus, Conrad Celtes, and Jan Sommerfeld.

10 Szelińska, 217–226 and 249–250. Note that Swolszowice may have taught Copernicus, and some scholars speculate that Copernicus received some instruction in Greek from Urceo in Bologna. See, for example, Malagola, Aufenthalt, 17–119, esp. 40–48. However, Birkenmajer, Mikołaj Kopernik, 99–127, argues extensively to the contrary. 11 Liber diligentiarum, 18–32. See also Morawsky, 2: 220–234. 12 Knoll claims that the Collegium minus enrolled forty percent of students in the 1450s and 1460s. See Zarębski, “Okres wczesnego humanizmu,” 176–179. Morawski, typical of the older historiography, depicts the relation between humanism and scholasticism as antagonistic, but such accounts seem to exaggerate the opposition and, in any event, do not reflect the circumstances regarding Copernicus’s education, teachers, and friendships going back to his studies at Cracow.

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Lawrence Corvinus (ca. 1462–1527) matriculated at the University of Cracow in 1484, received his B.A. in 1486, and the M.A. in 1489. From 1489 to 1494 he taught both scholastic and classical works as an adjunct instructor. In 1494 he left the university and spent the rest of his career, mostly in Wrocław, as a school master and town notary. He had a reputation as an effective teacher and promoter of humanistic studies. He may very well have instructed Copernicus, and the two were in contact at least as late as 1509.13 Because of the social world that fostered humanism, one expects to find humanistic circles outside of the university, and Cracow was no exception. Philip Buonacorsi (also called Callimachus), an Italian humanist was active in Cracow from 1472. He exercised a strong influence on the spread of humanism, especially on Conrad Celtes who influenced Corvinus in turn. Celtes attended the university briefly, where he received instruction in astronomy from Albert of Brudzewo. He founded an official humanistic society, the Sodalitas litteraria Vistulana, which, though it did not long survive his departure from Cracow, was a vehicle for the support of humanistic interests.14 Representative of the new direction and success of humanistic influence is Jan Sommerfeld (d. 1501), a member of the faculty, associated with the Jerusalem hostel, and an avid book collector. His collection consisted of over 230 items representing all fields of scholarly activity. His library contained works of Boccaccio, Flavius Biondo, and Pomponius Laetus.15 What is especially of interest from the point of view of classical studies and the return to other classical authors was Corvinus’s interest in Platonism and Neoplatonism, an interest that he and Copernicus evidently shared. The complete evidence for Corvinus’s interest in Plato does not appear until 1516, but his acquaintance with Plato’s dialogues in the translation by Ficino goes back to his days at Cracow.16 Callimachus and Celtes brought Renaissance Neoplatonism with them to Cracow. Celtes, Corvinus’s teacher, had studied under Ficino in Florence. This new emphasis on Plato reinforced an earlier 13 Krókowski, “Laurentius Corvinus,” 152–172, esp. 154–155 and 163–164. See also Segel, 107–109. 14 Compare Segel, 36–97 with Krókowski, 155. See also Spitz, Conrad Celtis; and Lhotsky, Wiener Artistenfakultät, 198–204; Rupprich, Briefwechsel. For more on Celtes’s teaching at Vienna, see Ameisenova, Globe, 47–48. 15 Szelińska, 152–176. 16 Krókowski, 164–165.

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Neoplatonic stream that entered Cracow by way of Hungary and a group of scholars who were also connected directly with Ficino and the Florentine Academy.17 Throughout the fifteenth century, then, we find evidence that Renaissance humanism influenced the culture of Cracow by means of which university faculty and students imbibed its characteristics. Earlier scholarship tended to emphasize scholastic resistance to humanism and humanists’ attacks on scholastic barbarism. There was resistance, and attacks occurred, but scholars studying Polish humanism have followed the general historiographical trend that has shifted discussion away from conflict and towards greater accommodation.18 Although the process was very gradual, the return to the classics affected the curriculum in the liberal arts. Even scholastic philosophers started to comment more on the texts of Aristotle with somewhat less reliance on scholastic commentaries. Even those still dependent on scholastic commentaries preferred the methods of textual exposition developed by thirteenth-century scholastics rather than relying on later medieval approaches.19 Scholars began to depend more on other ancient authors. In the 1480s a number of Cracow residents formed a Renaissance society to encourage the study and writing of humane letters. As noted, several late fifteenth-century faculty became book collectors, and many of their collections later became the property of the Jagiellonian Library. In short, the fifteenth century marks a period of political expansion and commercial growth for the middle class that supported an intellectual and cultural revival with lasting consequences for the arts and literature of Poland. The sixteenth century saw the flowering of the earlier efforts, leaving us with a balanced picture of the fifteenth century as a period of proto-humanism. The cultural environment stimulated developments not only in philosophy and theology but also in the mathematical disciplines, especially geography and astronomy.

17

Knoll, “World,” 28–32. On Callimachus, see Filozofia, 517–551. Seńko, Tendances. Seńko provides a picture of general receptivity to humanist reforms, reducing the resistance (32) to the period in which Michael of Biestrzykowa returned to Cracow from Paris and added Scotism to the philosophical curriculum. The university documents support the confrontation between Biestrzykowa and the humanist critics of the sorts of philosophical distinctions on which Scotism thrives. 19 As we saw in chapter four. See Markowski, Filosofia przyrody, 14, 20–24, 29–31, 47, and 148–150. For a summary of Markowski’s monograph, see Goddu, “Teaching,” 39–52. 18

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The interest in the sciences although pre-dating the interest in humanism benefited from the humanist revival. One may see some motivation here from the sciences, and perhaps this is consistent with Vienna. Before we turn to the teaching of astronomy at the university, then, we must look briefly at the state of astronomy in the fifteenth century and the major developments that occurred primarily in Vienna and that exercised an enormous influence on astronomy at Cracow in the 1490s.20 The following summary is necessarily selective, dictated in part by Copernicus’s reaction and also by efforts in the fifteenth century to improve tables and observational accuracy. With these qualifications in mind, we select the following as the principal astronomical questions and objections in the tradition of Ptolemy.21 First is the fact that Earth is not the unique geometrical center of the planetary motions. Opponents of the Ptolemaic models continued to search for a perfectly concentric solution. One of the earliest influential critics of Ptolemaic models was Ibn Rushd (Averroes). There are several important concentrists in the fifteenth century and homocentrists in the sixteenth century.22 Second come the efforts to combine eccentric-epicycle-deferent models with spheres and orbs that amounted to a compromise solution to the problem of a “homocentric” cosmos. While epicycle-deferent models are eccentric and the orbs in which they are contained are eccentric, the total sphere in which a planet moves is geocentric. This was a view widely held well into the sixteenth century. A typical and influential example is Peurbach.23 Third was the recognition or discovery of observational errors and the inaccuracy of astronomical tables. During the fifteenth century

20 The principal authority for the relation between humanism and mathematics remains Rose, Italian Renaissance, esp. chs. 2–5. See also Blair and Grafton, “Reassessing Humanism,” 535–540; and Pedersen, “Tradition and Innovation,” 457–460. 21 In general, cf. Ptolemy’s Almagest; Benjamin and Toomer, Campanus of Novara; Pedersen and Pihl, Early Physics. 22 On Averroes, see, for example, Aristotelis Opera cum Averrois commentariis, ff. 128–130 and 326–331; De coelo, ff. 196–199; Ibn Rushd’s Metaphysics, tr. Genequand, 176–184, commentary on Metaphysics 1073b10 (Textus 45)–1073b32 (Textus 47). On later developments, see di Bono, Sfere. 23 See, for example, Grant, Planets, 271–370; Lerner, Monde, I: 115–130; and Peurbach, Theoricae novae planetarum, 5–44. The significance of the difference between concentrism and homocentrism is not altogether clear, but see Granada and Tessicini, “Copernicus,” 433–437 and 458–464.

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in particular as scholars became aware of how corrupt the medieval manuscript versions of ancient texts were, some of them demanded improvements in the texts and in observational accuracy. Here the outstanding figures are Peurbach and Regiomontanus.24 Fourth is the non-conformity of lunar models, even Ptolemy’s fully refined lunar model, with observations. According to the standard geocentric model, the size of the Moon’s diameter should appear nearly twice as large as it does at the quadrature points. Although Henry of Langenstein recognized this flaw, Regiomontanus later emphasized it. Others realized that if the Moon circles on an epicycle, then to maintain the same orientation of its spots to Earth, they must place the Moon on a secondary epicycle with a rotation at the same rate as, but in the opposite direction to, the first epicycle. Representatives of this solution are Sandivogius of Czechel and Albert of Brudzewo.25 Fifth was the problem of calendar reckoning and determination of the solar year. This too was a centuries-old problem, but as more time passed, the more the inadequacies of the Julian calendar became annoying. These efforts at reform became bound up with ecclesiastical politics. They affected negotiations between Greek Orthodox and Roman Catholic leaders, and they became part of wider reform movements in Europe.26 Sixth was a difference in the ordering of the planets Mercury and Venus in relation to the Sun. Some (Ptolemy and the more common view) placed their epicycles and orbs between Earth and Sun. Others (Martianus Capella) placed the two planets in orbits around the Sun, and others (Plato) placed them beyond the Sun.27 Ptolemaic astronomers regarded angular distance as far more important than linear distance, and estimates of linear distance were based on the assumption that the celestial spheres are contiguous or nested without any

24

See, for example, Joannes Regiomontanus, Opera collectanea, esp. XXVI– XXVII. 25 On Henry, see Dijksterhuis, Mechanization, II: 150 (p. 216); III: 62 (p. 273). Cf. Gilson, History, 796, n. 55. On Sandivogius and Albert, see Rosińska, “Nasir al-Din alTusi,” 239–243. On Albert, see Albertus de Brudzewo, Commentariolum, 67–70. I am not aware of anyone at Cracow who noticed the problem of the doubling in the size of the Moon in Ptolemy’s lunar model. On the Viennese connection, see Markowski, “Beziehungen,” 133–158. See also Babicz, “Exakten Wissenschaften,” 301–304. 26 On the solar year, precession of the equinoxes, and the theory of trepidation, see, for example, Carmody, Astronomical Works. See also Neugebauer, “Thabit ben Qurra,” 267–299. 27 See, for example, Copernicus, De revolutionibus, Praefatio and I, 9–10.

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void spaces. However common this view was, it nonetheless rested on assumptions that later struck Copernicus as arbitrary, and the arrangement did not yield a mathematical principle on the basis of which linear distances or ratios of distances could be calculated. Seventh, related to the sixth, is the variation in distances of planets from Earth and the fact that the motions of the planets are linked to the Sun. Regiomontanus, among many, noted this peculiar coincidence, one that Copernicus may have seen as a clue.28 Eighth is the equant point. Because the motion of the epicycle center violated the principle of uniform circular motion around its proper center, the equant model seemed to some to violate one of the fundamental principles of ancient astronomy. Ibn al-Haytham (Alhazen) may have been the first to object to this model, and a major tradition of Islamic astronomy produced an alternative solution that Copernicus may have encountered.29 There were also a number of questions or problems reflected in the Theorica literature, some of which touch on philosophical and methodological issues about the reality of mathematical models. Scholars continue to debate these issues today. Cracow astronomers were very familiar with all, or nearly all, of these problems. 2. The Curriculum at Cracow As we saw in chapter one, students for the B.A. at Cracow received instruction on calculating the calendar (Computus) and introductory spherical astronomy (De sphera).30 Students normally received more instruction in astronomy and astrology after beginning their instruction for the M.A. From nearly the beginning of the fifteenth century, the university emphasized instruction in astronomy. Thanks to an endowment, a chair for the study of astronomy was funded around

28 See Copernicus, De revolutionibus I, 4 and 10. It is not clear whether we are dealing here with a clue or an afterthought. 29 We will discuss this issue more thoroughly in chapter seven. By way of example, see On the Revolutions (Rosen tr.), 417. See Mancha, “Ibn al-Haytham’s Homocentric Epicycles.” 30 For the mathematics curriculum in arithmetic and geometry, see Dianni, Studium 8–11 and 217–219. On the curriculum in the fifteenth century in particular, see A. Birkenmajer, Études, 455–569 and 620–635. On astronomy and mathematics, see Historia astronomii w Polsce, 1: chapters 5–7; Rosińska, “ ‘Mathematics’.” See also Markowski, “Mathematischen und naturwissenschaften,” 121–131.

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1405–1406. Several professors who occupied this chair modified the Alfonsine Tables in their Latin redactions from the fourteenth century for the meridian at Cracow. Known as Tabulae resolutae, these revised tables formed the basis of instruction in practical astronomy and of the contribution that Cracow astronomers made to the European reform of ancient astronomy in the fifteenth century. When another chair—this one for astrology—was established in 1459, the occupants continued and deepened the emphasis on practical astronomy.31 As a student at Cracow, Copernicus would have learned the basics of spherical astronomy (De sphera) and the account of planetary motions contained in the Theorica planetarum. He probably would not have begun to work on tables, observations, and the more advanced mathematical models of Ptolemaic astronomy until the fall of 1493. We know from the “Uppsala Notes” (in Copernicana 4, Uppsala University Library) that he acquired copies of the Alfonsine Tables and Tabula directionum of Regiomontanus as well as his copy of Euclid’s Elements (in Latin translation) while he was a student at Cracow. Although the “Uppsala Notes” contain entries from as late as 1532, some of the tables are unquestionably from his period of studies at the university for he copied versions of the tables used at Cracow in the second half of the fifteenth century. The handwriting also indicates that some tables and annotations were written before he left for Italy in 1496, after which time he adopted a chancery style of writing, clearly distinct from his previously more gothic style, although it displays characteristics similar to Gothica Antiqua.32 What did Copernicus learn about astronomy at Cracow? We divide this section into three parts: 1) De sphera and Theorica planetarum, 2) tables and canons, and 3) instruments. We will begin at a general level, descend to very particular and relevant assertions, and then conclude with a summary of the major contributors both to astronomy

31

See, for example, Rosińska, “‘Mathematics’.” See Rosińska, “Kwestia ‘Krakowskich’,” 72–94. For an extensive examination of Copernicana 4 and the “Uppsala Notes,” see Birkenmajer, Mikołaj Kopernik, 26–69 and 154–210. “Copernicana” is a reference to the shelf number of books thought to have been owned or annotated by Copernicus and located at Uppsala University Library. Copernicus’s copy of Euclid’s Elements is catalogued as Copernicana 6. See Czartoryski, “Library of Copernicus,” 354–396, at 365; and Goddu, “Copernicus’s Annotations,” 202–226, esp. 218–220. See also Dobrzycki, “Uppsala Notes,” 161–167. On Gothica Antiqua, see Derolez, Palaeography. 32

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at Cracow in the fifteenth century and to Copernicus’s education and training in astronomy. 2.1. De sphera and Theorica planetarum The De sphera of John of Sacrobosco was by far the most widely used introduction to astronomy at late medieval universities. It was of almost no practical use because it is largely qualitative, focusing on definitions and philosophically relevant questions. There were numerous commentaries produced in the Middle Ages, and certainly all of the major ones were known at Cracow in manuscript and/or printed editions of the late fifteenth century. Commentators distinguished various definitions of a sphere, deciding which is appropriate for the celestial spheres, how many celestial spheres there are, whether they are contiguous or continuous, and what essential characteristics they possess. In some cases the commentators cite ancient authorities including philosophers extensively, dealing with such questions as the relation of astronomy to natural philosophy and general questions about observations. For example, observations support giving precedence to the so-called Platonic axiom of perfectly uniform circular motion over the axiom of perfect geocentricity. Even at this level some commentators concluded that there is no unique center of all heavenly motions, although they often negotiated this problem by making distinctions based on the ambiguity of the term “center.” Occasionally, the commentators on De sphera also discuss issues relating to eccentric and epicycle models, often concluding that such mathematical models are fictions and imaginary, a conclusion that seems to follow from their definition of astronomy as a primarily physical rather than mathematical science. For the most part, however, such questions and criticisms appear in the commentaries on Theorica planetarum. There were at least two theorica, one known as Theorica planetarum Gerardi, and that by Campanus of Novara.33 The first has been attributed to Gerard of Cremona and Gerard of Sabionetta, but its authorship remains in doubt.34 Although inferior from a technical point of view to that by Campanus,

33

Campanus of Novara, ed. Benjamin and Toomer, 33–38; Pedersen, “Origins.” Pedersen, “Origins,” 120–122. Lemay, “Gerard,” 189, cites a manuscript from the twelfth century, and suggests that the author may have been John of Seville but reworked by Gerard of Cremona. 34

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the Theorica planetarum gerardi was published several times in the fifteenth and sixteenth centuries, while that of Campanus was known in that period only in manuscript.35 In these texts but especially in that attributed to Gerard of Cremona, the student encountered definitions and enumeration of spheres, but because the focus of this literature is on the motions of the Sun, Moon, and planets, there is somewhat more attention to observational details and models. The principal problem discussed in the Theorica literature is the reconciliation of Ptolemy’s exclusively mathematical models with the concentric cosmological system of Aristotle. The major development in this literature was the three-orb system of spheres, which allowed for an interpretation of the usefulness of the mathematical models while preserving the concentricity of the total sphere. In other words, the mathematical and predictive models were eccentric but the Earth is the geometrical and physical center of each total sphere and the cosmos as a whole. The mathematical models are necessary to save the phenomena, and the mathematical and physical descriptions should not contradict one another, although some incompatibility may be unavoidable. There were some astronomers, philosophers, and commentators who asserted the reality of eccentrics and epicycles (Albert of Saxony, Nicole Oresme, Peurbach, for example) and others who rejected them altogether in favor of homocentric astronomy (Averroes and Bernard of Verdun, for example). On the whole, it seems that most astronomers and philosophers accepted the need for eccentric and epicycle models. Some of these regarded the models as fictions (for example, John Buridan, Pierre d’Ailly, Albert of Brudzewo). Some philosophers, however, distinguished between demonstratio quia as the goal of astronomy (whereby bodies can be shown to move in a circle about a center) and demonstratio propter quid as the goal of natural philosophy. Such a distinction suggests a certain degree of agnosticism, skepticism, or just plain resignation about human ability to arrive at a final and complete understanding of the motions of the heavenly bodies. Some scholars have interpreted this commentary literature as supporting a complete separation of astronomy from natural philosophy, but this is very unlikely. Separation implies independence and autonomy,

35 “Theorica” usually refers to the one attributed to Gerard of Cremona, and it was printed eight times between 1472 and 1531. Campanus’s Theorica exists in many manuscripts and was cited frequently, but it was not printed until the twentieth century.

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and there can be little question about the fact that when it came to the question of the position of Earth in the cosmos, astronomy was subordinate to natural philosophy. That judgment holds certainly for homocentrists, and even for fictionalists it is clear that their fictionalism did not extend to natural philosophy. In spite of Copernicus’s commitment to realism, even he made a distinction between assumptions in mathematical astronomy and assumptions in natural philosophy, about which more in chapter ten.36 What is remarkable about this literature from the perspective of the fifteenth century is the advance made in practical astronomy. From at least the middle of the century we can see a spreading awareness that the observational base is flawed and that the models are inaccurate. Whatever the motives for the advances in practical astronomy—whether related to astrology, calendar reform, navigation, and the like—the production of tables constituted the principal activity of fifteenth-century astronomers at the University of Cracow. In other words, there was increasing specialization in technical proficiency in the fifteenth century, and much of this work of a more technical and calculatory nature is distinguished from mainstream natural philosophy. This development brings us, then, to the second category of works. 2.2. Tables and Canons The most important tables were the Alfonsine Tables in the Latin sexagesimal version produced at Paris in the fourteenth century. The canons contain instructions for calculating the equation of center (the difference between the true Sun and the mean Sun), the true argument (angle between the planet on its epicycle and the true motus of the center of the epicycle as measured from Earth), the mean argument (the angle between the planet on the epicycle and the mean motus of the center of the epicycle as measured from the equant point), and the equation of argument (the angle between the planet and the line

36 For an excellent overview of the tradition, see McMenomy, “Discipline.” For a comprehensive study of spheres in the tradition, see Lerner, Monde, Vol. 2. See also Markowski, “Nie znane,” 3–32; Grant, “Eccentrics,” 189–214; idem, Planets, 271–370; Peurbach, Theoricae; Aiton, “Celestial Spheres and Circles,” 75–114; Barker and Goldstein, “Realism and Instrumentalism,” 232–258.

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of true motus).37 The motus governs the position in the main eccentric circle, and the argument governs the position of the planet on the epicycle.38 There are also instructions for measuring the motion of the eighth sphere and elements of the lunar orbit for the purpose of finding the extent and duration of lunar eclipses. In fact, the tables are little different from those in the Almagest and are strictly unrelated to observation. They could have functioned as the basis for comparison against observation, but lectures and exercises on the tables were primarily textual. In Cracow there are versions of the tables that are calculated for the meridian at Cracow. As noted, such tables are called Tabulae resolutae. The first seem to have been compiled in 1424 as epoch for the meridian at Wrocław. The Wrocław tables reached Cracow where they were used as a textbook at the university. Martin Król of Żurawica composed a set of Tabulae resolutae in 1445 as epoch for the meridian at Cracow. In 1449, Andrzej Grzymala wrote Canones tabulatum resolutarum for 1448, and several more versions appeared over the next few decades, for example, by Albert of Brudzewo for 1482 and John of Glogovia for the years between 1487 and 1490. In the sixteenth century several versions were printed.39 The Tabulae resolutae were used in Cracow as a textbook on which professors lectured, explaining to students how to make practical computations and ephemerides. As we mentioned, Copernicus owned a book that contained the Alfonsine Tables (Venice, 1492) and Regiomontanus’s Tabula directionum (Augsburg, 1490), now catalogued as Copernicana 4 at Uppsala University Library. These books provided him with astronomical calculations for planetary theory and eclipses and for spherical astronomy respectively. At the end of Copernicana 4, as we indicated, are the “Uppsala Notes”, where “he copied parts

37

Compare Price, Equatorie, 75–92; “Extracts,” Source Book, ed. Grant, 465–487; and McMenomy, 118–121 and 127–133. Note that the so-called Alfonsine Tables in their fourteenth-century Latin version may have little to do with the original. On this issue see Poulle, Tables alphonsines; idem, “Alfonsine Tables”; idem, “Tables Alfonsines,” 51–69; and idem, review in Isis 94 (2003) 366–367. But see Goldstein, “Historical Perspectives,” 195, note 19. See also North, Richard of Wallingford, 3: Appendix 29, 168–200, for a detailed outline of the Ptolemaic theory of planetary longitude. 38 My description follows Price, 99–101, very closely. Note his emphasis on the use of the term motus. On mean motus, equation of center, and equation of argument, see also North, Richard of Wallingford, 170–171; and Poulle and Gingerich, “Positions.” 39 Compare Chabás, “Diffusion,” 168–178; and Dobrzycki, “ ‘Tabulae Resolutae’,” 71–77. See also Rosen, “Alfonsine Tables,” 163–174.

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of Peurbach’s Tabula eclipsium and a large set of planetary latitude tables related to those in the Tabulae resolutae.”40 The manuscripts of the Tabulae resolutae, however, do not contain any planetary latitude tables.41 Another set of tables is preserved in Cracow, namely, the planetary tables of Johannes Bianchini, which do include latitudes of the planets. Grażyna Rosińska has shown that Copernicus also copied Bianchini’s tables.42 It is reasonable to conclude, then, that Copernicus received instruction at Cracow on spherical and planetary astronomy and on the use of tables, which he partly supplemented evidently while he was still in Cracow by referring to other tables or by copying comments of his teachers.43 We will consider his computations and use of tables more extensively in chapter seven. 2.3. Instruments There is no direct evidence of instruction on the construction and use of astronomical instruments, but there are descriptions with instructions throughout the fifteenth century in Cracow. The fact that Cracow astronomers placed so much emphasis on practical astronomy gives us reason to believe that their commentaries and tables were not just scholastic lectures and exercises on books. It is very likely that students were taught how to make computations using the tables, and that they received at least some instruction on the construction and use of instruments. In fact, we have no evidence that Copernicus 40

Swerdlow, “Derivation,” 423–512; idem, “Summary,” 201–213; Swerdlow and Neugebauer, Mathematical Astronomy, I: 4 and 104. See also Curtze, Reliquiae copernicanae, 27–61; and Prowe, Nicolaus Coppernicus, II: 206–244, for the first efforts to decipher the tables. See Birkenmajer, Mikołaj Kopernik, chapters 2 and 7. The most important parts of these chapters are available in an English translation supervised by Gingerich and Dobzrycki, “Nicholas Copernicus.” See Gingerich, “Commemorative Practices,” 41, n. 15. According to Wasiutyński, Kopernik, 550, item 17, Birkenmajer completed Part II, “Biography” in fourteen chapters, and that the manuscript in the author’s own hand is in the Jagiellonian Library. 41 Chabás, “Diffusion,” 172–173. 42 Rosińska, “Identyfikacja,” 637–644; eadem, “Giovanni Bianchini,” 565–577; eadem, Scientific Writings, 476–487. 43 Compare Dobrzycki, “Tabulae Resolutae,” 72; Birkenmajer, Mikołaj Kopernik, 58–60 and the whole of chapters 2 and 7 where Birkenmajer demonstrates that several of Copernicus’s tables in Copernicana 4 and in the “Uppsala Notes” date from his years in Cracow. See also chapter 9 where Birkenmajer argues that Copernicus learned the principles of trigonometry at Cracow as well. Cf. Rosińska, “Krakowska szkoła,” 463–483; eadem, Instrumenty astronomiczne, 225–226, 358–359, and 476– 487; eadem, “Giovanni Bianchini,” 565–577; eadem, “L’École astronomique,” 89–91; eadem, “Nicolas Copernic,” 149–157.

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made any observations earlier than 1497 when he was in Bologna, but Rheticus’s description of Copernicus’s assistance to Domenico Maria Novara suggests that Copernicus had some experience in using instruments to make observations and measurements.44 In Rosińska’s register of 185 astronomical treatises in manuscript at Cracow mostly from the fifteenth century, thirty-two contain treatises on astronomical instruments.45 In these manuscripts are found canons or instructions on the use of the astrolabe, and there is evidence that an astrolabe was used to compute the latitude at Cracow around 1379. One manuscript also describes the procedure for using an astrolabe to determine the difference in longitude between two localities when one of them is known. The foundation of the Stobner chair for astronomy around 1405 required the occupant to prepare almanachs to determine the position of planets from the Cracow meridian. Several manuscripts of the time describe sundials, a portable gnomonic dial, astrolabes, quadrants, and equatoria of planets. The calculations made to predict solar eclipses in 1406 and 1409 suggest that they were based not just on a re-computation of the tables but also on observations. Throughout the fifteenth century there is some evidence that Cracow astronomers recognized inaccuracies in the tables, considered their results critically, but not much evidence that they checked their calculations against observations.46 Peter of Żwanow, a student from the first half of the fifteenth century, thanked his teacher Lawrence of Raciborz (1381–1448) for having instructed him on the use of various tables and instruments. The astronomers who taught theoretical astronomy by practice were distinguished from those who taught it by commentary on texts. In one of his lectures on astronomical tables, Lawrence says that the true place of a planet can be obtained from its mean place either by calculation from tables or by using an equatorium planetarum. Now, the 44 See Rheticus, Ephemerides novae in Hipler, Spicilegium, 225–232, esp. 227. Compare with Receptio copernicana, in Copernicus Gesamtausgabe, 8/1: 123, lines 37–38: “Vixerat cum Dominico Maria , cuius rationes plane cognoverat et observationes adiuverat.” 45 Rosińska, Instrumenty, 165. Elsewhere, “L’école astronomique,” 89, she states the numbers a little differently; 57 diverse works out of 186 codices, but this reflects the fact that several treatises were bound in one codex. 46 Rosińska, Instrumenty, 50–58; Włodarczyk, “Observing,” 176–180. But see Kremer, “Use of Walther’s Observations,” for a cautionary lesson about the use of observation to correct data or tables. See also Poulle, “Activité astronomique,” for cautionary remarks.

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equatorium is not an observational instrument and its use is dependent on a set of tables, but the comment does confirm the use of an instrument.47 Several manuscripts from the first half of the fifteenth century describe the construction of a flat astrolabe and a spherical astrolabe. Rosińska claims that the efforts to establish the geographical co-ordinates at Cracow with more precision were dependent on astronomical observations. Comments by Sandivogius of Czechel show that his students had a basic knowledge of how to handle an astrolabe and a quadrant.48 Martin Król of Żurawica occupied the Stobner chair around midcentury. In lectures he demonstrated knowledge of instruments by presenting the construction of an astrolabe as one way of projecting a sphere on a plane, and he described several other instruments.49 Again from about mid-century are manuscripts containing Prosdocimo de Beldomandi’s two treatises on the astrolabe, a treatise by Profatius (Jacob ben Nahir) on the construction of a new quadrant, and an anonymous description of a vertical sundial with the gnomon parallel to the Earth’s axis. Again, there is evidence that the results obtained by some astronomers were dependent on their own observations and not just calculations. The instruments of Martin Bylica of Olkusz were donated along with his books to the university after his death. Copernicus was probably a witness at the ceremony in 1494 celebrating the gift.50 For the period in which Copernicus studied at the university, the principal source is Albert of Brudzewo, who not only mentions the instruments used by Ptolemy but also explains their purpose and use. There are also manuscripts dating from this period describing a spherical astrolabe with instructions for its use. Copernicus most likely heard descriptions of the spherical astrolabe, the albion, a ring astrolabe, a triquetum, and the gnomonic quadrant.51 We may reasonably question the extent to which “practicing” academic astronomers at Cracow resorted to observation to check or 47

Price, Equatorie, 130; compare Rosińska, Instrumenty, 59–70. Rosińska, Instrumenty, 65–68; Włodarczyk, 180–188. 49 Rosińska, 71–78. 50 Ibid. 79–92. On Prosdocimo, see Markowski, “Prosdocimo de’ Beldomandi,” 29–37. On Martin Bylica, see Markowski, “Martin Bylica,” 125–132. 51 Rosińska, Instrumenty, 93–100; Włodarczyk, 177 and 183; Kremer, “Walther’s Observations,” 185; idem, “Use.” 48

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verify the accuracy of Ptolemy’s data, the Alfonsine Tables, and other tables. On the other hand, the emphasis on practical uses along with the critical tone of commentaries and instruction suggest that, in principle, astronomers trained at Cracow recognized inaccuracies in observational data and the need for a sounder observational base. Such criticisms along with theoretical objections to Ptolemy’s models support at a general level the conclusion that Copernicus benefited from a tradition of efforts to improve astronomical tables by means of mathematical calculation and observation. 3. The Criticisms of Ptolemaic Astronomy We now turn to a consideration of more specific theoretical issues relating to Copernicus’s criticism of the equant model, Ptolemy’s lunar model, and the disagreements over the ordering of the planetary spheres. In the subsequent section we will consider the courses that he may have attended, the connections of Peurbach and Regiomontanus to Cracow, and what Copernicus could possibly have thought about all of this as he left Cracow in 1495. As is now well known, some of Copernicus’s lunar and planetary models are so similar to earlier Arabic models that experts believe that he must have seen them somewhere.52 This guess may well turn out to be true, but there is one pattern to these speculations and reconstructions that is troubling. In almost every case scholars base their argument on the assumption that Copernicus must have encountered the complete solution, probably indirectly, from his Arabic predecessors. Mario di Bono has exposed a logical flaw in their reasoning and an error of fact. He is at least willing to entertain the possibility that Copernicus may have picked up hints that he then developed independently into the solutions presented in Commentariolus and De revolutionibus.

52 The literature on this point is extensive, and I cite here only the foundational and most recent studies in English known to me. Cf. Roberts, “Solar and Lunar Theory,” 428–432; idem, “Planetary Theory,” 208–219; Kennedy, “Planetary Theory,” 227–235; Hartner, “Islamic Astronomical Background,” 7–16; Swerdlow and Neugebauer, Mathematical Astronomy, 41–48; Saliba, “Role of Maragha,” 361–373; Ragep, “Two Versions,” 325–356; idem, Nasir al-Din al-Tusi’s Memoir, I: 51–53, and II: 194–222, and commentary, 348–361. But see also di Bono, “Copernicus,” 133–154. On al-Tusi, see Farhang.

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There are seven candidates for such hints or intermediary sources that have been proposed—Nicole Oresme, Henry of Hesse, a magister Julmann, Sandivogius of Czechel, Albert of Brudzewo, Peurbach, and discussions or sources available at Padua. Here I discuss the first four, and leave the last two for chapter seven.53 Nicole Oresme (ca. 1320–1382) presented what appears to be, according to Claudia Kren, a garbled version of Nasir-al-Din alTusi’s rolling device, and if so, then perhaps Oresme encountered a description in the fourteenth century. Again, Kren seems to assume that Oresme could not have proposed a way to produce an oscillatory rectilinear motion by combining two uniform circular motions. Oresme was addressing the Averroistic objection to eccentric and epicycle models. He responded to the objection by proposing a hypothetical device whereby the motion of a body on an epicycle can be constructed in such a way as to save the regular motion of the body, accounting for its apparent irregularity, and avoiding all of the dire consequences predicted by Averroes. The solution, such as it is, occurs in Oresme’s Questiones de spera. Because we know of no version of this treatise that Copernicus may have seen, we can at best conclude that it influenced an author whose work Copernicus did see or hear about. Now, the full argument here would be, then, that the geometrical proposition, however hypothetical in its presentation, could have inspired Copernicus to construct his own version.54 Likewise, Henry of Hesse (1325–1397) responded to Averroes’s objections to Ptolemaic astronomy by proposing concentric-sphere models to account for the motions of the Sun and Moon, and for the precession of the equinoxes. He seems to have relied on descriptions of Ptolemaic and Eudoxian models, as Claudia Kren explains.55 His

53 On Peurbach, see Dobrzycki and Kremer, “Peurbach and Maragha Astronomy,” 187–237. For Padua, see Swerdlow and Neugebauer, Mathematical Astronomy, 41–48. Both of these studies, however, assume that the intermediate source depended on a source that was derived ultimately from Maragha. Di Bono, “Copernicus,” esp. 145, questions that assumption. In an excursus on chapter seven that I have moved to an appendix, I will provide a sketch of how an alternative reconstruction might work. 54 See the reconstruction and interpretation by Kren, “Rolling Device,” 490–498. Kren presents the evidence modestly and without arguing for a possible inspiration for Copernicus. Garrett Droppers, Questiones, 458–462, has proposed a likelier reconstruction that fits Oresme’s description better than Kren’s does. On Oresme, see Clagett, “Nicole,” 223–230. 55 Kren, “Homocentric Astronomy.” In the texts that Kren cites, Henry always uses the term concentricus, not homocentricus. On Henry, see Busard, “Henry,” 275–276.

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proposed solutions for the motions of the Sun and Moon seem to rely on the intelligences moving celestial bodies non-uniformly although uniformly relative to the equant point.56 It is likely that Henry knew Oresme’s Questiones de sphera. Note how both Oresme and Henry violate without comment the Aristotelian prohibition against metábasis. It seems that already in the fourteenth century, philosophers interested in mathematics as a tool of analysis violated the prohibition routinely and without discussion or justification. Unlike Oresme, however, Henry relies on predecessors even if he does not name them all.57 There is not much known about magister Julmann (fl. 1377) except that he followed Henry of Hesse, and also proposed concentric-sphere solutions to account for Ptolemaic epicycle and eccentric models. It seems that Henry and Julmann may have seen some description of Eudoxan devices proposed by Ibn al-Haytham that derive from Maraghan planetary theory or from a tradition of Aristotelian objections to Ptolemaic eccentric-epicycle models.58 In a commentary on the Theorica planetarum, Sandivogius of Czechel (fl. 1430) described a lunar model to explain why, if the Moon moves on an epicycle, we see the spots on the Moon always oriented in the same way. His solution placed the Moon on a second epicycle that moves at the same rate as the first epicycle but in the opposite direction. Now, it is obvious that this is not the problem that either Maragha astronomers or Copernicus solved. But the point is the geometrical device itself, not the problem it proposes to solve.59 Again, we do not know whether Sandivogius encountered a description of the Maragha device or Oresme’s, or whether it was a Cracow invention or even, perhaps, his own invention. What has been established, however, is that Albert of Brudzewo repeated the solution in his Commentariolum, a text on which Copernicus very likely received instruction.60 The point is that Copernicus could have learned of the geometrical device in a lecture on Brudzewo’s Commentariolum. The application to the solution of the problem with the Ptolemaic lunar

56 This solution is similar to that offered by Ptolemy himself in Planetary Hypotheses, as interpreted by Pedersen, Survey, 397. 57 Mancha, “Ibn al-Haytham’s Homocentric Epicycles,” 73–78 and 81. 58 Mancha, 81. 59 Rosińska, “Nasir al-Din al Tusi,” 241–243; eadem, “Nicolas Copernic,” 152–155. 60 Ibid. Compare Albertus de Brudzewo, Commentariolum, 68–69.

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model and the “replacement” of the equant would have been Copernicus’s contribution. When Rheticus later referred Copernicus to the solution in Proclus’s commentary on Euclid’s Elements, Copernicus could not resist citing an ancient authority. But the fact is that he already knew a version of the so-called Tusi device when he wrote Commentariolus, which is to say no later than 1514.61 Experts have exaggerated the supposed identity between Copernicus’s and al-Shatir’s models and the Tusi couple. Di Bono explains the similarities plausibly as matters of notation and convention. Di Bono also shows that Copernicus’s use of the models required an adaptation, and, we may add, if he was capable of adapting geometrical solutions, then why not the solution in Albert’s treatise? The question should be reconsidered.62 More to the point of this section, however, note that Copernicus recognized an observational problem, and suggested that a secondary epicycle carrying the Moon and moving in the opposite direction to the first epicycle could solve the problem of the size of the lunar disk at the quadrature points.63 Aside from acquaintance with Averroes’s objections to eccentrics and epicycles, Copernicus also encountered in Cracow objections to the equant. In the Commentariolum, Brudzewo reports the problem of the irregular motion of the epicycle on the deferent that violates the maxim according to which the motions of the heavenly bodies are simple and regular because the motion of a simple body must be simple and regular.64 The solution, of course, is the equant model. As for the fact that the epicycle is moving uniformly not with respect to Earth or the deferent center but with respect to the equant point, Brudzewo argues that the motion of the orbs is not related to the equant. The equant has no relation to the motion of a real orb, for the equant is an imaginary circle posited by mathematical astronomers to account for appearances.65 Brudzewo clearly recognizes a physical problem with the equant model—it cannot refer to the motion of an orb. His solution, then, is 61 We will examine the details in chapter seven, and also move the date earlier to 1510. 62 See chapter seven for a more detailed summary and excursus on transmission. 63 Copernicus has the secondary epicycle rotating twice as fast as the first. 64 Brudzewo, Commentariolum, 26, 51, and 85. See also A. Birkenmajer, Études, 622, n. 35. 65 For a summary and citation of Brudzewo’s treatise, see section five below.

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to interpret the equant model as a mathematical fiction. This is, in fact, the interpretation that Brudzewo seems to adopt for all or nearly all of the mathematical models based on eccentrics and epicycles. Because he sometimes reports Peurbach’s view, he seems to agree with Peurbach’s realism about spheres, orbs, eccentrics, and epicycles, but his own view seems to be that several mathematical models and circles are “imaginary” or “imagined.”66 Because orbs are not concentric, there is no unique center, for different orbs have different centers.67 Brudzewo also noticed that the motions of the planets are linked to the motion of the Sun, which he describes as a natural connection because the planets are all illuminated by the Sun.68 Finally, he comments that the path of the Moon in one month has a nearly oval rather than circular shape. He does not mention, however, the observational anomaly this would cause regarding the size of the Moon at quadrature points.69 As for the observational anomaly of Ptolemy’s lunar model and the ordering of the spheres, we may turn to other sources and the question of their availability in Cracow. Of medieval authors known at Cracow, Henry of Hesse recognized that a consequence of the Ptolemaic lunar model should be a near doubling in the apparent size of the Moon at quadrature. Was this 66 Brudzewo, Commentariolum, 22 and 86. It is not altogether clear, however, whether he regards the lunar epicycles as real. After all they together explain an observational fact, but perhaps he regards these too as nothing more than imaginary models that save the appearances. Compare Jardine, “Significance,” 168–194; Campanus, ed. and tr. Benjamin and Toomer, 42–47; and Crowe, Theories, 46–47. These references relate to Ptolemy’s fully refined lunar model. The problem with lunar models and their reality goes back to Ptolemy himself and the details of the “crank mechanism.” Toomer, “Ptolemy,” 193–194, thinks that the crank mechanism was a real feature of the model and not just a convenient device for predicting the longitude. But if it is real, then this seems to strengthen Pedersen’s interpretation, Survey, 397, that the celestial mover is a vital force. The implication is that an Aristotelian-like intelligence or soul moves the body voluntarily by influence or calculation. For revisions of the usual story, see Shank,“Mechanical Thinking,” and Sarnowsky, “Defence.” 67 Brudzewo, Commentariolum, 30. 68 Ibid. 20 and 117. Some scholars have placed undue emphasis on this claim by Brudzewo, a claim similar to one made also by John of Glogovia. See L. Birkenmajer, Stromata, 95. Compare Markowski, “Szczyt rozkwitu,” 107–126, esp. 110; and Knoll, “Arts Faculty,” 137–156, esp. 148, the latter of which is careful to note, however, that the theories remain geocentric. Anyone familiar with the construction of Ptolemaic models would have been aware of the link between the planetary models and the motion of the Sun. 69 Brudzewo, Commentariolum, 124.

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problem noticed in Cracow? We do not know. It is possible—perhaps likely—that Copernicus first became aware of this problem from Regiomontanus’s Epitome in 1496 at the earliest or from Domenico Maria Novara during the winter of 1496–1497.70 On the ordering of the spheres, Ptolemy’s was standard, but alternative orderings were known. The Platonic places the spheres of Mercury and Venus beyond the Sun, and the Capellan, sometimes also called “Egyptian,” places the spheres of Mercury and Venus around the Sun. Copernicus certainly encountered these alternatives in Cracow, although the uncertainty about the ordering of the spheres probably did not trouble him until some years later.71 4. Copernicus’s Teachers at Cracow Next we consider Copernicus’s likely teachers in mathematics and astronomy at the university. We may first note that it is very unlikely that Albert of Brudzewo taught Copernicus astronomy. Albert did not teach any courses in astronomy between 1491 and 1495. It is possible that Copernicus may have taken private instruction from him, for we know that Conrad Celtes learned astronomy from Albert in this way. But we have no documentation at all to support such instruction while Copernicus attended the university. On the contrary, one scholar has argued that Albert would not have violated statutory restrictions on such instruction.72 Finally, Ludwik Birkenmajer’s efforts to demonstrate Copernicus’s direct acquaintance with Albert’s Commentariolum 70 For Copernicus’s relation to Novara and his lunar observation on 9 March 1497, see chapter six. See Birkenmajer, Études, 570 and 603. See also Lemay, “Astronomical School,” 337–354. Henry of Hesse, also known as Langenstein, ended his academic career in Vienna, where his ideas may have inspired Peurbach and Regiomontanus. See Dijksterhuis, Mechanization, II: 150, and III: 62; Zinner, Entstehung, 79–84, 116–117, 128–129, 131, 136, 205, 288, and 500–501. For more on Henry, see Steneck, Science, 66–72; Kren, “Homocentric Astronomy,” 269–281; Geyer, Patristische und scholastische Philosophie, in Ueberweg, Grundriss, II: 610–611; Hartwig, Henricus de Langenstein, II: 26; and Pruckner, Studien, 88. 71 See the representations of all alternatives conveniently gathered together in Heninger, Cosmographical Glass. There is some confusion in the literature about the names for the alternative ordering of the planets. The Platonic is also called “EgyptianPlatonic,” which apparently goes back to Macrobius’s Commentary, 16–18. The ordering adopted by Ptolemy is also called “Plinian-Chaldean.” The Capellan arrangement derives from Heraclides. See Eastwood, Ordering, chapters 2–4. 72 Palacz, “Nicolas Copernic,” 27–40, esp. 32–33. Unfortunately, Palacz does not provide the source for his claim, and I have been unable to confirm it. There is evidence

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have been almost universally rejected, even by his son Aleksander Birkenmajer.73 As best as we can reasonably reconstruct it, here follows the likely course of instruction that Copernicus followed along with a likely list of instructors who taught him. If Copernicus followed the order of courses towards degrees more or less as we have assumed, then he would have completed classes on Computus and De sphera by the spring of 1493. In that case he could have heard lectures on De sphera in the summer of 1492 from Nicholas Labischin, and on the Calendarium of Regiomontanus from John Gromaczky in the winter of 1492.74 It may have been at this time that he also heard lectures on Tabulae resolutae and/or Tabula eclipsium from Bernard Biskupie (winter 1492 or summer 1493). These were not required courses, but as we have seen, Copernicus acquired books of tables and knowledge of such tables at Cracow probably in 1493. He might have attended a lecture on Theorica but it is likelier that he heard his first lecture on this book between winter 1493 and summer 1495. The requirements for the M.A. included the standard quadrivial texts: arithmetic (Boethius), music (Johannes de Muris), Euclid’s Elements, Theorica planetarum, and Perspectiva. His teachers on these subjects may have been Martinus de Zeburk, Stanislaus Kleparz or Bartholomew of Oraczew, Simon of Sierpc on Euclid, Stanislaus of Ilkusz or James of Iszla on Theorica, and Simon of Sierpc again on perspective. In addition, he probably attended Albert of Schamotuli’s lectures on astrology (Ptolemy’s Quadripartita).75 Of significance on this list are the students of Albert of Brudzewo and John of Glogovia.76 One of them in particular, James of Iłzy (or Iszla), developed a reputation in his own right as an expert in astronomy. Aleksander Birkenmajer asserts that Copernicus almost certainly

of a professional and personal relation between Brudzewo and Celtes in Rupprich, Briefwechsel, 92–93. 73 L. Birkenmajer, in his edition of Albert of Brudzewo, Commentariolum, 55–56. See A. Birkenmajer, Études, 621–622, n. 37 in particular. Barker, “Copernicus,” 356, n. 15, accepts Birkenmajer’s evidence. The parallels cited by Birkenmajer are slim at best. Section five of this chapter summarizes the relevant parts of Albert’s treatise. 74 Liber diligentiarum, 22; Karliński, Żywot, Appendix III, Table 2. The Calendarium was often used in the instruction of Computus. See Poulle, “Activité.” Note Poulle’s cautionary remarks about results that depended on calculations, not observations. For biographical information on many of the teachers mentioned below, see chapter two. Cf. Birkenmajer, Stromata, 50–141. 75 Liber diligentiarum, 24–28; Karliński, Żywot, Appendix III, Tables 3–8. 76 Markowski, “Szczyt,” Historia, I: 115.

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attended the lectures of Bernard of Biskupie on the Table of Eclipses and of Albert of Schamotuli on astrology. The rest are conjectural.77 Jerzy Dobrzycki follows Ludwik Birkenmajer and considers it likely that Copernicus also attended lectures of Albert of Pnyewy, Simon of Sierpc, and Michael Falkener of Wrocław, all students of Albert and John.78 Dobrzycki also concludes that Copernicus left the university a competent astronomer who was aware of the need for reform.79 Markowski includes Albert of Pnyewy, Stanislaus Bylica of Olkusch, Bernard Biskupie, Stanislaus Biel, Albert of Schamotuli, Stanislaus Kleparz, Simon of Sierpc, Nicholas of Labischin, Martin Jezioran (Zeburk?) as students of Brudzewo and Glogovia.80 And Grażyna Rosińska, while dismissing Copernicus’s direct acquaintance with Brudzewo’s Commentariolum, also concludes that Copernicus was almost certainly taught Theorica in Peurbach’s version by one of Brudzewo’s students.81 Virtually all of Copernicus’s possible teachers in astronomy were students of Brudzewo and Glogovia. In short, Copernicus probably knew Brudzewo’s discussions of concentric and eccentric-epicycle models. Copernicus was well aware by 1495 of all of the following: differences among astronomers and among philosophers on the reality of models, some of the problems with Ptolemy’s lunar and equant models, differences about the order of the spheres of Mercury and Venus, the problems related to the accuracy of tables, and the calendar problem.82 What should be clear from Copernicus’s ownership of Regiomontanus’s Tabula directionum before 1495 and Brudzewo’s use of Peurbach’s rather than earlier versions of the Theorica is that they demonstrate an awareness of the Viennese achievements in mathematics and astronomy. Several Cracow figures belonged to the same circles as Peurbach and Regiomontanus, and here is where the connection between astronomical reform and Renaissance humanism takes on a special significance. Throughout the fifteenth century several masters

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A. Birkenmajer, Études, 565. Dobrzycki, “Mikołaj Kopernik,” Historia, I: 127–156, esp. 128–129. 79 Dobrzycki and Biskup, Nicolaus Copernicus, 31. 80 Markowski, “Szczyt,” Historia, I: 116–121. 81 Rosińska, “Traité astronomique,” 159–166, esp. 166. 82 Markowski, “Powstanie pełney,” Historia, I: 87–106, esp. 96–97. Martin Bylica copied Peurbach’s Theorica and brought it with him to the University of Cracow around 1475. See also Markowski, “Szczyt,” Historia, I: 113; Zathey, “Martin Bylica z Olkusza,” 40–54. 78

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at Cracow had also studied and lectured in Bologna, where they copied mathematical works of Prosdocimo de Beldomandi and Giovanni Bianchini and brought them back to Cracow. Bianchini’s tables were copied and adapted to Cracow. Martin Król of Żurawica was a friend of Peurbach’s.83 Martin Bylica met Regiomontanus in Padua, became his friend, and collaborated with him on working out the tables known as Tabulae directionum and produced an amended version of Regiomontanus’s Tabulae ac problemata primi mobilis. And as we have seen, it was Martin Bylica who introduced Peurbach’s Theorica at Cracow. Albert of Brudzewo was responsible for making Peurbach’s version of Theorica the basis of instruction at Cracow on the theory of the planets.84 5. Albert of Brudzewo’s Commentariolum I have already pointed to some comments in Albert’s treatise as part of Copernicus’s education in astronomy at Cracow. In this section I summarize the contents of Brudzewo’s treatise more thoroughly, emphasizing comments and arguments that Copernicus may have heard in lectures on Brudzewo’s commentary on Peurbach’s Theoricae novae planetarum. Brudzewo began lecturing on the Theoricae in 1482, and over the next few years completed at least two manuscript versions with copious marginal annotations, and an edition published in Milan in 1495 under the title Commentariolum super Theoricas novas planetarum Georgii Purbachii. In Cracow in 1900, the same year in which he published the first part of his monumental work towards a biography of Copernicus, Ludwik Birkenmajer published a modern edition with the same title based on the manuscripts, the glosses, and on the 1495 edition along with corrections of that edition completed in the late fifteenth or early sixteenth century.85

83 Domenkos, “Polish Astronomer Martinus Bylica,” 71–79, esp. p. 71. See also Markowski, “Martin Bylica.” Compare Mett, Regiomontanus, 184, where he comments that the astronomical sciences were taught at Cracow entirely in the spirit of Peurbach and Regiomontanus. In almost no other library were so many of their works available as in Cracow. 84 Compare Markowski, “Powstanie,” Historia, I: 96; and Domenkos, 73. 85 Brudzewo, Commentariolum, XLVI–LV. There may also have been an edition dated 1494, but Birkenmajer said nothing about it and did not rely on it in his edition.

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Brudzewo devotes most of the introduction to his treatise defending astronomical observations, and refuting Averroes’s criticisms of Ptolemaic models.86 The first question that he addresses is about the number of celestial spheres, explaining why astronomers posit the existence of spheres, and refuting Averroes’s objection to more than eight spheres. Brudzewo maintains that “any star whatever is a celestial sphere because it is a round celestial body, solid, at the center of which is a point from which all lines drawn to the circumference are equal.”87 He distinguishes three ways in which a sphere or orb is said to be one. In the first sense, a sphere is a spherical part of heaven, not separated from the whole, and in this sense there are as many spheres as there are stars. In the second sense, it refers to a sphere or orb that exists in itself whether it is concentric with the world or not. These are the orbs that astronomers posit to account for the motions of a star, for example, the Sun has three such orbs. The third sense refers to concentric orbs or the aggregate of all orbs that are necessary and sufficient for saving the motions of a planet both in longitude and latitude, and that are concentric with respect to the convex and concave surfaces. In other words, the third sense refers to the sphere containing all of the other orbs, and that sphere is concentric.88 After enunciating the fundamental Aristotelian propositions in natural philosophy about heaven as a simple body, the motion suitable to a celestial body, the motion of an orb by a single intelligence, and the doctrine that superior spheres influence lower ones but not the converse, Brudzewo then explains why he concludes with probability that there are ten spheres understood in the third sense. These are the seven planetary spheres, the eighth sphere is the starry vault, and because the eighth sphere has three motions (diurnal, annual, and in latitude) with the diurnal proper to it, then we must posit two additional spheres to account for the other two motions.89

86 Ibid. 1–21. For example, the opening sentence of the treatise: “Astrorum observatores studiosi experti quidem sufficienter sensu, ratione et instrumentis tradiderunt recte, virtute primae sphaerae omnium orbium lationes, nec non cunctarum stellarum fixarum volutationem, rotari.” 87 Ibid. 6: “Quaelibet enim stella est una sphaera coelistis, quia est corpus coeleste rotundum, solidum, in cuius medio est punctus, a quo omnes lineae ducibiles ad circumferentiam sunt aequales.” 88 Ibid. 6–7. It is very likely that Copernicus knew these distinctions along with the ones available in the literature on De sphaera, and we will return to them in chapter ten. 89 Commentariolum, 7–9.

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What Brudzewo meant by “sphere” in the third sense applies to each of the principal spheres encompassing the orbs needed to account for the motion of the star in that sphere. As becomes clear later, this meaning is not identical with the philosophical understanding of “sphere,” for when natural philosophers speak about heavenly motion, they mean the motion of the whole sphere, that is to say, the total sphere encompassing the entire universe that makes a complete circle in one day. Astronomers, however, consider not only the diurnal motion of the total sphere but also the proper motions of partial orbs. Brudzewo intended his distinction to neutralize the objections of natural philosophers like Averroes, and seems thereby to have proposed the autonomy of astronomy.90 As a consequence, astronomers devise models that describe the motions in plane circles. But these models do not exactly correspond to the real motions. For example, the Sun does not move in a circle contained by a single surface, but actually moves in an orb, a solid and spherical body. He concludes the introduction, then, by emphasizing astronomical observations and the models needed to account for the observations. In speaking of the motions of the planets, he concludes his comments thus: “We observe that the motions of the planets are related to the Sun; it is their standard of measurement by which it rules and devises them.”91 The remainder of the commentary follows the order of discussion in Peurbach’s treatise. Brudzewo at times expresses himself agnostically on the actual existence of eccentrics in the spheres of the planets,92 yet elsewhere he speaks as if they really exist, although he seems to be quoting Peurbach when he says so.93 The different centers of partial orbs are related to their different surfaces, but the total sphere is concentric. Much of the discussion of the Sun’s motion is concerned with proving the need for an eccentric orb. The Sun’s annual motion is irregular as the unequal length of the seasons demonstrates, hence the Sun moves non-uniformly around the center of the world but

90

Ibid. 17–19. Ibid. 20: “Et propter hoc, per respectum ad Solum omnium planetarum motus depraehensi sunt, et est eis mensura, qua regulantur et quaeruntur.” 92 Ibid. 26: “Qui quidem ecentrici an veraciter existant in sphaeris planetarum, nemo mortalium novit.” He goes on to quote Richard of Wallingford that eccentrics and epicycles are not real but inventions of the mathematical imagination, because without them we cannot treat the regular motions of the stars. 93 Ibid., for example, 57: “Iam Magister, posita declaratione ecentrici, qui est realis, . . .” 91

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uniformly around the center of the eccentric.94 Likewise, the Moon’s motion requires three orbs and an epicycle. Brudzewo refers to epicycles as “little spheres.” The three orbs are necessary to avoid penetration of spheres and the production of a void. He further describes an epicycle as having a short diameter, emphasizing the point by saying that the epicycle radius is as nothing in relation to the diameter of the eccentric.95 In commenting on the motion of the center of the epicycle through equal angles in equal times, Brudzewo expresses himself in a way that Birkenmajer thought Copernicus had read.96 However forced that speculation may be, Brudzewo’s proposal for a double-epicycle model, albeit to account for our always seeing the same side of the Moon, may have indeed impressed Copernicus.97 Of course, it is not necessary to suppose that Copernicus read Brudzewo’s text; he may have learned about it in a lecture on it. There is, finally, one more significant proposal in Brudzewo’s text that may have had an impact on Copernicus, namely, the idea in the Mercury model for generating a rectilinear motion from several circular motions.98 Again, that Copernicus may have heard of the geometrical construction in Cracow is significant. We will return to this

94

Ibid. 32–35. Ibid. 47–51. Note that Copernicus seems to have been concerned about the size of the Martian epicycle in particular. It obviously violates this description of an epicycle, and is distinctive among the superior planets for this reason along with the size of its eccentricity. Mercury and Venus also violate Brudzewo’s description, but at least in those cases the size of the epicycle is derived from the planets’ maximum elongations from the Sun. 96 Commentariolum, 55: “Correlarium primum habet veritatem, scilicet quod ecentricus super axe suo et polis et circa centrum suum movetur irregulariter, motum ipsius in Zodiaco computando respectu centri ecentrici et non respectu centri mundi. Sic enim et de Sole verum est, computando scilicet motum Solis in Zodiaco; respectu centri ecentrici et non respectu centri mundi. Sic enim et de Sole verum est, computando scilicet motum Solis in Zodiaco; respectu centri ecentrici motus suus est irregularis, sed si motus ecentrici Lunae absolute accipiatur (prout scilicet est in suo axe et polis et circa centrum ecentrici, non referendo ad Zodiacum), sic motus est regularis. Cuiuslibet enim orbis coelistis motus est regularis in se et simplex per unam maximam.” See Birkenmajer’s note 6. In De revolutionibus IV, 2, Copernicus expresses his first dissatisfaction with the equant model and its violation of the axiom about the uniform motion of celestial bodies. The parallelism between these two texts is not as close as Birkenmajer maintained. 97 Commentariolum, 67–69. 98 Ibid. 120. In note 10, Birkenmajer proposes that Copernicus adapted the idea to deal with the problem of constructing an oscillating motion out of circular motions in De revolutionibus III, 4. 95

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issue as well as the double-epicycle model in greater detail in chapter seven. For now it suffices to emphasize the likelihood of Copernicus’s acquaintance with some of Brudzewo’s ideas even though there is little concrete evidence that he read the Commentariolum. It is clear that Copernicus began to assemble some techniques that would later serve him in the completion of a project that he had not yet formulated. Perhaps even more important, his teachers alerted him to problems with Ptolemy and to the objections of natural philosophers like Averroes while also persuading him of the reliability of the sorts of observations that eccentric and epicycle models seemed to account for.99 *

*

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A question that the experts on Copernicus’s period in Cracow do not address adequately is the reason why Copernicus left the university in 1495. Indeed, if Cracow was so propitious in preparing Copernicus for more advanced work in astronomy, we must ask why he left it in 1495? Brudzewo died in 1495, but we have no evidence that Copernicus worked directly with him or had any reaction to his death. A narrative based on the achievements of fifteenth-century Cracow astronomers in practical astronomy is not sufficient. The training that Copernicus received in Cracow was undoubtedly important, but he sensed that the questions provoked by his teachers would not be answered there.100 Even if some project was beginning to form in his mind (unlikely at such an early date), he turned to Italy to refine the taste for Renaissance humanism that he acquired in Cracow. We began our reflections and conjectures about Copernicus’s career at the university in chapter one with questions about his failure to acquire degrees at Cracow and his decision to study in Italy. These are the reasons that stand out. Polish students with the financial means went to Italy or France to obtain degrees in law. While adequate for 99 In an important but unjustly neglected article by Świeżawski, “Matériaux,” he enumerates 213 citations to Averroes in Cracow sources of the late fifteenth and early sixteenth century. In fact, the references to Averroes far outnumber those to any author of the Latin commentary tradition. 100 Pedersen, “Tradition and Innovation,” 469–472, stresses the failure of faculties of arts to adapt to developments in mathematics and the understanding of nature. Even at Cracow the exodus of scientists from the university who realized that they could best continue with their work in a different intellectual environment is telling. Aside from Copernicus at Cracow, he points to others at other universities: Peurbach, Regiomontanus, Bernard Walther, Tycho Brahe, Kepler, and Galileo as other examples.

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instruction in the arts, Cracow was not suited to advance either Copernicus’s career or his intellectual development. Copernicus’s uncle received his law degree at Bologna. There were advocates of humanistic studies at Cracow in the 1490s. Some figures like Brudzewo benefited from Viennese advances. Others like Corvinus and Celtes were part of a circle of humanists, and some of these figures influenced or befriended Copernicus. Already as a student, Copernicus acquired treatises that placed him in the circle of those influenced by Cardinal Bessarion, Peurbach, and Regiomontanus. Finally, we have pointed to practical considerations involving his benefice and the conditions for enjoying its income. All of these reasons contributed to Copernicus’s decision to complete his studies in Bologna, and to his awareness that his intellectual growth and philosophical development depended on as direct acquaintance as possible with the Renaissance humanist revival of ancient thought as represented by Regiomontanus.

PART TWO

COPERNICUS’S EDUCATION IN ITALY, 1496–1503, AND RETURN TO POLAND

CHAPTER SIX

COPERNICUS IN ITALY 1. Introduction In Part I, I argued that as Copernicus approached the end of his education at Cracow, he still did not know whether he would be able to complete his education in Italy. The possibility that he might need a degree from Cracow required him to complete a course of studies equivalent to a bachelor’s and a master’s degree in arts. The training he received in logic, natural philosophy, and mathematics prepared him for advanced work in Italy. His later writings testify to the fact that he had some familiarity with the works of Aristotle and the commentary tradition as represented at Cracow. He later cited Aristotelian and scholastic philosophical principles, concepts, and arguments, sometimes from memory. We have little reason to believe that he deepened his acquaintance with the scholastic commentary tradition or acquired more philosophical training in northern Italy. In Italy he advanced in astronomy, began to learn Greek, studied law and, in his final two years, medicine. Throughout these years he also collected numerous books that summarized ancient views or data on astronomy and philosophy as well as books on medicine. He spent a few months in Rome, probably as an intern with the Varmian representative to the Roman chancery. He left Italy with a degree in canon law from Ferrara and with two years of training in medicine, mostly in the preparation of medicinal drugs, from the University of Padua. In sum, he left Cracow in possession of the following tools and ideas. In logic, he knew about the construction of arguments based on dialectical topics. He may already have developed a view about the relation between hypotheses and conclusions. At the very least, he understood that where a causal connection was involved, it is not possible for a true conclusion to follow validly from a false premise. He also learned in all probability, however, that a weaker connection such as relevance between a hypothesis and conclusion could be used as a criterion to prefer one hypothesis over another.

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In natural philosophy, he learned above all that scholastic authors and schools had modified Aristotelian principles, and adapted them to problems and questions that were, at best, peripheral to Aristotle’s project. In astronomy, he developed sufficient competence, and received sufficient training to work with tables, and to use observational instruments. He may have already adopted some inspiration from the humanist revival of Plato and Neoplatonism to re-evaluate the place and role of mathematics in the ordering of the disciplines, and also to believe that Platonism and Aristotelianism were reconcilable. At this point it would be going too far to conclude more from his education at Cracow. We have no reason to believe that he had developed any new cosmological theory. He was aware of problems with Ptolemaic astronomy and its compromises with Aristotelian natural philosophy. He was prepared to take advantage of the works of his predecessors and contemporaries to address those problems. * * * We know very little about what Copernicus did in 1495–1496. In August of 1495, Nicholas succeeded John Zanau as a canon of Varmia upon the latter’s death. In November of the same year the account book of the Varmia chapter listed Nicholas among those late with their payments for church vestments, but we do not know where he was. Some speculate that he returned home to Toruń and visited Varmia, and others that he traveled and perhaps visited some German universities, but to this day no one has found the slightest evidence in support of either conjecture. Would Copernicus have visited Nürnberg to consult mathematicians and sources related to Peurbach and Regiomontanus? We do not know.1

1 Bernhard Walther, a self-proclaimed student of Regiomontanus, had moved to Nürnberg in 1467 and remained there until his death in 1504. See Schmeidler, Kommentar, 3/1: 166. The three Nürnberger observations of Mercury reported in De revolutionibus V, 30 could not have relied on a printed source any earlier than mid-1532. See Zinner, Regiomontanus, 144–147, 193–194, and 318–310. Compare with Rosen, Commentary, Copernicus, On the Revolutions, 432–434, who thinks it more likely that Rheticus, who knew the recipient of Walther’s handwritten observations, Johann Schöner, transmitted the information to Copernicus in 1539. But see also Zinner, Entstehung, 588 (note to p. 166), and also Schmeidler’s introduction to Regiomontanus, Opera collectanea, XXI and XXVII.

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In the fall of 1496 Copernicus entered the University of Bologna as a student of law and member of the German nation.2 Scholars have already studied the curriculum in law at Bologna and in medicine at Padua. My purpose in examining his years in Italy is not to repeat those results—although some repetition is unavoidable—, but rather to examine what Copernicus encountered that would have contributed to his arguments, and that will help us to characterize his relation to the Aristotelian tradition. The statutes regarding canon law were specific about assignment of books and the structure of the curriculum. We cannot assume that professors actually followed the statutes, but the entire tradition of legal commentary, as with all scholastic exercises, involved the application of logic and dialectic to the reconciliation of texts, editions, customs, and laws.3 Copernicus would have encountered a similar process in medicine at Padua. Our task is to develop a sense for Copernicus’s intellectual development and for the skills that he would have learned for the practice of both law and medicine. As we saw in chapter five, Copernicus could not have used Regiomontanus’s Epitome of the Almagest earlier than 1496. We know from Rheticus’s testimony that Copernicus met and worked with Domenico Maria Novara in Bologna. It was also during these years (1496–1500 in Bologna and 1501–1503 in Padua) that Copernicus began to learn Greek. In this chapter, then, we take up these subjects in the following order: Copernicus’s studies in law, work with Novara on astronomy, study of Greek, sojourn in Rome, medical studies at Padua, and degree from Ferrara. 2. Copernicus’s Education in Canon and Civil Law Scholars who have taken up questions about Copernicus’s education have focused understandably on the inspiration for his discovery of the heliocentric system—an important question, to be sure, but not the only question to ask about Copernicus’s education. Copernicus

2 Acta nationis germanicae, 4 and 248. See also Documenta copernicana, ed. Kühne and Kirchner, Copernicus Gesamtausgabe 6/2: 36–43; and Biskup, Regesta, 36–39, Nos. 23–28. For an excellent general survey, see Berman, Law and Revolution. 3 Denifle, “Statuten,” 3: 196–408. Note the comment, 199, that there are no manuscript sources for the statutes prior to 1507. See also 238 and 244–247. Compare Müller, “Student Education,” 326–354, esp. 342–344; Rosen, “Copernicus and his Relation,” 127–137, esp. 129; Prowe, Coppernicus, I, 1: 229; and Malagola, “Aufenthalt,” 39–40.

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arrived at his solutions of astronomical problems as a result of working through technical, mathematical problems, but his path to a new cosmological theory depended on a dialectical and critical reading of summaries of Ptolemaic astronomy.4 For that reason we have proposed that his education prepared him in two ways to challenge traditional astronomy. First, it provided the logical foundations for a dialectical reading of the sources. Second, it contributed later to his presentation, arguments, and the wider aim of persuading his readers to adopt a view that contradicted common sense, the still dominant natural philosophy of the age, and Scripture literally interpreted. In regard to his argumentative techniques, the studies on Copernicus have been deficient, however helpful they may be in helping us to understand Copernicus’s cultural milieu. For example, Cesare Vasoli’s learned essays on Copernicus’s education in Italy, while informing us of Copernicus’s training in humanistic methods of textual analysis, tell us nothing of his education in law and medicine.5 Here again, we must consider reconstructions based in part on the evidence of Copernicus’s later activity as an administator and physician.6 In the case of law, we know at least that Copernicus received a degree in canon law from the University of Ferrara in 1503. Alas, because of Ferrara’s reputation as a “degree mill,” we cannot be absolutely certain that he actually attended any courses, let alone all of those required for a degree; the argument here, then, proceeds in an indirect way. Copernicus later served as a church administrator. He acquired the experience that he needed to perform his duties, and so we suppose that he learned some of the content and techniques requisite to the practice of law. If that seems plausible, then the question we pose is about the content and methods of education in law at Bologna, especially those parts of it that would have contributed to his skills in argumentation, expression, and persuasion.7

4 As the reader will see in chapter seven, we argue that Copernicus arrived at his new cosmological theory before transforming Ptolemy’s geocentric models into heliocentric ones. 5 Vasoli, “Copernic,” 161–174. In fairness, we must acknowledge that Vasoli’s own restrictions and qualifications (174) support a more nuanced conclusion. 6 Perhaps it would be more accurate to call him a medical practitioner. He did not receive a degree in medicine, nor was he ever licensed to practice medicine. 7 Malagola, “Aufenthalt,” 30–34; Biskup, Regesta, 43, No. 44; Grendler, Universities, 105. See the review of Grendler’s book by Lines, 715–716.

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We do not know to what extent Copernicus studied civil law. The documents are not completely in agreement, some suggesting that he was enrolled as a student of both civil and canon law, others that he studied only canon law.8 His later practice in church administration and involvement in the Varmian struggle against the Teutonic Knights suggest that he needed a knowledge of both civil and canon law. On the possibility that Copernicus entered Bologna initially as a student of canon law and then later added civil law,9 we begin with a description of the curriculum in canon law. The academic year began on 19 October 1496. At that time masters conducted classes in canon and civil law at their residences or in private quarters that they rented.10 For the period during which Copernicus studied law, professors of law constituted over sixty percent of the faculty teaching at the university.11 Although the official opening of the academic year was usually 18 or 19 October, lecturers did not begin formal classes until after 1 November with ordinary lectures held usually on Monday through Wednesday and on Friday and Saturday, extraordinary lectures on Thursdays and holidays. Professors were likewise differentiated between ordinary and extraordinary, and still others were designated as holiday professors and university lecturers. Regardless of rank or prestige, professors lectured only once a day although ordinary professors lectured five days a week. Evidently, university lectureships were one-year student lectureships designated for the student rector of the law organization and for selected law students in their last year of study. Classes were distributed throughout the day beginning around 7 a.m. with the last session completed by 5 p.m.12 Italian universities awarded only doctorates. By the end of the fifteenth century, the bachelor’s degree had disappeared from most Italian universities in all fields except theology. There was nothing unusual,

8 Biskup, Regesta, 39, no. 30; 40–41, no. 32; 45, no. 44; Rosen, “Copernicus and Italian Science,” 127; and Malagola, “Aufenthalt,” 21–25. 9 As Rosen, “Copernicus and Italian Science,” 127, implied. 10 Malagola, “Aufenthalt,” 25–28; Prowe, 262–263. See I Rotuli, 1: 161–175. 11 Grendler, Universities, 9. Most of the information that follows is based on Grendler, supplemented with information on Copernicus. 12 Grendler, 143–147. Some of the information is based on the curriculum at Rome, which Grendler describes as “typical.” See Lines’s critical comment without explanation of Grendler’s description of ordinary as opposed to extraordinary professorships, 716.

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then, about students without a bachelor’s degree in arts studying law at Bologna.13 “Colleges” of doctors, not professors, conducted examinations. Candidates were given a number of passages from the Corpus iuris canonici for canon law, or the Corpus iuris civilis for civil law, or from both for someone seeking a doctorate in both laws. The candidate had one day to prepare the passages in collaboration with two or three promoters to help him. Candidates evidently took the examination until they received the required two-thirds favorable votes from the members of the college.14 It may well be that some students preferred universities known to confer the degree after the first examination, especially if they were under time constraints. Success in the examination did not mean that the candidate had attended all of the required lectures. Presumably, experienced promoters could coach capable students within a day at some universities, although it is hard to believe that even capable students could pass without some course preparation or its equivalent. The indispensable text for canon law was the Decretum, the title given to Gratian’s Concordia discordantium canonum. Since the late twelfth century, canonists and several popes had added to the collection so that by about 1500 the texts and opinions had become known as the Corpus iuris canonici. The techniques used in the commentaries are intimately bound with the development and application of logic and dialectical inquiry that was used, as we have noted, in natural philosophy and medicine. The approach developed by Italian legal scholars is called mos italicus, which went beyond glosses on a single word to develop a coherent legal system with aspirations to universality. Here again we find evidence of the extent to which medieval students were trained to think and write logically. Legal scholars found the common principles on which they based their efforts to reconcile local and universal law in Roman law. As governments evolved, new legal issues challenged them to reconcile the law with the experience of the real world. This is the reason, in part, why so many students went to Italy to study law, for in both civil and canon law Italy had retained the strongest common legal tradition and links to ancient Rome.15 13

Grendler, 172. Grendler, 174–177. Bologna required a minimum of three promoters, but Ferrara apparently required only two. 15 Grendler, 431–434. Grendler, 434, also comments on the weaknesses of their 14

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The texts used for teaching and, in principle, the order of instruction followed the order of the books—the Institutes (an abridgment of the Digest in four books), the Digest (also called Pandects) in fifty books, the Codex of Justinian in twelve books, the Novellae, and Libri feudorum (books of feudal laws). In canon law, Gratian’s Decretum constituted the foundation, followed by the Extravagantes and the Decretals of Gregory IX. The Decretals was a more uniform collection of texts that served the faculties of law at Bologna and Paris as a complete course of instruction and that eventually supplanted the Decretum. The Liber Sextus of Boniface VIII was the fourth part. The Clementinae of Pope John XXII was the fifth part, to which later compilations, Extravagantes and Extravagantes communes, were added.16 The last text dates from 1501 to 1503, after Copernicus had completed his studies at Bologna. Humanists tried to reform legal education and practice as they did the liberal arts and theology. Because jurisprudence depended on knowledge of the history and language of Rome, jurists required humanistic philological and historical training, especially to correct all of the fanciful mistakes made by scholastics. As purists, the humanists missed the point that contemporary legal scholars did not need to know history—it was not their aim to restore or revive the past but to know how to deal with new situations that often required them to invent new words. They relied on ancient Roman law as a starting-point and not as an end in itself. In short, the humanists’ criticisms were not entirely relevant to the teaching and practice of law. The scholastic method of dialectic was far more useful than humanist philological exercises for the practical goal of expressing harmony and discord between ancient laws and modern customs, local practices and universal principles. What humanists could and did contribute were

assumptions and on the limitations of their interpretations. As a canon in Frombork after 1510, Copernicus’s principal obligations were administering and defending ecclesiastical estates. On feudal and manorial law, see Berman, Law, 1: 301–332. Copernicus’s education here was evidently of the on-the-job variety, a feature that suits the customary, particularistic, local, and diffuse nature of manorial law. The struggle with the Teutonic Knights also involved the spread of Lutheranism. In 1525, the Grand Master became a Lutheran and dissolved the Order in East Prussia. See Berman, Law, 2: 58. More recent scholarship on Gratian has challenged the story of reconciliation of discordant texts. See Pennington, review of Meyer, Distinktionstechnik, 282–284, where he says, “Only the last, much-expanded, version of the Decretum can be described as an attempt to bring comprehensive harmony from dissonance.” 16 Grendler, 434–443.

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more accurate and authoritative versions of the ancient texts. This process was well underway by the 1490s but not completed until much later. Copernicus’s education was not likely influenced by the results of humanistic efforts, although humanist critiques may have influenced his view of the actual instruction that he received. The technique known as mos gallicus (French method) was humanistic jurisprudence, and, though developed in Italy in the first half of the sixteenth century, its center was France.17 These developments were later and hence of little relevance to what Copernicus may have learned as a student of law. In canon law, the major changes also occurred in the sixteenth century, more as a result of the Protestant Reformation and the Catholic response of the Council of Trent,18 events that also postdate Copernicus’s education. Because Copernicus spent six semesters at Bologna, it is possible that he completed the entire sequence of books in canon law in 1498. He could have added civil law in the academic year 1498–99, which might explain his self-designation in 1499 as a student of both laws. As a Varmian canon, Copernicus could have found knowledge of feudal law useful in his capacities as an administrator of Church properties in a diocese that tried to preserve some degree of independence from both the Teutonic Knights and the Kingdom of Poland. But the Libri feudorum were not taught in the period 1496–1500, hence his focus in civil law was evidently elsewhere.19 As we noted, financial reasons and the exhaustion of his permitted leave of absence from Varmia led Copernicus to get his degree in canon law from Ferrara. “Ferrara was more important as a university at which to obtain a degree than as a place to study law,” comments Grendler in speaking about Ferrara in the later sixteenth century, but the comment applies to the earlier period as well. As for the influence of humanism, Grendler adds: “although humanistic jurisprudence never toppled mos italicus, it broadened the study of law.” The comment can be extended to other fields. Humanistic transformation of rhetoric and poetry influenced the reading of ancient texts in philosophy, medicine, and mathematics. Humanists did not destroy scholas-

17 Blair, Theater, 86, maintains, by contrast, that Alciato at the University of Bourges founded mos gallicus, but she agrees that it was historicist and relativist in opposition to the universalist claims of mos italicus. 18 Grendler, 443–447. 19 Rotuli, 161–175; Grendler, 447–469, esp. 453–456.

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ticism, but they did influence the creation of medical humanism, the production of “Renaissance Aristotelianisms,” and the development of mathematical techniques.20 With these very general comments as background, we descend gradually to more particular observations, and conclude with an account of the use of dialectical reasoning in legal jurisprudence. Logic and law in Italian universities were intimately related. The tradition of reconciling ancient Roman law with medieval local customs and of canon law with the evolving circumstances of religious practice relied on techniques of dialectical discourse. The scholastic method institutionalized these techniques by making them the basis of academic lectures and disputation. Although Copernicus was introduced to these techniques as an undergraduate at the University of Cracow, his education in canon and civil law would have reinforced his lessons in logic through application to legal issues and by introducing him to dialectical topics that were specific to the law. We actually know very little about the lecturers at Bologna and about the precise content of their lectures. We cannot reconstruct their teaching to the same extent as we did the teaching of professors at Cracow. We begin with some general comments on the teaching of legal reasoning and dialectic, keeping in mind that Copernicus entered Bologna at a time when humanistic critiques of scholastic method had not yet become very influential. We may suppose that Copernicus was sympathetic to humanistic ideals, but there is little evidence of an antischolastic agenda in his career. In the 1490s and early 1500s, however, we find a confluence of humanistic values, printed books, and the legal tradition of reconciling authoritative texts and customs with changing circumstances. This confluence did contribute to creating the cultural milieu that Copernicus first encountered in Cracow and that was reinforced in Bologna.21 In both dialectic and jurisprudence, humanists placed great value on the most efficient organization of one’s ideas and the most effective way of presenting them to one’s audience. For all of the humanist criticism of scholastic method, however, university professors recognized the value of Peter of Spain’s treatises, and the Bartolists in 20

Grendler, 510. Westman, “Humanism,” 83–99, esp. 84–86. On the faculties in canon and civil law between 1496 and 1500, see Dallari, Rotuli, 161–175; Alidosi, Li dottori bolognesi; and Sorbelli, Storia della università, 1: 233–267. 21

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Italian-university law faculties defended late medieval traditions. As we indicated, humanist critique was, in fact, more influential in France than in Italy.22 Mos italicus certainly predominated at Bologna while Copernicus was there.23 We may infer that Copernicus was influenced by humanistic values to compare sources and texts, to learn Greek, and to attempt a reformation of astronomy. The printing press made such comparisons and reconstructions possible, allowing scholars to set disparate texts side by side. Italian legal scholars whose aim was to achieve the concordance of discordant texts would have absorbed and accommodated humanistic critiques to the extent that they advanced their main goals.24 We cannot conclude from his later degree that Copernicus actually attended any classes, but we also cannot assume that he shirked them altogether. The well-defined puncta taxata may have enabled him to make prudent selections.25 Copernicus took responsibility for his own education, and while not all of his efforts were successful, he showed himself capable of achieving some of his goals. From his later practice also, we cannot say much about his education in canon or civil law. There is some evidence that he was acquainted with legal principles. As far as we know, however, he did not own a single legal text. Of course, an episcopal or chapter library would have owned standard legal texts, but we have no concrete evidence that Copernicus consulted them. The year that he spent in Rome may have been an apprenticeship, providing him the practical experience of day-to-day administrative tasks and dealings with the papal curia. His decision to obtain a degree from Ferrara was based in part on costs but also on the near certainty that he could pass the examination with the assistance of his promoters on the first try. Finally, his years as his uncle’s assistant from 1503 to 1510 very likely prepared him for his later duties. Despite his degree in canon law we have little reason to consider Copernicus a legal scholar. If Copernicus did attend courses in canon and civil law, he would have received instruction not only in application of Roman legal principles to matters of Church and civil law but also repetition and further application of dialectical methods of argumentation. We

22 23 24 25

Wieacker, “Einflüsse,” 423–456, esp. 435–442 and 453–456. Mortari, “Dialettica e giurisprudenza,” 293–401. Eisenstein, Printing Press, 2: 685–686. Denifle, Statuten, 238.

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have mentioned the books and alluded to the techniques, but the latter are worthy of more detailed comment. Vincenzo Piano Mortari has produced the most comprehensive and authoritative study known to me of dialectic and jurisprudence in Italy. Mortari’s emphasis is on treatises of legal dialectic in the sixteenth century, but his account reflects medieval traditions and developments during the Renaissance.26 The background is largely defined by the controversy between mos italicus and mos gallicus and between Bartolists and humanist critics of scholastic logic. Aristotelian logic was foundational with Peter of Spain’s Summulae remaining the major handbook down to about 1515. In the meantime, Roman jurisprudence was influenced by Cicero, as interpreted by Boethius, and Quintilian. Well into the early sixteenth century we find Bolognese legal scholars using medieval logical sources and the fundamental forms of Aristotelian-scholastic reasoning (syllogism, induction, enthymeme, and example). Above all they illustrate the various dialecical topics and principles with concrete application to legal cases. Legal scholars conceived of dialectic as less a speculative science and more as an art of discourse or argument.27 They cite standard medieval logicians like Lambert of Auxerre, William of Sherwood, and Peter of Spain. Later in the sixteenth century references to authors like Rudolf Agricola, Philipp Melanchthon, and Peter Ramus do not alter the use of topics for the purpose of discovering or finding arguments. The legal treatises are dedicated exclusively to treating dialectical topics useful in jurisprudence. Even later in the sixteenth century, legal scholars continued to use Peter of Spain’s Summulae.28 Dialectic was viewed as a discipline propaedeutic to the law. Among the Bartolists, authority and reason constituted the essence of laws. Mortari devotes his long second section (pp. 310–357) to the contents of treatises of legal dialectic. Although these are treatises mainly from the later sixteenth century and thus reflecting the Ciceronian and Boethian tradition, they are dominated, of course, by the concept of topics or commonplaces as the seat of arguments, and of argument 26 Mortari’s study, “Dialettica,” begins with a review of the literature and of the medieval and Renaissance background. His bibliography is extensive. 27 Mortari, 298–299, where he refers to Pietro Andrea Gammaro, Dialectica legalis (Bologna, 1514). On Gammaro, also called Pietro Andrea Gambari and Petrus Gambarinus de Casali, see Dallari, Rotuli, 193–213; Fantuzzi, Notizie, 4: 54–58, both of whom correct Alidosi, Dottori, 196, and Appendix, 8 and 50. 28 Mortari, 299–302.

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as the reason that produces belief about something doubtful.29 As we encountered in scholastic manuals dependent on Cicero and Boethius, topics are divided between intrinsic and extrinsic with more or less the same distinctions that any medieval student would have learned from classes on dialectic. Specific to legal reasoning are topics based on etymology, allusion, and conjugates as subcategories of topics from definition and from description. These subcategories were amplified by humanistic techniques, and so constitute one of the specific contributions of humanism to legal dialectic.30 Legal dialecticians preserved the traditional distinctions, although they gave greater prominence to some. For example, the topic from the whole was distinguished into integral, quantitative, and modal, but in practice they used the topic from the integral whole above all.31 The most important dialectical topic, however, was that from similitude as the most applicable in jurisprudence.32 The topic from similitude was the main tool used by jurists in the comparison of laws, customs, and texts, and for reconciling contradictory or discordant laws, customs, and texts. The most widely recognized and used topic, however, was the topic from authority. This is not surprising in the case of law, and it is a topic on which both Bartolists and humanists agreed in principle, however differently interpreted. For the Bartolists, the common opinions of the doctors continued to be valued, while the humanists emphasized historical and philological authority.33 In practice the Bartolists won out, relying on humanistic critiques where they were useful and otherwise ignoring them as of purely antiquarian interest. Without belaboring the point, we may surmise that Copernicus would have entered Bologna well prepared to follow lectures on canon and civil law. He would have reinforced techniques learned as an undergraduate and how to apply them to legal cases. Dialectic aims to support conclusions that are more probable than alternatives. Copernicus may have been especially impressed with the topics from integral whole, similitude, and authority, either inspiring or reinforcing his thoughts on the reform of astronomy and his hope of achieving old goals by means of partly traditional and partly new paths.34

29 30 31 32 33 34

Mortari, 311: ratio quae rei dubiae fecit fidem. Mortari, 326. Mortari, 332–334. Mortari, 334–340. Mortari, 342–357. To paraphrase Eisenstein, 693, in part.

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Because of the emphasis that we will later place on the topic from integral whole, we may note Mortari’s own emphasis on the relation between the integral whole and its parts as constructive only in the affirmative sense. By contrast, the topic from part to integral whole can be used only negatively or destructively. From the existence of the house we may infer the existence of walls. From damage to or the non-existence of a wall we may infer damage to or the non-existence respectively of the house (if the wall is not, then the house is not), but from the existence of a wall we may not infer the existence of the house.35 With respect to the relation between antecedent and consequent in conditional arguments, legal dialecticians interpreted the relation in real, causal terms. In other words, juridical consequences were treated like necessary consequences, meaning that in legal cases, aside from what was considered valid in general logic, the acceptance or truth of the consequent implies the acceptance or truth of the antecedent!36 Regardless of the theoretical positions that logicians adopted in conditional logic, scholars applying these principles to real cases modified them to make them relevant to their disciplines. We will exploit the consequences of these modifications and adaptations for Copernicus’s critique of Ptolemaic astronomy and his own solution in chapter eight on the logic of Copernicus’s arguments. Among the authors cited by Mortari, Pietro Andrea Gammaro stands out. He began teaching at the university in 1506–1507 as a university lecturer when he conducted disputations. He could not have taught Copernicus. His work on legal dialectic is also referred to as books on topics. Gammaro studied under Giovanni Campeggi and Antonio de Sala, both of whom taught canon law at the university during the years that Copernicus attended the university.37 The argument made here is modest. Copernicus’s education in law at Bologna may have contributed to his understanding and application

35 Mortari, 332–334. As we will see, however, Copernicus does argue for one constructive version of the inference from integral part to whole. 36 Mortari, 322–324, esp. 323–324: “E concesso antecedenti conceditur id quod est consequens; concesso consequenti conceditur etiam antecedens; destructo antecedenti, destruitur consequens; remoto consequenti necessario removetur et antecedens erano le formule adoperate quasi sempre per esprimere i vari aspetti della correlazione logica tra i due concetti o, per meglio dire, le possibilità argomentative implicite nella loro correlazione dialettica.” 37 Fantuzzi, 556; Dallari, 161–175; and Alidosi, 196. Alidosi says that Gambari served as apostolic nuncio to Poland, but see Fantuzzi, 56.

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of dialectical reasoning. Humanistic influences and the availability of printed texts may also have opened possibilities that inspired him to undertake a reform of astronomy. His mind was continuing to develop, and the resources available to him continued to expand. Circumstances at Bologna permitted Copernicus a degree of freedom and opportunity that he did not waste.38 We know from Rheticus’s testimony that in 1497 Copernicus assisted Domenico Maria Novara in observations and that he may have resided in Novara’s house for perhaps two years.39 As for courses in Greek, rhetoric, and poetry, Antonio Urceo da Forlì (known as Codro) lectured only on afternoons and feast days, whereas Philippus Beroaldus lectured mornings and afternoons in an alternating fashion.40 When we take into account Copernicus’s interest in astronomy and that he began learning Greek while in Bologna, it seems very unlikely that he would have attended any lectures in philosophy. Scholars have speculated that Copernicus attended the lectures of the Averroist Alexander Achillini or knew Achillini’s De orbibus libri quattuor (1498).41 Copernicus’s teachers at Cracow had already introduced him to the ideas of Averroes and especially Averroes’s criticisms of Ptolemy.42 An examination of the archival records in Bologna demonstrates that professors of philosophy relied on the commentary tradition with some evidence that they turned more frequently to some of the ancient commentators as well as those of the Middle Ages. They followed the scholastic method including formal disputations. Nevertheless, in the next chapter I will summarize Achillini’s work, and examine its possible contribution to Copernicus’s proposal and arguments. The other important Aristotelian at Bologna, Pietro Pomponazzi, rejected Averroism and tried to remove the non-Aristotelian elements from scholastic Aristotelianism. He taught philosophy at Bologna until 1496 when he received his medical degree. From 1499 to 1509 he taught philosophy at Padua, where Copernicus could have heard of him. An inspection of the topics of the principal disputations shows that they focused on problems relevant to ideas on the soul and mind and also 38

Compare Prowe, I, 1: 235 and 257; Rosen, “Copernicus and Italian Science,” 129. Rosen. “Copernicus and Italian Science,” 129. 40 In the Rotuli for 1496–1497, 164, Urceo’s name is given as Antonius de Forlivio. 41 For example, di Bono, “Copernicus,” 153, n. 72; and Barker, “Copernicus and Critics,” 350. Note how authors conflate “concentric” theories with “homocentric” theories. 42 As Barker, “Copernicus,” 347–348, notes. 39

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on ethical questions. Few of the professors listed in the Rotuli published any work on philosophy. Most of them studied philosophy as propaedeutic to the study of medicine and then later taught and/or practiced medicine. I have found no reason to believe that Copernicus would have attended these courses and disputations. Bologna may have permitted students the freedom to attend any courses that they wanted, but the evidence of any direct connection between them and Copernicus’s ideas requires closer scrutiny. Among other well-known Italian philosophers of the era, Agostino Nifo commented on Aristotelian logic, but in his treatises he focused on categorical syllogisms. Nifo did recognize other forms of inference, and evidently followed Pseudo-Scotus in adopting the paradoxes of strict implication, at least during the years that Copernicus was in Italy.43 In his early commentaries on Aristotle, Nifo relied on Averroes, but later after he learned Greek, he relied more on the Greek text and on Greek commentators. In the Recognitiones on the Physics (Venice, 1526), Nifo rejected the position that he had adopted in his commentary on the Physics from 1508. In the later treatise he maintained that we learn the cause of an effect through a merely hypothetical syllogism. The knowledge of the cause remains conjectural because the knowledge of the cause can never be as certain as knowledge of the effect, for the latter rests on sense experience.44 As indicated, this is not a doctrine that Copernicus would have encountered in the early sixteenth century in Italy, and we have no evidence that he consulted Nifo later. All of these considerations taken together lead me to conclude that Copernicus probably did not attend classes in philosophy, a subject that he had already studied in Cracow, and probably did not read the works of Italian scholastics on philosophy.45 On the other hand, there is one significant exception. We know that Copernicus cited Pico della Mirandola in De revolutionibus. His

43

Ashworth, “Nifo’s Reinterpretation,” 355–374. Mahoney, “Nifo,” 122–123. Mahoney interprets this change as a result of Nifo’s greater reliance on Greek texts and commentators, yet the view is also congenial with Ockham’s severe restrictions on demonstration in the strictest sense and his version of an empiricist theory of knowledge. See Longeway, Demonstration. 45 Bologna, Archivio di Stato. There is an extensive bibliography related to the teaching of philosophy at Bologna around 1500. See, for example, Matsen, Alessandro Achillini; idem, “Students’ Arts’ disputations,” 169–181. See also Nardi, Studi. Cf. Cambridge History of Renaissance Philosophy; and the still useful comments of Copleston, History of Philosophy, 3, 2: 26–31. 44

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reaction there also fits with the critique of his predecessors and his complaints about differences in the ordering of the planets.46 Edward Rosen showed that Copernicus’s reference in De revolutionibus I, 10 to Averroes’s supposed observation of Mercury and Venus in front of the Sun could have come from Pico’s Disputationes adversus astrologiam divinatricem (Bologna, 1496).47 Robert Westman points out that in Book X, chapter 4, Pico uses disagreements among astronomers over the ordering of Mercury and Venus with respect to the Sun to criticize astrology. As we saw in chapter five, there were three theories about the ordering of Mercury and Venus, and Copernicus surely encountered them in Cracow. Pico’s citation of Averroes and other authorities confirms his claim that the order of the planets remained uncertain. If the order is uncertain, argues Pico, then how can astrologers be certain about the supposed power of the planets relative to each other and to Earth? As Westman rightly emphasizes, Copernicus refers to Averroes in the very chapter where he refutes his predecessors’ views, and argues for his unique ordering of the planets. The uncertainty over the ordering of the planets may have led Copernicus to propose the orbital motion of Earth, a problem that in De revolutionibus he first emphasizes in Book I, chapter 4. We will examine Copernicus’s reading and his steps to the heliocentric theory more thoroughly in chapters seven, nine, and ten. In concluding this section, some methodological remarks are in order. It is important to consider the possibility that Copernicus became acquainted with other significant figures such as Alessandro Achillini, Girolamo Fracastoro, and Giambattista Capuano da Manfredonia in Italy. There are, however, two cautionary principles to bear in mind. First, scholars must consider and examine the content of teaching at Cracow, and show exactly what Italian sources added or contributed to Copernicus’s understanding. Second, we must distinguish sources related to Copernicus’s formulation of the heliocentric theory (prior to 1514) from those related to his writing of De revolutionibus (certainly after 1514 and probably 46

Westman, “Copernicus and the Prognosticators,” 1–5. On the ordering of the planets and astrology, Westman emphasizes Copernicus’s acquaintance with Pico della Mirandola’s refutation of astrology, another possible source aside from those he would have encountered in Cracow for Copernicus’s perplexity about the proper ordering of the planets. Rheticus, Narratio prima, in Rosen, Three Copernican Treatises, 127, also refers to Pico’s critique. 47 Rosen, Commentary, 356–357, referring to On the Revolutions I, 10: 19, lines 24–27.

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after 1524 through 1542). Achillini’s book appeared in 1498, so it could be related to both periods. To my knowledge, however, there is no evidence that it was ever in Varmia, meaning that Copernicus would have had to use it prior to 1503.48 Capuano’s commentary on De sphera was published three times before the middle of the sixteenth century, in 1499, 1504, and 1518. There was a copy of the 1499 edition in Varmia but in Braniewo, not Frombork or Lidzbark-Warmiński.49 Only the 1518 edition has been definitively placed in Copernicus’s circle, but there is no conclusive evidence that he in fact ever saw or used it.50 Even if he did, it could relate only to De revolutionibus and not Commentariolus. The kind of evidence that we need in such cases includes annotations in the books that we know Copernicus owned or read, expressions in De revolutionibus or in Commentariolus that parallel uniquely arguments or comments in sources that he consulted, or quotations and facts that we can show he borrowed from another author (for example, Copernicus’s evident reliance on Regiomontanus’s Epitome). Other than this quality of evidence, conjecture and speculation based on similarities can often be traced back to another text common to all possible intermediaries, such as one by Aristotle, Ptolemy, De sphera, or some version of Theorica planetarum. Such speculation leaves us with no way of knowing whether Copernicus responded to a suggestion in some commentary or reacted directly to the original text. 3. Copernicus and Novara Domenico Maria Novara (ca. 1454–1504) was a well-known mathematician, astronomer, astrologer, and physician when Copernicus arrived in Bologna.51 We do not know whether he went to Bologna to work with Novara. After all, Novara constituted a direct link to

48 Hipler, “Analecta,” 335–381. Of course, the list could be incomplete, but the title is unusual, and the catalog includes three books by Pico della Mirandola and books by Regiomontanus. Granada and Tessicini, “Copernicus and Fracastoro,” 433, n. 3, and 435, also emphasize the failure to distinguish works that influenced the writing of Commentariolus from those that influenced De revolutionibus. 49 Kolberg, “Inkunabeln,” 129. 50 Michael Shank, in a paper to appear in Early Science and Medicine 14 (2009), a festschrift honoring John Murdoch, argues for the possibility that Copernicus knew the 1518 edition. See Goddu, “Copernicus’s Annotations,” 207–208 and 220. 51 Birkenmajer, Mikołaj Kopernik, ch. 19; Malagola, “Aufenthalt,” 52. See also Nobis, “D[ominicus] Maria de Novara,” Lexikon, 3: 1189–1190.

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Giovanni Bianchini, and through him, a link to Cardinal Bessarion, Peurbach, and Regiomontanus. Once in Bologna, Copernicus apparently began assisting Novara with observations and perhaps resided in his house.52 Ludwik Birkenmajer devoted an entire chapter of his monumental work on Copernicus to Novara. Following on Rheticus’s comments and the mention of Novara in Copernicus’s autograph copy, Birkenmajer surveyed the scholarship on Novara down to 1900.53 The writings of Novara that have survived are mostly astrological forecasts from the late fifteenth and early sixteenth centuries. In an earlier prognostication for 1489, Novara observed what he thought were changes occurring every century that affected geographical latitude and that led him to speculate that the Earth’s axis undergoes a slight shift, namely, of 1˚ 10´ since the time of Ptolemy. The significance of this conjecture is obvious, for it suggests that Novara may have inspired Copernicus to consider the Earth’s motion. Novara evidently proposed a motion of the north terrestrial pole in the direction of zenith as a change in the axis of rotation. Others, however, have speculated that Novara was referring to the phenomenon of precession and, thus, discovered prior to Copernicus the motion of the terrestrial axis to account for the apparent motion of the so-called eighth sphere.54 Birkenmajer devoted most of his chapter to proving mainly two conclusions. Novara’s observation of a shift in geographical latitude was based on an error in measuring the latitude of several cities. Birkenmajer showed that Copernicus accepted the conclusion that geographical latitudes are fixed, thus indicating that he recognized Novara’s error

52 Birkenmajer, Kopernik, 424–426; Malagola, “Aufenthalt,” 27–28; Prowe, I, 1: 236–237. Rheticus is the source for assertions about Copernicus’s relation to Novara. See Narratio prima (1540), in Rosen, Three Copernican Treatises, 111; Ephemerides novae (1550), Preface. See also Biliński, Alcune considerazioni. Though a little dated, this is a largely bibliographical essay that summarizes much of the important Polish scholarship and the research on Copernicus’s education in Poland and on Novara and Copernicus. 53 The reference to Novara was cancelled in the autograph, and therefore was not included in earlier editions of De revolutionibus. See Malagola, “Aufenthalt,” 47–54 and 98–99. 54 Birkenmajer, Kopernik, 426–430. Birkenmajer, 516, n. 6, also refers to a peripatetic gloss by Alexander Achillini that “secundum observationes mathematicorum . . . ellevatio poli artici . . . super nos Bononiae habitantes graduum 44 cum dimidio . . .” See Achillini, De orbibus, f. 12v, col. 2, ll. 36ff.

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and rejected his hypothesis about the Earth’s motion.55 Aside from pointing out the error, Birkenmajer also argued that Novara’s solution has nothing to do with the precession of the equinoxes.56 Although Novara is not the source for Copernicus’s conjecture about the third motion of Earth, could he have inspired Copernicus to begin thinking about the motion of Earth? This is a much more difficult question to answer. Speculation that Regiomontanus in his Epitome published in 1496 proposed the possibility of Earth’s motion is unsupported by the text.57 Novara could not have gotten the idea from him; he surely would have cited the authority of Regiomontanus if he had. But Pliny in his Natural History, Book 36, chapter 15, (10), 72–73, also mentioned a variation in geographical latitudes and reports the fact that some attribute it to the possibility that Earth has been displaced from its center.58 Either Pliny and/or Novara, then,

55 Birkenmajer, 429. See Rosen’s Commentary, On the Revolutions, 369, note to p. 61: 22. See also Rosen, “Copernicus and Italian Science,” 131–136. 56 The phenomenon, Birkenmajer adds, was refuted by William Gilbert’s recognition of miscalculations, and that there has been no variation in the magnetic axis of Earth. Gilbert, in fact, quotes Novara without citing his source: “Ego inquit superioribus annis contemplando Ptolemaei geographiam, inueni elevationes poli Borei ab eo positas in singulis regionibus, ab ijs qui nostri temporis sunt, gradu vno et decem minutis deficere: quae diuersitas vitio tabulae nequaquam ascribi potest. Non enim credibile est totam libri seriem in numeris tabularum aequaliter deprauatam esse. Eapropter necesse est polum Boreum, versus punctum verticalem delatum concedere.” See Guillelmus Gilbertus, De magnete, 213. See Birkenmajer, Kopernik, 428, and note 1. Compare with Prowe, I, 1: 240–243. See also Rosen, “Copernicus and Italian Science,” 132–135. 57 See the remarks by Schmeidler in Regiomontanus, Opera, XIII–XIV and Epytoma I, conclusio tertia (p. 66): “Terram in medio mundi sitam esse” and conclusio quinta (p. 69): “Quod terra localem motum non habeat declarare.” See Zinner, Entstehung, 99–100 and 585–586. See also Schmeidler, “Supplements,” 313–324. 58 And this despite the fact that in Book 2, chapters LXIV–LXXIX, he says nothing of a shift in Earth’s axis in his discussion of the position and shape of the Earth and its latitudes. Different editions and translations vary slightly in how they cite the numbers in Pliny’s text. They all agree on the book number, but after that there can be confusion. What Birkenmajer cited as Book 36, chapter 10 appears in the Teubner edition as XXXVI, 10. (15), 72–73. In one French edition and translation we find XXXVI, XV (10), 72–73. In a modern German edition and translation we are given XXXVI, XV, 72–73. In an older English translation the text is given as Book XXXVI, chap. 15 (10.). The Loeb edition cites it as XXXVI, XV, 72–73. All the texts agree in reporting that an obelisk in the Field of Mars was used as a sundial. Later the observations were found not to agree, leading to speculation about changes in the heavens, displacement of Earth from the center, an earthquake, or inundations of the Tiber. The exact references follow. See C. Plini Secundi naturalis historiae, 332–333. Cf. Pline l’Ancien, Histoire naturelle, 74–75; C. Plinius Secundus der Ältere, Naturkunde, 56–59; Pliny, Natural History, 334–335; and see Birkenmajer, Kopernik, 429–430, note 5.

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could have stimulated Copernicus to begin thinking about the motion of Earth. Not even Edward Rosen was moved to reject the speculation about Novara’s possible influence on Copernicus altogether.59 What Copernicus did get from Novara without question was Novara’s measurement for the obliquity of the ecliptic made in 1491.60 Copernicus attributed to Novara the value of 23 degrees and a little more than 29 minutes, and in another passage referred to reports by others of the same result.61 Copernicus’s own value was 23 degrees, 28.4 minutes. Despite his medical degree, reputation as an astronomer, and his astrological prognostications, we do not know in detail what Novara thought of astrology.62 He clearly believed in celestial influence, and recognized problems of accuracy, but competing astrologers criticized the accuracy of adversaries’ measurements and predictions. His almanachs were a statutory requirement of his position as a salaried doctor in astronomy. Whatever his beliefs may have been, Novara shared the view of his fifteenth-century predecessors and contemporaries who recognized the need to correct astronomical tables and reform astronomy based on more accurate observations.63 It has always been something of a curiosity to explain Copernicus’s virtual silence about his contact with Novara and about astrology. One of the main practical occupations of mathematical astronomers was astrology, especially for those who also practiced medicine. Copernicus says almost nothing about astrology, either in his capacity as an astronomer or as a practicing physician. His assistant and disciple,

59

Rosen, “Copernicus and Italian Science,” 137. On the other hand, Rosen may have made this suggestion for the purpose of discounting Swerdlow’s reconstruction of Copernicus’s reading of Regiomontanus’s Epitome. In addition, scholastic commentaries routinely considered the motion of Earth, even if only to reject it. 60 Birkenmajer, Kopernik, 432–436. 61 Birkenmajer, Kopernik, 434, thinks that Copernicus was also referring to Novara’s estimate in the second passage as well. See De revolutionibus III, 6. It was in this passage that Copernicus made a reference in the margin of the autograph to Novara, which he later cancelled because he replaced it with a reference to Regiomontanus whose measurement agreed better with Copernicus’s own. See also Prowe, I, 1: 243– 244. Cf. Rosen’s translation and commentary, 129 and 386. 62 Birkenmajer, Kopernik, 436–443. See also the details provided by Biliński, Alcune considerazioni, 29–41. On Novara’s published prognostications, see Gesamtkatalog der Wiegendrucke, 7: columns 578–581, nos. 8658–8673, spanning the period from 1484 to 1501. 63 Birkenmajer, Kopernik, 446–447, note 2. See also Prowe, I, 1: 237–238.

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Rheticus, was devoted to astrology, and Copernicus is not known to have disabused him of the pursuit. Scholars continue to examine Copernicus’s cultural context and the place of astrology in that culture, but I have nothing to say on the subject except to remark about Copernicus’s curious silence, and to refer to Robert Westman’s interpretation of his familiarity with Pico della Mirandola’s polemic against astrology.64 We noted above the importance of the ordering of the planets in this connection. Here, however, we acknowledge Westman’s proposal that astrological contexts and texts on astrology influenced Copernicus’s thinking about problems that almost certainly led him eventually to propose the orbital motion of Earth as a solution to the problem of the uniquely true ordering of the planets.65 When we speak of testing models against observations, we must be careful not to exaggerate the capabilities of pre-Tychonic astronomers. The evidence from prognostications shows that Novara was an industrious observer. Copernicus very likely perfected his use of instruments, and may have begun to focus his attention on observations that test the accuracy of Ptolemaic models, but in fact Copernicus’s

64 62 See Westman, “Humanism,” 83–99; Lemay, “Late Medieval Astrological School,” 337–354. I do not share Rosen’s apodictic declarations about Copernicus’s rejection of astrology. On the other hand, Copernicus’s silence suggests that astrology was peripheral to his interests. For a re-evaluation, see Westman, “Copernicus and the Prognosticators,” 1–5. The complete analysis by Westman is forthcoming. See also Biliński, Alcune considerazioni, 29–41, for further references. Schmeidler, Kommentar, 179, also dismisses claims that Copernicus believed in astrology, although he does acknowledge Ludwik Birkenmajer’s observation that Copernicus occupied himself with astrological forecasts as a student. See Birkenmajer, Stromata, 51–53, where he refers to a treatise that Copernicus acquired while in Cracow. It is now identified as Copernicana 6 at Uppsala University Library, and it contains Euclid’s Elements and Albohazen Haly, In judiciis stellarum. In the second book, on f. 73v appears an annotation making an astrological comment. Birkenmajer speculated that Copernicus might have been reflecting the view of Albert of Szamotuły, who lectured on Ptolemy’s so-called Quadripartitum opus while Copernicus was in Cracow. On the back cover of this codex appears a recipe for a prescription, the only indication in a book owned by Copernicus of a connection between a recipe and a work on astrology. The recipe itself, however, makes no reference to astrological variables. What is worse, two authors doubt Birkenmajer’s attribution of the annotations to the text by Haly. See Czartoryski, “Library,” 366. Valentin, “Herkunft und Echtheit,” 152–158, proved that the recipe on the inside back cover is not in Copernicus’s hand. 65 Rabin, “Nicolaus Copernicus,” 2 and note 2, says that Copernicus studied astrology at Padua. His later practice and most of his medical annotations, however, rather suggest that he studied the preparation of drugs and their effects. There is little indication that he considered astrological variables in his preparation and administration of medications that he prescribed.

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principal concerns remained theoretical.66 His observation or criticisms of observations served him in evaluating the measurements of the sidereal and tropical year, the obliquity of the ecliptic, the problems with lunar models, and, eventually, the effectiveness of his own models. The freedom permitted Copernicus at Bologna gave him the opportunity to assist Novara in his observations, an opportunity that he evidently did not waste, but we again should not exaggerate these results.67 The Rotuli of the University of Bologna list all of Novara’s lectures as morning classes, which suggests that Copernicus could have assisted him in observations and still attended morning lectures on law or other subjects.68 Whether Copernicus was convinced of a need to reform astronomy before he left Poland we cannot say with certainty. But it is likely that Novara introduced him to Regiomontanus’s Epitome and possibly “infected” him with the idea that the whole art of astronomy was in disarray and in need of reform. Though in error about a shift of the North Pole and about a motion of Earth, Novara dared to challenge the authority of Ptolemy and Aristotle. Perhaps as a result of such suggestions and his growing perplexity over uncertainty about the ordering of the planets, Copernicus began to think about the possibility of Earth’s motion, but he was far from formulating a clear hypothesis in 1500. The lunar observation of 1497 (an occultation of Aldebaran on 9 March at 11 p.m.) was likely connected with his reading of passages in the Epitome that contributed to his later hypothesis. Copernicus later used the observation in De revolutionibus to support his computation of lunar parallax, a test of Ptolemy’s lunar theory suggested by Regiomontanus’s Epitome. But there is no evidence that Copernicus had yet formulated in 1497 any hypothesis about the motion of Earth.69

66 Malagola, “Aufenthalt,” 50. See Kremer, “Walther’s Astronomical Observations,” and “Use,” where he indicates that the idea of checking data against observations took some time to develop, and does not appear to have become crucial until after Copernicus. 67 Prowe, I, 1: 225 and 257; Rosen, “Copernicus and Italian Science,” 129. 68 Dallari, 161–172. 69 For the date 9 March 1497, see De revolutionibus IV, 27; and Biskup, Regesta, 39, no. 29. See Rosen, “Copernicus and Italian Science,” 137; idem, “Biography,” 322–324. Some sources, for example, Nobis, Lexikon, 1190, give the date as 7 March. It appears that the observations were conducted over three nights, 7–9 March. In this paragraph I have departed substantially from Birkenmajer, who suggested that Copernicus left Cracow in 1495 already with a hypothesis about Earth’s motion. See Birkenmajer, Kopernik, ch. 2, esp. 57–60. See also A. Birkenmajer, Études, 601. To my knowledge,

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We may also add that astrological inaccuracies had less to do with observational accuracy than with theoretical differences such as the ordering of the planets. These kinds of differences had more to do with the analysis of available data than with the acquisition of more accurate data. Working his way through Regiomontanus’s Epitome, as we shall see in the next chapter, would be crucial and indispensable for Copernicus’s solutions. It is likely that it took him several years to master it. Of course, Novara was not the only astronomer in Bologna. Copernicus probably met the other professors and students. Of other professors, Scipio del Ferro was the best known, but there are no references by Copernicus or Rheticus to any contact, and there is nothing about Copernicus’s education to link him with del Ferro.70 4. Copernicus’s Study of Greek Why did Copernicus learn Greek? We might suppose that he wanted to consult the major works in astronomy, especially Ptolemy, directly. In fact, this assumption is dubious.71 It is true that he familiarized himself with the names of the months and wanted to solve some problems involving Arabic additions to the mathematical-astronomical corpus.72 But Copernicus relied mostly on Latin translations and Latin sources, even resorting to handbooks, summaries, and encyclopedias. Was his desire to learn Greek evidence of his ambition to be regarded as a

no one today agrees with Birkenmajer’s early dating. I will turn to the observation of 1497 in my discussion of Copernicus’s reading in chapter seven where I examine his use of Regiomontanus’s Epitome. See Rheticus, Narratio prima, Rosen tr., 133, who in discussing Copernicus’s lunar theory makes a direct reference to Regiomonatanus’s comment in Epitome about the predicted size of the Moon at quadrature. 70 Malagola, “Aufenthalt,” 54–56. Earlier speculation that Copernicus studied mathematics with del Ferro was based on the false assumption that Copernicus studied liberal arts in Bologna. As the previous chapters have shown, Copernicus spent his undergraduate years at Cracow. Cf. Prowe, I, 1: 247–248. On the faculty in mathematics and astronomy between 1496 and 1500, see Dallari, 161–175; and Sorbelli, Storia della Università, 241–254. 71 Prowe, I, 1: 248–260. Cf. Birkenmajer, Kopernik, chs. 5 and 10, and pp. 242, 264–285. 72 Birkenmajer, the French summary of Kopernik, in Bulletin international, 206– 207, note 1 and numbers 6, 17, 18, 20–25, 29, 32, 34–35, 45, and 46; Rosen, “Copernicus and Italian Science,” 139–147.

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humanist?73 In the opinion of classicists, it seems that Copernicus’s reach exceeded his grasp. His translation of Theophylactus’s letters was published in Cracow. It confirms Copernicus’s ambition to be perceived as a humanist scholar, and the fact remains that his translation was the first publication in Poland of a Greek work into Latin, thus assuring himself of a place in histories of Renaissance humanism in Poland.74 As we noted in chapter five, the fifteenth-century astronomical tradition in Cracow was intimately connected with Renaissance humanism. As Copernicus began to assemble books, first in Cracow and then in Italy, he was able to compare several works together side by side, and understood the need to correct versions of ancient authors. Editorial practices were in the process of being formed. Indeed, one might argue that as scholars become aware of newly perceived problems, they are constantly revising standards.75 Aside from the confusion in nomenclature in the astronomical and medical traditions, Copernicus encountered numerous confusions in orthography, identification of ancient authorities, and the like. As he began the process of collecting and comparing authorities, and once he had formulated the decision to reform astronomy, he realized that he had two major problems before him. Aside from the task of constructing a mathematically detailed analysis, which would require correcting numerical errors or selecting between conflicting numerical data, he also had to correct many historical and philological errors. In short, he could hardly separate two enormous tasks, one astronomical and the other humanistic. Both would require at least a working knowledge of Greek, and the evidence suggests that he realized the need in at least three instances to consult Greek originals, either because the available Latin translations were inadequate or completely non-existent. His translation of Theophy-

73 Rosen, “Introduction,” Minor Works, Complete Works, 3: 4, maintains, however, that Copernicus wanted to acquaint himself with the works of Greek authors, recognized that the available Latin translations were unsatisfactory, and so decided that he must learn Greek. If so, then why did he not seek more formal training in Greek instead of trying to teach himself by translating some of the letters of Theophylactus? See Rosen’s extensive comments in the introduction to his translation, 3–24. 74 Segel, Renaissance Culture; Rosen, “What Copernicus Owed,” 161–173; Rosen, “Copernicus’ Quotation,” 369–379, esp. 376–377; Rosen, “Copernicus the Humanist,” 7–61, esp. 59–60; Malagola, “Aufenthalt,” 45–46. Swerdlow and Neugebauer, Mathematical Astronomy, I: 5, call Copernicus “proficient, although not distinguished” in Greek. 75 See, for instance, the complications involved even today in the editing of the works of Francis Bacon. For a brief overview, see Vickers, “Bacon For Our Time.”

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lactus’s Letters marked a beginning, not the end. It provided him a basis from which to develop his ability to consult ancient authorities in the Greek when the need arose. By 1508 Copernicus completed his translation of the Letters. His most important resource for this undertaking was the Greek-Latin dictionary by Crastonus. Copernicus may have first encountered the Letters in Bologna, perhaps as a student of Urceo. Copernicus praises the Letters, but he evidently chose them because he considered them a way to improve his knowledge of Greek. His decision to have it published, however, indicates his ambition at the very least to be counted among the earliest translators of a Greek text in Poland. As said already, he did consult Greek mathematical and astronomical works where Latin versions were deficient or in disagreement. In fact, he later annotated in Latin and Greek the Greek edition of Euclid with the commentaries by Theon and Proclus that he received as a gift from Rheticus after 1533. But to the Greek edition of Ptolemy’s Syntaxis, which he received from Rheticus after 1538, he added only geometric figures drawn in the margins and a few notes mostly in Greek.76 He may have begun the translation of the Letters while still a student in Bologna, or at least copying the Greek texts that became the basis for his translation. In the period 1504–1510 he was still immersing himself in the culture of antiquity with the intention of establishing his reputation as a humanist scholar and developing his philosophical views about the place of astronomy among the liberal arts. Certainly his later treatises on astronomy began as works of restoration and reform however revolutionary his cosmological ideas became. Copernicus himself was evidently aware of inadequacies in his dictionary to which he made a number of corrections, especially additions to Crastonus’s Greek terms for the months of the year.77 And for their additions one of his sources may have been the Suidae lexicon.78 76 These editions are Uppsala, Copernicana 9 and 10 respectively. See Czartoryski, “Library,” 355–396, nos. 5 and 7, and SPS 148 and 149. Some of his annotations in the 1515 edition of Almagest are in Greek. See Czartoryski, 372, No. 17, Copernicana 17. 77 Prowe I, A: 407, note *, and 411–413; Hipler, “Analecta,” 120–121; and Curtze, Reliquiae copernicanae, 3. Why Copernicus purchased this dictionary rather than using those of Ficino or Poliziano is not known. The answer is probably related to availability and price. On the dictionaries of Ficino and Poliziano, see Mandosio, “Les lexiques,” 175–226. 78 On the Suda, see Knox, “Ficino,” 333–366, esp. 346, n. 46, where Knox cites the following: Suidae Lexicon, ed. Adler, 3: 119–120, No. 1640, a text related to Copernicus’s theory of elemental motion. At this moment I do not know which edition of the lexicon Copernicus might have used and where he could have consulted it. It is very

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Scholars have assumed that Copernicus studied Greek in Bologna either with Urceo or Philip Beroaldo. Urceo taught afternoon classes and Beroaldo was especially known for teaching students from the German nation.79 Copernicus purchased a Greek-Latin lexicon about 1500. His annotations in it and the selection of Theophylactus’s Letters for translation suggest that he may have received some elementary instruction but on the whole it seems that Copernicus used the Letters as a means of learning Greek. The annotations in the dictionary also show that his knowledge of Greek was beyond that of a beginner.80 For the most part, then, Copernicus appears to have been an autodidact in Greek, and he acquired an acquaintance with ancient authors, especially Greek and Arabic authors, by means of translations or encyclopedic summaries in Latin, especially Regiomontanus, Cardinal Bessarion, Georgio Valla, Marsilio Ficino, and Pliny the Elder.81 But there is additional evidence that he consulted in a Greek original pseudo-Plutarch’s (that is, Aëtius Amedinus) De placitis philosophorum, possibly Plutarch’s Moralia, and the other Greek lexicon mentioned above and known as the Suda.82 We may conclude this section by repeating Ludwig Prowe’s fair comments on Copernicus’s knowledge of Greek. Prowe defends the

likely that he consulted the edition from Milan, 1499 (Hain *15135 and Proctor 6077). See also Knox, “Ficino and Copernicus,” 399–418, esp. 415–417. Knox claims that Copernicus’s annotations in his copy of Crastonus’s dictionary prove that Copernicus consulted the Suda. In correspondence Knox has pointed to evidence of corrections that seem to follow entries in the Suda. In my view, Knox’s evidence is persuasive. See Knox, “Copernicus’s Doctrine of Gravity.” See chapters seven and nine below for further comments. 79 On Urceo: Rosen, “Biography,” 325; “Copernicus’ Quotation,” 372–275; Prowe, I, 1: 248–260; Malagola, “Aufenthalt,” 40–43. On Beroaldo: Garin, Ritratti, 107–129. Birkenmajer, Kopernik, chapter 5, rejected all such reconstructions. Of course, he did not know the later arguments, but his analysis convinced him that Copernicus learned Greek in Padua. 80 We will turn to this evidence in chapter seven. On Copernicus’s copy of the Greek-Latin lexicon, see Czartoryski, “Library,” 366, no. 3; Prowe, I, 1: 258; Malagola, “Aufenthalt,” 41–42; Birkenmajer, Kopernik, ch. 5, 216. On Theophylactus as a learning exercise and Copernicus’s annotations in his lexicon, see Rosen, “Copernicus’ Quotation,” 374–377. 81 On Giorgio Valla: Rosen, “Copernicus and Valla,” 139–147; on Sophocles: Rosen, “Copernicus’ Quotation”; on Bessarion: Birkenmajer, Kopernik, chapter 6; on Ficino: Knox, “Ficino and Copernicus,” 399–418; on Pliny: Rosen, Commentary, 341. 82 Rosen, Commentary, 342, reference to Plutarchi opuscula, 328. See Knox, “Ficino and Copernicus” 404, n. 23, and 415–418; also Knox, “Ficino,” 346, n. 46. We will return to the Suda and Copernicus’s sources in chapter seven; for now we merely note that the catalogs of Varmian libraries do not specify a copy of the Suda in their collections, and the copies at Uppsala (Inc. 32:22 and K. 36) are not from Poland.

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earliest attempts to translate Greek works because of the limited dictionaries and handooks available. He also refers to the Suda as not useful for instruction, and he provides no example of what sources Copernicus might have used for his corrections of Crastonus’s dictionary.83 For our purposes we have no reason to dwell any longer on Copernicus’s study of Greek in Bologna. 5. Copernicus in Rome In early 1500 Copernicus went to Rome partly to participate in jubilee celebrations but also in all likelihood to get some practical experience as an intern of sorts in the offices of his cathedral chapter’s representative to the Roman curia.84 This practical experience may have prepared him for his later examinations and certainly for his later experience as an administrator in Varmia. Rheticus reports that Copernicus lectured on mathematics in Rome and made a favorable impression on his audience.85 We have no documentary evidence about the precise nature of the lecture or lectures. We may speculate that he reported on his work with Novara, drawing attention to problems in Ptolemy with respect to lunar anomalies, the obliquity of the ecliptic, the ordering of the planets, and the problem of measuring the solar year and its relation to calendrical reform. In other words, this may have been an opportunity for Copernicus to portray himself as a Renaissance humanist. By bringing his audience up to date on the achievements of fifteenth-century astronomy and alerting them to the need for more work in the restoration of ancient astronomy and the fulfillment of its principal goals, he may have made the impression he wanted. Whatever books Copernicus may have already purchased, he returned to Varmia briefly to obtain permission to remain in Italy an additional two years. Certainly during this next period he devoted more effort and money to selecting and collecting books, some for the cathedral library in Varmia and some for his own private collection.

83

Prowe, I: 398–413. Biskup, Regesta, 41–43; Prowe, I, 1: 279–298. Cf. Dobrzycki and Biskup, Nicolaus Copernicus, 34: “Der Zweck dieses Aufenthaltes war ein Praktikum im Kirchenrecht an der römischen Kurie.” 85 Rheticus, Narratio prima, tr. Rosen, 111. 84

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When Copernicus received permission in 1501 to study medicine for two years at Padua, he obviously had no intention of obtaining a medical degree.86 The statutes at Padua required three years of study to obtain a degree in medicine. Copernicus was evidently confident that he would be able to practice as a consulting physician offering advice on medicines and regimen without a degree or license in medicine. Again we do not know what courses he may have attended and, once again, some scholars have speculated that he may have studied natural philosophy, mathematics, and even law in Padua. In 1503, as we noted, Copernicus did receive a degree in canon law from Ferrara, but this hardly would have required him to take classes at Padua. His promoters in Ferrara were evidently able to prepare him within a day to pass his examination and receive a degree. We will examine the curriculum in medicine at Padua briefly to suggest what sort of education he received. From the books that he purchased and later used and annotated, we can also make some inferences about his instruction in Padua. Some of the notes in his books may well derive from his days in Padua.87 Earlier speculation that Copernicus received most of his education and a medical degree from Padua was based on the mistaken belief that he remained in Italy until 1506. We now know that he returned to Poland, never to return to Italy, in January of 1504 at the latest.88 In short, all of the speculation about studies with famous Paduan Aristotelians, classicists, and Platonists, and about the study of law is completely groundless. Padua was known especially for its teaching of and contributions to logic, but no one has investigated these developments and how they might relate to Copernicus if, that is, we had reason to think that he had the time and opportunity to avail himself of such lectures.89 The likeliest candidate for influence on Copernicus might be Agostino Nifo, who moved from an Averroistic interpretation of Aristotle to one that incorporated a more Platonic reading of Aristotle,

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Biskup, Regesta, 43, No. 38; 45, No. 44. Copernicus, Opera minora, Gesamtausgabe 5: 175. 88 Biskup, Regesta, 46, No. 45. 89 Grendler, Universities, 252–279. On Platonism: Grendler, 297–309. As for study of law at Padua, as Prowe, I, 1: 303–304, observed, Copernicus would have enrolled in the faculty of arts, not law, for the study of medicine. 87

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but Nifo left Padua in 1499 and taught philosophy and medicine at Naples and Salerno from 1500 to 1513.90 The eclecticism of Paduan Aristotelianism does not quite fit with Copernicus’s use of Aristotle. Paduan Aristotelians developed the empiricist side of Aristotle’s doctrine while focusing on demonstration and demonstrative proof. They continued to neglect mathematical proof. These were hardly features that Copernicus would have found congenial. His later arguments suggest even more that Paduan Aristotelianism was precisely the interpretation that he thought required modification.91 The medical degree at Padua required three years of study with the last year devoted to a practicum and disputations. The medical curriculum was divided into four main areas: the first part of medical theory (Avicenna, Hippocrates, and Galen), the second part of medical theory (Avicenna), practical medicine (fevers and various disorders), and surgery. Partly for canonical reasons, partly for lack of time, Copernicus did not study surgery and probably not anatomy. Two of the best-known teachers of theory from 1501 to 1503 were Bartolomaeus da Montagnana and Marcus Antonius della Torre. Copernicus probably attended some of their lectures. His later practice, however, leads us to think that he focused most of his time and effort on practical medicine. The two best-known professors of practical medicine were Johannes d’Aquila and Petrus Trapolin of Padua. Copernicus did not remain in Padua long enough to participate in the practicum or disputations.92 If Paduan Aristotelianism was of no use to him, the influence of humanism on medicine and on the medical curriculum seems a more promising direction to pursue. From his interest in drug treatments and prescriptions along with his dependence on Pliny’s Natural History, we might have reason to think that Leoniceno’s critical reading of Pliny may have influenced Copernicus. But Leoniceno exercised more influence on medicine at Ferrara and Bologna than he did at Padua

90

Cambridge History, 828. Cf. Copleston, History, 3, 2: 26. Grendler, Universities, 277–279 and 310–312. See also Cochrane, “Science and Humanism,” 1039–1057, esp. 1044–1045, where he cites similar objections from scholars who try to link Galileo with Paduan Aristotelianism. This is not to say that Galileo did not adapt Aristotelian views, but rather to question his reliance on Paduan Aristotelianism. We will look in detail at Copernicus’s adaptation of Aristotelian doctrine, and substantiate these conjectures. 92 Favaro, “Hochschule Padua,” 18–46. See the documents on 50–60. 91

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in the 1490s and early 1500s. Copernicus’s use of Pliny fits in with his reading, not necessarily his education at Padua.93 If we turn our attention now to Copernicus’s later practice and the few medical annotations that he left behind, we may venture the following remarks. He acquired most but not all of the medical books that he owned before he left Italy. Many of the books that he used were library books, although he evidently purchased some of them for the episcopal library at Lidzbark and not for his private collection.94 It is not much to go by, but the evidence gives a strong impression that Copernicus used medical books like florilegia. He mined them for what was useful. This means that we have no evidence of his having questioned the fundamentals of medical theory and method, but was simply concerned in an ad hoc fashion with what was of use in his practice. Would he have known what his later activity would be while he was still a student? It is likely that he was acquainted with the predominant illnesses of some of his likely future clients, especially his uncle and other canons that he already knew, and the region where he knew that he would practice. After all he had requested and been given permission in 1501 to study medicine for the practical service that he would be able to perform upon his return. His patients and the treatments that he prescribed allow us to draw the following conclusions. Copernicus treated patients in the capacity of a “physicus” and consultant who prescribed a number of drug and herbal remedies for their illnesses. There is no indication that he practiced surgery, nor any indication that he prescribed treatments related to recovery after a surgery. In Varmia, barbers generally performed surgeries, especially amputations. There is, however, the possibility that he treated an infection that followed the amputation of a leg.95 When we take his military duties (1516–1519 and 1520–1521) at Pieniężno (Mehlsack) and Olsztyn (Allenstein) into account, it is surprising that there are so few annotations dealing with wounds.96

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On medical humanism and Leoniceno, see Grendler, Universities, 324–328. Czartoryski, “Library,” 368–371. See also Rosenberg, “Das ärztliche Wirken,” 97–137, esp. 106–113. 95 Rosenberg, 121. 96 Rosenberg, 119–121. On surgery, see Kirschner and Kühne, 199–208. Copernicus tended to ignore surgical advice, for example, about bloodletting. See Kirschner and Kühne, 211–219. Cf. Rosen, “Biography,” 346–350. On the place names, see Kühne and Kirschner, Documenta, Gesamtausgabe 6, 2: 405 and 409. See also Biskup, “Biography and Social Background,” 137–152, esp. 146. 94

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Copernicus developed a reputation for the effectiveness of his advice and medications. The emphasis on practice, the books that he used, and the annotations leave us again to suppose that as a student at Padua, Copernicus focused on practical medicine. There is no indication that he concerned himself with theoretical issues and philosophical discussions about method or methodology. There is not even much indication that he bothered to acquaint himself with the humanist improvements of ancient texts or their critiques of Arabic medicine.97 It is possible that his knowledge of practical medicine derived mostly from the books that he collected and used. He may have used his time at Padua to find and select the most useful books for the kind of practice that he could expect to encounter, as well as some of the other books that he collected. Only in one case does there seem to be evidence of annotations that derive from the period in Padua, a treatment for dysentery.98 What scholars and the sources also suggest is that Copernicus as a practicing physician followed in the steps of his Varmian predecessors, including both members of the cathedral chapter and of the Teutonic Knights.99 Unlike Bologna, we have no Rotuli from the Paduan archives, but there is a document from Venice that lists masters of arts and medicine for 1500. The courses in theory, practice, surgery, and on Avicenna’s Canon are listed.100 Some of these professors also lectured on logic, natural philosophy, and some even on mathematics, confirming the close relationship at Padua between natural philosophy and medicine. Two of the professors were listed for surgery, one of whom published a work on anatomy.101 Copernicus may very well have attended the lectures of Bartolomaeus de Montagnana, Junior, for Copernicus annotated the Consilia published in 1514 that was probably written by Montagnana’s father.102

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Reeds, “Renaissance Humanism,” 519–542, shows that the advances by humanist scholars on medicines and botany at Renaissance universities post-date Copernicus’s years at Padua. See also Dilg, “Pflanzenkunde,” 113–134. 98 Kirschner and Kühne, 171 and 175. 99 Rosenberg, 126–129; cf. Kirschner and Kühne, 169–171. 100 L. Birkenmajer, “Niccolò Copernico,” 177–274, esp. 192–193. 101 Birkenmajer, Omaggio, 194–195. 102 There is some question about whether the author is Montagnana, Junior or his father, who also wrote a Consilia medica that was published in Venice in 1499. The editions of 1499 and 1514 appear to be identical. Birkenmajer, Kopernik, 573–576, mistakenly attributed the annotations in the 1499 edition to Copernicus. GolińskaGierych discovered the genuine Copernican annotations in the 1514 edition. See

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The book is devoted mainly to medicines and prescriptions, precisely that part of medicine that we know Copernicus later practiced. For the most part, Copernicus purchased books on practical medicine, some for his private collection, some for the episcopal or cathedral library. The annotations that scholars have definitely identified as his suggest that he focused on descriptions of illnesses and the drug prescriptions that were supposedly effective in treating those illnesses. Only in one case does a text that he may have annotated refer to specific astrological circumstances and contexts, but we do not know whether Copernicus paid it any particular attention.103 All of the medical books that he owned or annotated are on practical medicine, and all of his annotations of any length are prescriptions.104 As we noted, Copernicus knew some of the medieval and Renaissance critiques of astrology. As with several issues about which there were disagreements (for example, Aristarchus’s heliocentrism, the finiteness or infinity of the universe, and other like disputed questions), Copernicus was either silent or noncommittal. That said, we have several reasons for thinking that Copernicus had at least some interest in astrology—his work with Novara, Rheticus’s explicit interest in astrology, his own astrological horoscope, and the possibility that he took astrology into consideration in one of his medical annotations.105 An early Cracow reaction to De revolutionibus with excerpts from the first book includes a section after Chapter 10 on astrology.106 The excerpt relates planetary characteristics with major historical events, and thus has led some to speculate that the writer of the excerpts may have had access to a now lost text by Copernicus, and that Rheticus too may have relied on genuine

Czartoryski, “Library,” 370–371, No. 12, now catalogued at Uppsala as Copernicana 44; and 376, No. 28, catalogued at Uppsala as Copernicana 22. 103 Curtze, Reliquiae copernicanae, 57–58, attributes astrological annotations to Copernicus. See Kirschner and Kühne, Opera minora, 186–187 and 223–226, who review the literature on these annotations, and conclude that the exclusion of these may be due to prejudice or bias. If authentic, the annotations show that Copernicus took astrological contexts for granted, at least with respect to advice related to regimen and hygiene. On the other hand, Kirschner and Kühne do not definitely attribute them to Copernicus, but leave the question open. 104 Czartoryski, “Library,” 368–371. 105 De revolutionibus I, 8; I, 11 (Warsaw ed. and Rosen translation, 25); Gesamtausgabe 2: Appendix I, 488–490. On Copernicus’s horoscope, see Biskup, Regesta, illustration 22, opposite p. 192. 106 Rc, 363 and 573.

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Copernican ideas. In short, such summaries contribute to the mystery surrounding Copernicus’s beliefs about astrology. We conclude this section with a summary of the important questions. Was Copernicus drawn into discussion about logic, demonstration, probable reasoning, dialectical use of topics, and scientific method at Padua? Was he influenced by Paduan Aristotelians to conceive method in a more empiricist way? And did humanists influence his knowledge of drugs and prescriptions? We do not have definitive answers to these questions. He seems to have adopted a thoroughly practical and efficient approach to medicine, focusing his attention on illnesses that he treated. All of this suggests that Copernicus regarded medicine as more an art than a science. Copernicus surely knew that medicine is less certain than mathematics.107 7. Copernicus’s Degree from Ferrara Here, for once, we do have specific documentary evidence about his degree. The document is a record of Copernicus’s canonical status, study at Bologna and Padua, promoters from the University of Ferrara, examiners and witnesses, and conferral of a degree in canon law. The circumstances give every indication of the process having been a rushed affair. Nicholas’s promoters were Philippo Bardella and Antonio Leutus, both professors at the university. Bardella was among the oldest professors of the law faculty, but little else is known about him. Leutus, on the other hand, was better known. His contemporaries regarded him as among the most important jurists of the day. Leutus handed Copernicus his doctoral diploma. The documents, however, tell us nothing about the examination.108 What their connection to

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Copernicus seems to have been oblivious to the developments in logic and medicine recounted by Maclean, Logic, Signs. See the review of Maclean by Ashworth, 168–170. Compare Gilbert, Renaissance Concepts, 13–15, 45–47, and 98–102. Copernicus concerned himself with issues of method only in regard to astronomy, and probably saw little methodological relation between astronomy and medicine. There may be a relation between his argumentative techniques and medical thinking, but we have too little evidence to make any definite connections. Unlike his education in philosophy and probably in law, his focus on medical practice may have insulated him from discussions on logic and method in that discipline. 108 Prowe, I: 312–316. Compare Boncompagni, “Intorno ad un documento,” 341–397. Boncompagni seems to have listed everyone who referred to Leutus and editions of his works, but the article sheds little new light on his relationship with Copernicus.

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Copernicus may have been other than as assistants who prepared him for the examination is unknown. In a standard history of the University of Ferrara, the author makes much of the fact that Copernicus received his degree from Ferrara, but fails to inform us about the promoters or explain why we should consider the degree as particular evidence in support of Ferrara’s reputation.109 In short, the judgments rendered by most scholars seem just. Copernicus’s allowed time in Italy was about to expire. He did not want to return to Poland without a degree, and so resorted to what many scholars of the time did. He went to a nearby degree mill, paid his fees, prepared for the examination with promoters, one of whom was well known, both probably experienced tutors, passed the examination on the first try, and received a degree in canon law. In 1503, shortly after receiving his degree, Copernicus returned to Poland. He was soon working for his uncle in Lidzbark. * * * In sum, I draw together for emphasis the principal results of this chapter. Copernicus received a degree in canon law from the University of Ferrara in 1503. He went to Bologna to study law, one document attesting to his matriculation in 1496 in canon, and another to study of both civil and canon, law. Other documentary evidence confirms that he advanced his knowledge of astronomy in both theory and practice, began to learn Greek, and purchased several books. He received permission to study medicine at Padua for two years (1501–1503). The degree in canon law, his first and only degree, would attest to his attendance of courses at Bologna because there is no record of matriculation at Ferrara, and we presume that he devoted himself to medicine at Padua. Unfortunately, Ferrara had the reputation of a degree mill. We know very little about the two sponsors who facilitated his

109 Visconti, Storia, 32–34 and 46–48. We could hardly expect Visconti to ignore the fact that Copernicus received his degree from Ferrara, yet he says nothing that would lead us to believe that the process was anything other than a convenience for Copernicus. On the document confirming Copernicus’s degree, see Biskup, Regesta, 45, No. 44. See also Pepe, ed. Copernico for photographic reproductions of the documents. Pepe comments, 31, that the examiners were required to confirm the preparation of the candidate for the examination and the public discussion of the puncta. Unfortunately, Pepe and his colleagues provide no additional information about Bardella and Leutus. We may also note here that Novara received his degree in medicine from Ferrara, but we do not know whether his connection to the university had anything to do with Copernicus’s plan and decision to get his degree in law from Ferrara.

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promotion. The months spent in Rome, 1500–1501, may have constituted an internship with the Varmian representative to the Holy Office in Rome. But we must again reconstruct his studies and activities in Bologna from 1496 to 1500, based on later testimony, the reputations of some of the university’s professors, the books that he purchased or used, and the knowledge that he later exhibited of astronomy, Greek, ancient literature, and law. Because he went to Bologna ostensibly to study law and to receive a degree in law, I began with a sketch of the curriculum and professors in law, focusing our attention on canon law with some consideration of his later practice as an ecclesiastical administrator in Varmia. The statutes of the university indicate that the curriculum was clearly structured, divided between the theoretical and practical, and with a stable faculty. If Copernicus attended these courses, then he received additional instruction in dialectical techniques, rigorous comparison of legal codes and texts, and practical instruction in notarial and epistolary style. His presumed internship in Rome would have provided him with an opportunity to practice the skills learned in Bologna and to appreciate the pitfalls of dealing with Roman bureaucracy. The curriculum at Bologna was divided between civil and canon law. Some courses in civil law may have served him practically on the relations between Roman and feudal law and through courses in notarial practice.110 There is reason to believe that Copernicus’s handwriting changed from a more gothic to a more Italian cursive style, and we may suppose that he began to change his hand in the late 1490s while in Bologna. That the process was gradual, however, is attested by a comparison between earlier and later correspondence, and evidence of marginal annotations in the books that he owned or used. Dating based on the characteristics of his hand, however, is conjectural, allowing us only some discrimination between decades at best. On a few occasions Copernicus had to use the services of a notary, confirming that he was familiar with the practice and required formulas. I will examine his most relevant book acquisitions in chapter seven, but I emphasize here his work with Novara and purchase of Regiomontanus’s Epitome (1496), very likely in 1497. Copernicus first

110 Although classes on feudal law were not offered while Copernicus was in Bologna, as noted above, teachers may have inserted relevant comments on feudal law in their lectures on Roman law.

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learned the details about Ptolemy’s Almagest and his mathematical models from the Epitome.111 Copernicus understood Ptolemy better than any of his predecessors, a consequence to a large extent of Regiomontanus’s Epitome.112 The aim of the first six chapters was to reconstruct Copernicus’s education. By 1503 he completed his formal education. After 1503 he continued his intellectual development privately by means of reading, translating the letters of Theophylactus, and correspondence. In the following chapter I will summarize the most important information that we have about his books and reading, and try to reconstruct the developments that led to his first heliocentric theory and the adoption of the project that resulted in De revolutionibus.

111 The most important and detailed description of Copernicus’s reliance on the Epitome is by Birkenmajer, Mikołaj Kopernik, chapter 1. Unfortunately, Copernicus’s copy has disappeared. Birkenmajer documented extensive parallel passages in Epitome and in De revolutionibus. My translation of Birkenmajer’s first chapter, relying on the translation supervised by Dobrzycki and Gingerich, is now available online: http:// www.stonehill.edu/Documents/Physics/Birkch.1.pdf. I intend to supply a commentary that will bring Birkenmajer’s sources up to date along with a correction of his assertions that later scholarship has confirmed. It will also point out the claims made by Birkenmajer that are correct and that have been neglected by others. A preface to this project and a table of contents of the proposed translation are also online: http:// www.stonehill.edu/Documents/Physics/BirkCopPref.pdf, and http://www.stonehill .edu/Documents/Physics/Birk%20Cop%20contents.pdf. 112 Evans, History and Practice, 425–427.

CHAPTER SEVEN

COPERNICUS’S READING AND PROGRESS TOWARDS HIS FIRST HELIOCENTRIC THEORY 1. Introduction Copernicus spent the first twenty-two years of his life in Poland in towns along the banks of the Vistula—mostly Toruń and Cracow. In the course of his stay in Italy, he made one journey back to Varmia. Located to the east of the Vistula delta, Varmia was a territory carved out of the Order Estates. Its principal towns were Frombork, Braniewo, Lidzbark-Warmiński, Olsztyn, and Pienężno.1 In 1510, Copernicus moved to Frombork, and it remained his principal residence to the end of his life. Frombork lies on the Vistula Lagoon (Zalew Wiślany), protected from the Baltic Sea by the Vistulan Sandbar (Mierzeja Wiślana), and fed by the Vistula delta and one of its tributaries, the Nogat River.2 In De revolutionibus Copernicus reports that he made most of his observations in Frombork, and also explains some of the difficulties he encountered because of the adverse conditions of this location.3 Lucas Watzenrode’s episcopal residence was in Lidzbark, not the town of Frombork where Nicholas’s cathedral chapter was located. Nicholas returned to Varmia from Italy in late autumn or early

1 The German equivalents are, respectively, Frauenburg, Braunsberg, Heilsberg, Allenstein, and Mehlsack (or Melzak). There is another Lidzbark in northern Poland, but I henceforth refer to Lidzbark-Warmiński as Lidzbark. See the map of Eastern Pomerania and Varmia in chapter one. 2 Mincer, “Prusy Książęc,” 190–206, esp. the maps on 191–192. Braniewo lies about ten kilometers east-northeast of Frombork, Lidzbark about sixty kilometers southeast of Braniewo, Olsztyn about forty kilometers south of Lidzbark, and Pienężno between Frombork and Lidzbark about twenty-five kilometers southeast of Frombork. Cf. Times Index-Gazetteer, 660, with a reference to Times Atlas of the World, 3: Map 62, M1. See also Oxford Atlas, 265, and Plate 54, D7. 3 Aside from fog from the lagoon, Copernicus’s tower has windows too small for observation, and the views from the walkways to the south and northeast of the tower make observations to the east, especially the horizon, very difficult. See De revolutionibus IV, 7 and V, 30, in the latter of which Copernicus explains why he had to rely on observations of Mercury that were made in Nürnberg.

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winter of 1503. Perhaps after a brief visit to his hometown of Toruń, he immediately went to Lidzbark where he became a part of his uncle’s retinue, traveling with Bishop Lucas on his visitations and participating in official meetings of the Estates. The episcopal residence in Lidzbark was the center of Nicholas’s activities, and he remained there until 1510.4 By that time Copernicus had already collected a few books. With this chapter I begin to focus on the sources available to him as he began his major reformation of ancient astronomy. Proposed dates are not absolutely certain, for Copernicus had acquired some books during his student days in Cracow. We do know with certainty many of the books that Copernicus owned. Some books bear his ownership signature, or there is testimony that he had either received a book from someone or had given it to someone as a gift. We also know several books that are annotated unmistakably in his hand. In 1626–1627 troops of the Swedish king, Gustavus Adolphus, carted off books from the library at Frombork and took them to Sweden.5 Among them were books owned by Copernicus, books that he annotated, later owned by the libraries in Varmia where he worked, and still other books that he probably consulted for the writing of his major work. Today, most of the books are located at Uppsala University Library. The most important questions that I will try to answer are about Copernicus’s acquaintance with the works of Plato, Regiomontanus and his circle, above all Cardinal Bessarion, Ficino, and several other sources on which we know Copernicus relied for his discovery of the heliocentric cosmology and his first version of the theory. Above all in this chapter (and in chapter ten and the conclusion), I attempt to clarify as far as the sources permit, why Copernicus bound his heliocentric cosmology so inseparably and obdurately to the perfection of circles and spheres. All of the works discussed below were an integral part of what Paweł Czartoryski calls Copernicus’s “astronomical workshop.”6 These are the sources that informed Copernicus, provided him with facts, observational data, and alternative opinions and theories,

4 Schmauch, “Rückkehr,” ZGAE 25, 1 (1933) 225–233, refutes the views of Franz Hipler, Leopold Prowe, and Ludwik Birkenmajer on the date of Copernicus’s return from Italy. 5 Collijn, Katalog, XXI–XXV and 477–478. 6 Czartoryski, “Library,” 355–396, esp. 365.

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stimulated his questioning of the Aristotelian and scholastic traditions, guided him in his development as a humanist, inspired him to adopt the goals of ancient astronomy, and provoked him to formulate a radical solution in the service of a deeply conservative project. In his major study on and summary of research on Copernicus’s library, Paweł Czartoryski questioned many of the annotations identified by Ludwig Birkenmajer. I reviewed Czartoryski’s conclusions, and revised the results of the investigation that he and his colleagues conducted in the mid-1970s.7 Here we select for special treatment only the most relevant results along with the appropriate evidence.8 Among the most important questions is Copernicus’s acquaintance with the works of Plato. Czartoryski placed one item in the class of books difficult to identify unambiguously. In his list the book is numbered “49.” The description follows: 49. SPS 170. Copernicana 31. Plato, Opera, tr. Marsilius Ficinus (Florence: Laurentius de Acopa, 1484), Part I. This book was formerly catalogued as Uppsala, Inc. 32:81. It bears the ownership signature of the library at Frombork—“Liber Bibliothecae Varmiensis.” Collijn, Uppsala 1235. The correct date is 1484.9

Czartoryski concluded that the small number of annotations “makes its definite identification very difficult.” The principal evidence consists of three items—the enumeration of the titles of Plato’s works in Arabic numerals from 1 to 16, a note on f. sig. e5ra (i.e. f. 42ra) that reads quid aduerti oporteat circa hyppotheses,10 and corrections of minor printing

7 Czartoryski, “Library,” 365, 372, and 381. Compare with Goddu, “Copernicus’s Annotations.” See also Sprawozdanie. “Uppsala Copernicana” refers to the shelf number of the collection of books supposedly owned or used by Copernicus in the special collections of Uppsala University Library, henceforth referred to as “Copernicana.” 8 All results with photographic evidence are in Goddu, “Copernicus’s Annotations.” Had it been available to me at the time, I would have adapted the Lieftinck system of description as modified by Derolez, Palaeography. Of course, Derolez describes bookhands, and most of my analysis of Copernicus’s hand deals with annotations; however, we can compare it with Copernicus’s holograph copy of De revolutionibus. Copernicus’s hand displays characteristics of a fundamentally Gothico-Antiqua script, but in a cursive form reminiscent of northern Italian chancery hands. 9 Aurivillius, Catalogus; idem, Inventarium. See Collijn, Uppsala 1273, 1274, 1275, and 1276. At Uppsala University Library one must consult Aurivillius for the library’s shelf number. See Kristeller, Supplementum Ficinianum, LX–LXI, for his conclusion about the place and date of publication. See also Czartoryski, 382; Birkenmajer and Collijn, Nova copernicana, 31, and Birkenmajer, Stromata 306–307. 10 Misread by Czartoryski as quod admitti oporteat circa hypotheses. In “Copernicus’s Annotations,” I offered a tentative explanation of the spelling “hyppotheses,”

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errors in the page headings in the upper margins of the book. Czartoryski was right that this is not much to go by, and suggested that a study of Part II could perhaps help. The numbers written in the table of contents bear a strong resemblance to Copernicus’s numbers, especially the number “5.” Copernicus had a distinctive way of writing that number, and the “5” in this list is identical to Copernicus’s “5.” Second, the comment about hypotheses appears in Ficino’s translation of Plato’s Parmenides. From the point of view of both its content and the handwriting, it seems very probable that Copernicus wrote that comment. Third, the correction of printing errors does not exclude Copernicus’s hand. Fourth, there are a few other annotations in Part I that are clearly not in Copernicus’s hand and that are different from the hand that is similar to Copernicus’s. On balance, then, I conclude that Copernicus did not own the book but he very likely annotated it.11 Aside from his use of Pliny’s Naturalis historia, I would add that Copernicus drew on Plato’s Parmenides from Part I of Ficino’s translation to develop and/or support his views about hypotheses and the place of mathematics among the disciplines. Working from the results of Czartoryski’s examination, we conclude that Copernicus owned with certainty fourteen books containing twenty-seven treatises. To keep the conclusions as clear as possible, we exclude the books that he wrote himself and copies of books by associates and friends that he probably did own, for example, Rheticus’s Narratio prima (Gdańsk, 1540).12

noting that in the autograph of De revolutionibus Copernicus spelled the word consistently with one “p.” I pointed out that he wrote his name with a double “p” until around 1529. I now consider it likelier that he had the Latin word “suppositio” in mind as he wrote “hyppotheses” and inadvertently transferred the double “p” of “suppositio” to “hyppotheses.” Ficino used the word “suppositio” to translate “hypothesis.” See Copernicana 31, fol. sig. e4vb, reproduced in “Copernicus’s Annotations” as Plate 42. A detail of fol. sig. e5ra is in Plate 1 below in the section on Ficino. 11 The details about Copernicus’s hand are in Goddu, “Annotations,” 209–220. Identification of the annotations in Part II remains in doubt. As for what happened to Part II, see ibid. 215–220 and 225. See also Hipler, “Analecta,” 316–488, esp. 426–429; Kolberg, “Inkunabeln,” 94–137; idem, “Bücher,” 496–512 and 534; and Brachvogel, “Bibliothek,” 274–358. For a brief review, see Brachvogel, “Bibliotheken,” 35–44. 12 Such books possibly owned by Copernicus have disappeared as far as we know. This conclusion is contrary to Jarzębowski, Biblioteka, and Rosenberg, both of whom add to Copernicus’s private collection books by nearly everyone he knew personally. While certainly not impossible, there is no documentary evidence aside from his acquaintance with these individuals or from the catalogues of Varmian librar-

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With the above results and criteria guiding us, we may turn to the books owned by Copernicus before 1514. He had already pruchased a copy of the Alfonsine Tables (ed. 1492) and of the Tabula directionum et profectionum (ed. 1490) of Regiomontanus (both in Copernicana 4), Euclid’s Elements and Albohazen Haly, In judiciis astrorum (the last two in Copernicana 6) in Cracow around 1493 before he went to Italy. During his stay in Italy, Copernicus acquired a number of books. While his collection was small in comparison to those of large collections of the era, it was by no means negligible.13 It would eventually comprise close to thirty works, a part of which he had already assembled by 1510. I will describe the books relevant to my analysis already owned or purchased in Italy and the books that he probably added to his collection by 1510. Then we will turn to the collection of books available to him in the cathedral library of Lidzbark. In Italy between 1496 and 1503 he purchased the following: Johannes Crastonus’s Greek-Latin Dictionary containing at the end an index of Latin words prepared by Ambrosius Regius, and three works bound together—Pontanus’s Opera, three essays by Bessarion, and Aratus’s Phaenomena with Theon’s commentary.14 Of the books that Copernicus purchased during his stay in Italy, he certainly began using some of these books while still in Italy, for example, Regiomontanus’s Epitome, but probably not the ones acquired in

ies supporting such speculation. We cannot conclude that every book of interest to Copernicus in those libraries had been in his private possession. 13 A. Birkenmajer, Études, 592–593. 14 Czartoryski, nos. 1 (SPS 145, Copernicana 6), 3 (SPS 144, Copernicana 5), and 4 (SPS 142, Copernicana 3). See also Prowe, Nicolaus Coppernicus, 1, A: 405–406. Copernicus probably did not own the Greek edition of the Letters of Theophylactus Simocatta, which he translated and then published in 1509. The library at Frombork possessed a book entitled Epistola diversorum philosophorum, which has evidently disappeared. The provenance of the Uppsala University Library copy eliminates it as the copy from Varmia. See Collijn, Katalog, No. 528 and pp. 476 and 488, showing that the copy of Epistolae graecae variorum auctorum (Venice, 1499) came from Denmark. See Hipler, “Analecta,” 361. Rosen, in Copernicus, Minor Works, 4, points out that Copernicus’s finances were inadequate to purchase his own copy of the expensive Letters. He regards it as likelier that Copernicus borrowed the book while residing in Bologna and transcribed the portion containing the Letters. In this edition Copernicus may also have read and transcribed the spurious letter by Lysis to Hipparchus, to which he refers in De revolutionibus in connection with the Pythagorean doctrine. See Prowe 1, A: 408–410. I leave aside here the medical works, for which see Czartoryski, nos. 8, 9, 10 (SPS 146, Copernicana 7), 11 (SPS 153, Copernicana 14), and 12 (Copernicana 44). See also Copernicus, Gesamtausgabe 5: 199–208.

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1503, and he continued to use them over the next several decades. Among the books that at this stage of his development were likely influences on him, we focus on Bessarion’s In calumniatorem Platonis, a book that he owned, Ficino’s translation of Plato’s Works, Giorgio Valla’s De expetendis et fugiendis rebus opus containing translations of works of pseudo-Plutarch, and Pliny’s Natural History. The libraries of Lidzbark and Frombork owned copies of Ficino’s translation and Pliny. The copy of Ficino’s translation of Part I at Uppsala is from Frombork. The edition at Lidzbark is also the 1484 edition, but, for reasons explained later, this is not the copy at Uppsala. Before leaving Lidzbark for Frombork in 1510, he may have used Ptolemy’s Geography.15 We do not know for certain whether Valla’s De expetendis et fugiendis rebus opus and Plutarch’s Opuscula were available at Lidzbark, although it does appear that he consulted Valla for the writing of Commentariolus, and so must have had a copy of Valla at Lidzbark. The Latin edition of Ptolemy’s Almagest, owned and used by Copernicus, was published in 1515, and hence was not available for the composition of Commentariolus. Some of these books (for example, those owned by Copernicus) were certainly in Lidzbark and then later taken to Frombork. These are the books that helped him to formulate his mature philosophical views on astronomical hypotheses and the principles of natural philosophy. Reconstructing the collections available to Copernicus is difficult. Fifteenth and sixteenth-century catalogs of libraries are little more than lists of authors and texts, often providing only the first text in a codex. From these lists and the books that have survived we can attempt to reconstruct the collections to a certain extent. Franz Hipler, Ludwik Birkenmajer, Josef Kolberg, and Eugen Brachvogel in particular published the results of their search for the intellectual sources of Copernicus’s worldview.16 We begin with the catalog at Lidzbark, which I have attempted to match with the books taken to Sweden in the seventeenth century. I focus on mathematical and philosophical works. The episcopal library at Lidzbark, not surprisingly, collected mostly theological and juridical books. No book in Sweden has an entry indicating that it belonged to the library at Lidzbark. Most books from Varmia 15

For the correction of Czartoryski’s misidentification of this copy, see Goddu, “Copernicus’s Annotations,” 204–206. Uppsala University Library has re-catalogued this book as Copernicana 45. 16 Hipler, “Analecta,” Kolberg, and Brachvogel, all in ZGAE.

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indicate that they belonged to the library of Varmia (“Liber Bibliothecae Varmiensis”), meaning that they were in the library at Frombork where the cathedral chapter was located. There were several inventories of the various Varmian collections from the fifteenth to the early eighteenth centuries, with the 1598 visitation catalog of the Frombork collection the most extensive.17 Some books in the Lidzbark collection, we know, were later taken to Frombork and were thereafter identified as belonging to the library at Varmia. There are also books that were later owned by the College of Braniewo (Braunsberg) established by the Jesuits in 1565.18 Some of their books were originally in Frombork or Lidzbark. The story has to be told backwards for it was only after Hipler, O. Walde, Anton Kolberg, Barwinski-Birkenmajer-Łoś (SPS), Collijn, Josef Kolberg, and Birkenmajer (Stromata) reported their findings that Brachvogel was able to identify the books that had been in Lidzbark. Hipler listed authors and titles without further identification. Josef Kolberg went over these lists and compared them against the collections in Swedish libraries. He tried to determine how and when the books became the property of Varmian libraries, which aids us in deciding whether Copernicus could have consulted these works. Kolberg found that Uppsala University Library alone possesses approximately 100 books containing 141 treatises from the library of the Varmian chapter. In addition, Uppsala University Library has 200 books containing 430 treatises from the Jesuit College in Braniewo. Brachvogel based his findings largely on the catalog of the episcopal library in Lidzbark that had been prepared by Bishop John Dantiscus about 1540. Brachvogel also identified Dantiscus’s ownership seal on which he based his conclusions, rejecting Collijn’s suspicion and Walde’s assumption that all of the books belonging to the Jesuit College at Braniewo had originally belonged to the episcopal library in Lidzbark. After Dantiscus’s death the collection did not grow appreciably. Most of the incunabula, about 121 books, were taken to Frombork in 1842. The Lidzbark catalog of 1633, then, contains mostly works from before 1540. There were at least two major losses of books to Sweden—in 1626–1627 and 1704–1705.19 From the catalog of 1633 Brachvogel 17

Hipler, “Analecta,” esp. 359–381. Hipler, “Analecta,” 383. 19 Hipler, “Analecta,” 318. On 427, Hipler also refers to a Swedish plundering in 1656, and expresses his suspicion that many books were lost in transport. 18

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listed and enumerated authors, works, and, wherever possible, the place and date of publication. He divided the collection into four categories—theology (including collections of sermons), history (including philosophy, works by classical authors, and dictionaries), law, and secular and heretical works (including Philipp Melanchthon’s works on dialectic). Focusing on works in logic, natural philosophy, and mathematics, copies of which Copernicus did not own, we find several works of Cicero, especially Rhetorica (no. 120 in Brachvogel’s list), the writings of Copernicus (not further specified, no. 215), the two volumes of Plato’s works in the translation by Marsilio Ficino (Florence, 1484; Hain *13069), Pliny’s Natural History (Rome, 1473), the works of Plotinus translated by Marsilio Ficino (Florence, 1484), and Latin translations of works of Ptolemy (Cosmographia, Vicenza, 1475; Almagest, Venice, 1528; and Liber quadripartiti, Venice, 1519). As for the period before 1540, we may exclude the works of Ptolemy published after 1510. Copernicus relied on his own private collection, but when he needed to consult other books, the library at Lidzbark was not of much use to him with one major exception. There is almost nothing in the collection that would have contributed to the writing of the Commentariolus which leads us to suppose that he either had his own copy of Regiomontanus’s Epitome, or that a copy was later taken to Frombork. He had a copy of Euclid’s Elements with the commentaries by Theon and Proclus. We know he had astronomical tables and very probably access to John of Sacrobosco’s Sphaera mundi. As for the Suidae lexicon, the old catalogs list several dictionaries without specific information. Perhaps one of them was the Suidae lexicon. Neither the copy at Uppsala nor the one at Stockholm is from Poland, so we must suppose that the copy presumably used by Copernicus has disappeared.20 Copernicus’s earliest reading of Regiomontanus’s Epitome, Ficino’s translation of Plato’s Works, and Pliny’s Natural History probably occurred in the years between 1496 and 1503, and in some cases possibly earlier. For example, he may have seen Ficino’s translation and Pliny’s book in Cracow. Bessarion’s work was not published until 1503, so he probably first read it in Lidzbark. As we noted, his copy of 20

Collijn, Katalog Uppsala, XXI–XXV, 354–355, 477–478, and 483; Collijn, Katalog Stockholm, 228, No. 1002; and compare Collijn, Katalog Linköpings 33. On Copernicus’s use of the Suda, see Knox, “Ficino, Copernicus,” 333–366; and idem, “Ficino and Copernicus,” 415–418.

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Bessarion’s defense of Plato, the copy of Pliny that he used, and Part I of Ficino’s translation that he annotated have survived, and it is likely that he used all three for the writing of Commentariolus. We begin with the Epitome, focusing on what he likely derived from it, relying in part on the findings of Ludwik Birkenmajer, Felix Schmeidler, Noel Swerdlow, Edward Rosen, and Bernard Goldstein. My argument is that mostly after his undergraduate education, Copernicus benefited from the printed versions of about a dozen works. By means of these books either gathered by 1503 or available to him in the library at Lidzbark, Copernicus achieved breakthroughs in his evaluation of Ptolemaic astronomy, the interpretation of hypotheses, and the relation between astronomy and natural philosophy. In other words, by 1515 at the latest Copernicus had formulated the chief philosophical principles that would guide him through to the completion of his project. In this chapter, I summarize Copernicus’s principal reading between 1496 and 1510, and how these texts are related to his first heliocentric theory. Above all, the chapter attempts to reconstruct Copernicus’s philosophical development, while taking into consideration the simultaneous evolution of his thinking about the problems with the order and motions of the celestial spheres. Thanks to the preservation of books and the efforts of many previous scholars, we can examine much of Copernicus’s library and the books available to him at Lidzbark and later at Frombork.21 2. Regiomontanus’s Epitome The most important astronomical work acquired by Copernicus in Italy was the Epytoma Joannis de monte regio In almagestum Ptolomei (Venice, 1496), referred to in its anglicized form Epitome.22 Copernicus’s early, detailed knowledge of Ptolemy’s Almagest came almost entirely from the Epitome, which included Peurbach’s summary of the first six books of the Almagest and Regiomontanus’s additions to that part and his summary of the last seven books. The Epitome,

21 Because Copernicus was so reticent about sources or references in Commentariolus, I also refer to De revolutionibus in what follows for specific references to the books he owned, annotated, or consulted. 22 Joannes Regiomontanus, Opera collectanea. The text was completed in the early 1460s, according to Schmeidler, Opera, XXV.

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however, was more than a summary; this is especially true of those parts reworked by Regiomontanus, the relevant details of which we will point out below. As we have mentioned, the copy owned by Copernicus has disappeared.23 There is no doubt, however, that he used it.24 The fact that he already owned a copy of Regiomontanus’s Tabula directionum (1492) while in Cracow and began working with Novara, a student of Regiomontanus, offers strong prima facie evidence that he acquired the Epitome in 1497.25 He continued to use it throughout the writing of De revolutionibus.26 In the absence of Copernicus’s copy and lacking his annotations, scholars have had to reconstruct his use of it from the Commentariolus and De revolutionibus. Even a brief and selective summary of is contents, however, is instructive. After the dedication to Cardinal Bessarion in the 1496 edition, the preface follows Ptolemy in the division of the speculative sciences, attributing the division to Aristotle. The distinctions between the invisible and immobile God, on the one hand, and the corruptible sublunar region of matter and qualities, on the other, correspond to the disciplines of theology and natural philosophy respectively. Concerned with local motion, shape, continuous and discrete quantity, and place and time, mathematics falls between theology and natural philosophy. Mathematics serves, on the one hand, as the best human approximation to theology because through exercise it can lead us to the celestial divinities where by means of its arithmetical and geometrical proofs

23 Copernicus, Opera omnia, 2: 359. The copy at Uppsala (Collijn, No. 843) is from the Jesuit College of Olmütz in Bohemia, not Poland. 24 The most extensive analysis is in Birkenmajer, Mikołaj Kopernik, chapter 1, to which I refer extensively below. See my translation available online: http://www .stonehill.edu/Documents/Physics/Birkch.1.pdf. Otherwise, see, for example, Zinner, Entstehung, 587. Schmeidler points out several examples in his commentary, including errors that Copernicus evidently copied from Regiomontanus. See, for example, Schmeidler, Kommentar, 160, 164–165. Edward Rosen also points out passages that Copernicus evidently knew, but Rosen, in his translation of Commentariolus, Minor Works, 111, n. 200, also doubts that Copernicus was familiar with the entire book at the time that he wrote Commentariolus. 25 Schmeidler, Kommentar, 150. Schmeidler does not explain his dating, but Copernicus arrived in Bologna in the fall of 1496, so we may infer that he would have bought the book in late 1496 at the earliest. 26 Birkenmajer, Mikołaj Kopernik, 3–25; Dobrzycki, Commentary, 359; Schmeidler, Kommentar, passim; and Swerdlow and Neugebauer, Mathematical Astronomy, 50–54 and passim.

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we find nothing obscure and nothing disordered. Mathematics also confers a measure of comprehension and order on the variable world of matter by distinguishing the properties that reveal the essential differences between the natural and celestial—the corruptible as opposed to the incorruptible, rectilinear motion as opposed to circular motion, heavy and light as opposed to what is neither heavy nor light.27 Regiomontanus follows these remarks with six “conclusions.”28 First, heaven has a spherical shape and it moves in a circle. Regiomontanus supports this conclusion by adducing what he calls “experiential, refutative, and rational syllogisms.”29 The experiential rely on the ordinary sense observations of the heavenly motions. As an example of the refutative, Regiomontanus argues that all who dismiss the sphericity of heaven are either compelled to reject the proper motion of the lower spheres or to acknowledge that the celestial bodies suffer intersection.30 Because the alternatives are inappropriate, the assumption

27 Epitome, 64–65. These notions, of course, follow Ptolemy closely, including the intellectual and moral benefits that mathematics confers on its practitioners. See Ptolemy’s Almagest, 35–37. 28 See Swerdlow and Neugebauer, 51–52, for the conclusion that Regiomontanus wrote this part, a conclusion that Swerdlow based on manuscript evidence. Ernst Zinner, Regiomontanus, 52, calls the conclusions “axioms.” But Regiomontanus clearly adduces arguments and evidence in support, which hardly makes them axiomatic. 29 Epitome, 65: “Triplici ad hoc confitendum iudicimur syllogismo: experimentali videlicet: confutativo: et rationabili.” 30 Ibid., 65: “Si quis aliam quam sphericam celo primo figuram deputauerit: aut spheris inferioribus motum proprium abnegare coges: aut corpora celestia scissionem pati fatebitur.” The word “scissio” is also used in some of the Theorica planetarum literature, but I have been unable to determine its source, leading me to wonder whether Regiomontanus himself introduced the word. The word does not appear in Peurbach’s Theoricae, so that is not the source. Campanus of Novara alludes to a similar problem in Theorica planetarum V: 238, lines 391–397: “At uero secundum partes illas de quibus semidiameter terre est pars una possibile est nobis easdem magnitudines inuenire si supponamus supremum eius ad quod peruenit luna esse infimum eius ad quod peruenit mercurius sicud dictum est in precedentibus. Nisi enim ita fuerit necesse esset planetas proprias speras exire aut inter eas locum esse uacuum aut eas esse maiores quam ipsorum planetarum motus requirat; quorum duo prima inpossibilia, tertium uero superfluum esse uidetur.” Benjamin and Toomer make the following comment, 412, n. 47: “There are four possibilities: (1) The spheres are contiguous and as small as possible. This Campanus accepts. (2) The spheres pass through one another, so that, e.g., the lowest point reached by Mercury would be lower than the highest point reached by the moon. This possibility is expressed by the rather ill-chosen phrase “the planets go outside their own spheres”: better would have been “the planets enter one another’s spheres.” That is impossible for Campanus; he supposes the spheres to be solid, and so to allow one solid to pass through another would be to suppose that two bodies occupy the same space, which is contrary to Aristotelian thinking. (3) The spheres are not contiguous.

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is unacceptable. Rational arguments appeal to the capaciousness of a sphere to include everything in the universe most efficiently. It is also fitting for a sphere to rotate in a circle. All of these syllogisms, we may point out, are not demonstrative but inductive or dialectical and probable. Second, Earth is spherical.31 Third, Earth is in the middle of the universe. Fourth, Earth is as a point in relation to the heavens. Fifth, Earth has no local motion. Sixth, there are two heavenly motions.32 Book I concludes with twenty-five propositions of spherical trigonometry. Book II describes the basic features of the celestial spheres in forty-five propositions. Book III treats models of solar motion in thirty propositions; Book IV lunar models in nineteen propositions; Book V lunar instruments, inequalities, size and distance in thirty-two propositions, and Book VI solar and lunar eclipses in thirty propositions. Books VII and VIII treat the motions of the fixed stars and the stars of the zodiac in ten and fifteen propositions respectively. Book IX determines the order of the celestial spheres, describes the diverse motions of the planets, and introduces the model for Mercury in twenty-three propositions. Book X elaborates the models for Venus and Mars in twenty-five propositions; Book XI the models for Jupiter and Saturn in nineteen propositions, and Book XII discusses the attributes of the

This possibility would mean that there is empty space between them. That, too, is rejected as impossible, for Aristotelian thinkers rejected the existence of void . . . (4) The spheres are contiguous, but not as small as possible, so that, e.g., there would be an interval between the highest point reached by the moon and the lowest point reached by Mercury in which no movement would take place, but which would be filled by the “quinta essentia” only, whether belonging to Mercury’s sphere or the moon’s or both. Campanus admits the possibility of this, but objects to it on the ground that it involves superfluity (the supposition is that the Creator always does things in the most economical way possible).” Although Campanus does not use “scissio,” his second objection is precisely the problem here, namely, an intersection of spheres would occur. Note that “solid” here does not necessarily mean “hard.” Even if it means only “three-dimensional,” it is a body, and one body cannot occupy the same place as another. The only other author known to me who uses the word “scissio” is Albert of Brudzewo. See Commentariolum, 25. Birkenmajer, XLVIII–LVI, shows that Albert wrote his commentary between 1482 and 1495, the year in which he died, and the book was first published in Milan. It is obvious that Albert was not Regiomontanus’s source, but did Albert get the word from Regiomontanus? We do not know. Finally, some sources describe the problem as “penetratio.” See Lerner, Monde, 1: 314, n. 82. 31 The “conclusions” correspond, of course, to Ptolemy, Almagest I: 3–8. 32 That is to say, a daily eastward motion along the equator and an annual westward and alternating southwards and northwards motion along the ecliptic. See Epitome, 68.

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diverse planets with their stations and retrogradations in fourteen propositions. Book XIII, finally, describes the motions of the planets in latitude in twenty-nine propositions. In the thirteen books there are a total of three hundred and sixteen propositions. If Copernicus assisted Novara with his work, attended classes, and began to learn Greek, it must have taken him several years to work through its details. Before we continue, we should recall that Copernicus had already learned the basics of celestial astronomy, instruments, and observations. We focus here, then, on what Copernicus learned in a general way from the Epitome, and will consider specifics when we turn to a discussion of Commentariolus later. The Epitome was Copernicus’s source for his knowledge of al-Bitruji’s ordering of Mercury and Venus, and his belief in the variability of the obliquity of the ecliptic.33 His concern with physical problems in spherical astronomy may derive from the Epitome.34 He was probably already aware of the problem with Ptolemy’s lunar model, but the Epitome confirmed its seriousness.35 While Copernicus began to master the mathematical details by means of the Epitome, he was content initially with a relatively more qualitative consideration of the problems. After concerns over the correctness of Ptolemaic models, what soon dominated his attention were two problems. The first is the problem of the ordering of the spheres.36 The second is the emphasis placed by Regiomontanus on the link between the motions of the planets and the motion of the Sun.37 Copernicus had almost certainly encountered these ideas in Cracow, but the Epitome cast a light on them that caught

33 Copernicus, De revolutionibus, Opera 2: 374 and 376; Birkenmajer, Kopernik, 7, 12–13. Cf. Rosen, On the Revolutions, Complete Works, 2, commentary, 355, 368–369; Swerdlow and Neugebauer, 105. 34 Swerdlow and Neugebauer, 55. 35 Compare Swerdlow and Neugebauer, 250–251; Zinner, Entstehung, 131; Rosen, Commentariolus, 3 and 104. Rheticus, Narratio prima, Rosen tr., 133, also refers to Regiomontanus. 36 Goldstein, “Copernicus and the Origin,” 221–222, provides a penetrating analysis of Copernicus’s concern here. 37 Zinner, Regiomontanus, 334–335; Rosen, Revolutions, Commentary, 355. Compare Wattenberg, Johannes Regiomontan, 14–15. The image of the Sun as king may have come from a number of sources, but Copernicus certainly read it in the Epitome even if not for the first time. As suggested in chapter four, he probably heard it in lectures from or on John of Glogovia. Achillini, De orbibus. f. 13r, also compares the Sun to a king: Tum quia sol est maximum planetarum imo maior est stellis fixis ex magnitudine autem corporis nobilitas conuincitur est enim tamquam rex cui assistunt consiliarij. See Zinner, Entstehung, 128–132.

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his attention. Whether discussions of the motions of Earth influenced him yet is difficult to assess. He certainly encountered such ideas in Cracow as well. Peurbach and Regiomontanus discuss them, only to dismiss them, and Novara, as we know, made a proposal that Copernicus rejected; nevertheless, all of these discussions may have stimulated his own speculation. More important is the fact that some of these discussions concern Earth’s orbital motion, a consideration that is not always clearly emphasized in the scholastic discussions.38 Certainly, these discussions familiarized him with all of the objections. Regiomontanus’s syllogisms are inductive or dialectical, not demonstrative, a fact that almost certainly did not escape Copernicus’s attention, encouraging him to approach the arguments in a questioning fashion. When he began using the Latin translation of the Almagest in 1515, he was already a heliocentrist who read Ptolemy’s arguments critically and dialectically. Finally, we may point to Regiomontanus’s treatment of spherical and planetary models together, which may account in part for Copernicus’s own approach to the models and to the physical problems.39 To make the point as clearly as possible, the Epitome was not the only source for Copernicus’s acquaintance with the above facts or problems. The Epitome brought them together in a way that Copernicus had not yet encountered, and this confluence of comments about details, sources, problems, and solutions (or their absence) and of his work with Novara constitutes a turning point where Copernicus began to consider the problems seriously and critically. 3. Bessarion’s In calumniatorem Platonis What other connections did Copernicus have with Regiomontanus? How much did the philosophical traditions of Platonism and Neoplatonism exercise on Copernicus? I pursue some answers to these questions in this section, and begin to examine Copernicus’s understanding of the relation between Plato and Aristotle. When Copernicus went to Italy in 1496 and began working with Domenico Maria Novara, he attached himself more directly than he could have in Cracow to the tradition of fifteenth-century humanist 38 39

Wattenberg, 34. A point given some emphasis by Zinner, Regiomontanus, 339.

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astronomers, Peurbach and Regiomontanus. Peurbach taught Regiomontanus, who, Novara claimed, taught him. When Regiomontanus met Cardinal Bessarion in Vienna, he returned to Italy with him and at his request.40 Under Bessarion’s inspiration and guidance, Regiomontanus learned Greek and undertook the task of collecting and mastering the Greek mathematical corpus with the intention of producing competent Latin translations, and thus complete the ancient goal of making progress in the discipline of astronomy. Copernicus’s realization of problems with the observational data, however, took much longer to develop.41 His initial focus, and one that obsessed him for several decades, was on the models themselves, inconsistencies among astronomers about the ordering of the planets, and puzzles related to variations in the distances of the planets relative to Earth.42 The observational anomaly with the Ptolemaic lunar model did not make him suspicious of Ptolemy’s observational data; it rather led him to examine alternative models. The second major development in Italy was direct contact with the Platonist revival.43 This topic and its confusion with Pythagoreanism and neo-Pythagoreanism have been much contested in the scholarship on Copernicus. I approach the question of Copernicus’s knowledge of Plato from what Copernicus read. In this section, I focus on his reading of Bessarion’s treatise, In calumniatorem Platonis, a work that Copernicus owned and annotated. In the following section I will examine what we know of his reading of Plato and questions about his acquaintance with Marsilio Ficino’s translation of and commentary on the works of Plato. The reintroduction of Plato’s ideas in the West is largely attributable to the efforts of Bessarion, cardinal of Nicaea and patriarch of Constantinople. In calumniatorem Platonis was written to defend Plato

40

On Bessarion, see Mohler, Kardinal Bessarion, 1: 1–15; idem, “Wiederbelebung,” 41–48. 41 Swerdlow, “Regiomontanus,” 165–195, at 166. As Swerdlow points out, Copernicus was also concerned with problems with the Alfonsine Tables, but his focus lay in more theoretical issues. 42 The puzzles about distances as suggested in De revolutionibus I, 10, involve the large spaces or gaps taken up by the epicycles of Venus and Mars as well as inconsistencies regarding the positions of Mercury and Venus as opposed to the superior planets based on their elongations from the Sun. I return to this issue in section eight below on the Commentariolus, and discuss the problem of distinguishing between clues and afterthoughts. 43 Mohler, 1: 325–357.

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from the critique of George of Trebizond, and to argue for the congeniality between Plato’s ideas and Judaeo-Christian doctrines.44 George of Trebizond argued for the superiority of Aristotle for Christian theology, but Bessarion did not defend Plato by attacking Aristotle. Bessarion had great respect for both, not to the point of harmonizing them, but rather to show how both were useful for the explication of Christian doctrine in different ways. Bessarion regarded Plato as superior in this regard, but because Aristotle had also adopted much from Plato, the Cardinal thought himself justified in arguing for some fundamental points of agreement between them.45 This strategy may have been rhetorical, approving Aristotle wherever he could be interpreted as deriving the truth from Plato.46 Still, despite slips where he displays a more anti-Aristotelian hand, the innocent reader will come away convinced of his even-handedness.47 In calumniatorem Platonis, written around 1458–1469, contains four books.48 Book I explains the circumstances under which Bessarion felt compelled to defend Plato, explaining why Plato adopted the dialogue form and such an enigmatic style of philosophizing. Early in his defense he cites the letter of Lysis to Hipparchus on the Pythagorean motif of esoteric doctrine.49 After citing the testimony of ancient Greek and Roman authors about the wisdom of Plato, he defends Plato’s rhetorical style as using ordinary language to express doctrine and persuade readers by eloquence and thereby lead them to true wisdom.

44 Although I have examined Copernicus’s copy in Uppsala, I rely for this summary on Mohler’s edition. Trapezunt is located on the northeastern coast of the Black Sea, although George was born in the Venetian dominion of Crete. See Hankins, Plato, 165. 45 Aside from referring to both authors extensively, he also translated Aristotle’s Metaphysics into Latin. See Mohler, 1: 335–345. See also di Napoli, “Cardinale Bessarione,” 327–350, for a summary of the tradition of Neoplatonism and Bessarion’s defense of both Plato and Aristotle. Bessarion opposed the speculative theology of the schools, as Hankins, Plato, 226, points out. There can be no question that he regarded Plato as superior to Aristotle, and his critique supported the anti-Averroist attacks of humanist authors. 46 Hankins, Plato, 246–247. 47 Ibid. 257. Hankins summarizes the argument and its effect, 245–263. 48 Mohler, 1: 358–365. 49 For this summary I have relied on Mohler’s edition, but see his summary in Kardinal, 1: 366–383. See Mohler’s edition, 12–15 for the letter. Copernicus later translated the letter himself, but it is clear that he knew the Cardinal’s translation. See De revolutionibus, Gesamtausgabe 2: 488, line 27–490, line 4; Opera 2: 341. Rosen, Revolutions, Commentary, 361–362, shows how closely Copernicus followed Bessarion’s translation by referring to the parallel texts in Birkenmajer, Kopernik, 132–134.

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Book II explains why Plato’s ideas are more congenial to the Christian religion than those of Aristotle. He begins by referring to the Church Fathers who cite Plato above all gentile authors. Because the texts of Plato are now so unfamiliar, Bessarion explains what Plato says about the principle of all being in Parmenides (137e–142a), and how consistent his words there are with his other expressions of divine things. In a long chapter (II, 6), he summarizes Plato’s account of the creation of the world in Timaeus (28a–37e). This text emphasizes the perfection and goodness of the artificer in looking to the eternal as an exemplar for creating the most perfect order possible, referring to the universe as a machina mundi (p. 121, line 2).50 Here too he cites Plato and others on matter and chaos as infinite and form as limiting and finite (p. 121, ll. 27–35), from which two principles the creator caused the divine and intelligible machine of the world. After defending Plato’s account of matter by distinguishing different levels and degrees of eternity, Bessarion critiques Trebizond’s interpretation of Aristotle (II, 7). In II, 8, he summarizes Plato’s doctrine of the soul and the role of mathematics in training the mind for instilling in humans the recollection of divine things (p. 160, l. 36–p. 161, l. 17), a doctrine that Bessarion attributes to the Pythagoreans. In II, 11, he turns to Plato’s opinions on the principles of nature, especially the resolution of the elements into plane and linear figures (p. 199, ll. 5–7; 201, ll. 27–34). Plato posits the four elements, but follows the Pythagoreans in seeking for the explanation of the qualities out of which the elements are composed (p. 203). To Aristotle’s objection that bodies cannot be composed out of dimensionless lines and points, Bessarion responds that the figures proposed by Plato and the Pythagoreans are natural, not merely mathematical, figures (p. 205). He also argues that the Pythagoreans and Plato may not have maintained that the principles of natural things are really geometrical figures. And here Bessarion adds that the models proposed by astronomers do not really exist in the heavens, for their purpose is to save the appearances. The Platonic doctrine of plane figures should be understood in the same way. Bessarion defends Plato for trying to understand fundamental

50 Of course, in De revolutionibus, Preface to Pope Paul III, Copernicus also uses the expression machina mundi, and he refers to God as opifex. Bessarion refers to God as auctor, creator, and opifex. A little further in his defense, 127, l. 38, Bessarion also refers to Hermes Trismegistus, also mentioned by Copernicus in I, 10. See Rosen’s comment, 359.

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principles and proposing an explanation that he judged to be of value until something better appeared.51 Book III deals explicitly with theological and religious doctrines and metaphysical issues concerning the prime mover, a section of the book that relies greatly on Neoplatonic authors and St. Augustine. In much of this, Bessarion refutes Trebizond’s interpretation of Aristotle. Near the end of Book III (ch. 26), he returns to Plato’s views on mathematics in discussing questions about the rational soul and its immortality. The defense is based on the abstractness of mathematics, which makes the soul suited for trying to understand divine things. Book IV defends Plato from charges of immorality. In chapter twelve he defends Plato from the charge that mathematics is to be taught to those who wish to be divine. Mathematics, indeed, is the most worthy of a free man and prepares the mind for higher things and also for service to the community, but even the most adept mathematicians are far from divinity. The book ends with references to Pope Nicholas V supporting the translation of Plato’s works into Latin. Indeed, Ficino read Bessarion’s book in Florence, where he founded a Platonic academy, and translated Plato’s works into Latin.52 Copernicus bought the Aldine edition of 1503 in his last year in Italy. Copernicus’s interest and admiration for Plato derived in part from his reading of Bessarion’s book. In it Copernicus encountered, in fact, a Neoplatonic reading of both Plato and Aristotle, and, above

51

Mohler edition, 205, line 30–207, line 6: “Licet tamen etiam aliter hanc opinionem tueri, quod videlicet nec Pythagorei nec Plato principia rerum naturalium huiusmodi triangulos tamquam rem certam posuerint. Sed quem ad modum astrologi, cum causam quaererent inaequabilis motus caelestium corporum, qui scilicet aequabili, certo et ordinato eorum motui contrarius est, alii excentricos, alii epicyclos, alii revolventes sphaeras introduxerunt, non quod varietas ista in caelo sit, sed quia principiis huiusmodi positis servari possunt ea, quae praeter rationem videbantur accidere, cum tamen omnia caelestia corpora orbe suo et aequabiliter moveantur, sic illi cum generationis rationem nullo modo servari posse existimarent, nisi quantitas aliquo modo prior consideraretur et, quoniam indeterminata esset, ad figurarum rationem simplicium et similitudine proportioneque cohaerentium aptius referretur, idcirco figuras ita pro principiis simplicioribus posuerunt, ut eiusmodi quantitas sub notitiam suae qualitatis, quae certa figure est, caderet et, quamquam non ita esset, quasi tamen ita esset, intellegeretur.” On 207, a few lines later (27–30), he adds: “Sic igitur Pythagorei et Plato in exquirendis naturae principiis ulterius, quam elementorum sumerunt qualitates, comperire simplicius aliquid conati sunt, et quod compererunt, tamdiu servandum censuere, donec melius aliquid occurreret.” 52 Mohler, 384. Di Napoli, 345–349, also points out important differences between Bessarion and Ficino. See also Monfasani, “Marsilio Ficino,” Article IX (pp. 179–202).

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all, a summary of Plato’s ideas on language, logic, the natural world, and the mathematical arts. Bessarion’s translation of selective texts recounting Plato’s praise of mathematics undoubtedly made a deep impression on Copernicus, familiar as he already was with Ptolemy’s high regard for mathematics, at a time in his intellectual development when he was coming to grips with the relation between mathematics and natural philosophy. 4. Ficino’s Translation of Plato’s Works Did Copernicus read Plato? Did he know Marsilio Ficino’s translation of Plato’s works? What influence did Plato exercise on Copernicus’s thinking? Did Copernicus necessarily have a clear understanding of the differences between genuine Platonism and genuine Aristotelianism? I suggest in this section that Copernicus’s goals did not commit him to scholarly or academic precision about the doctrines of ancient authorities. This is not to argue for the opposite extreme, namely, that he blended and confused them, but rather to suggest that he was motivated to minimize the differences that he and others recognized. As far as we know, Copernicus did not own Ficino’s translation, but used the copies in the libraries available to him. We do not know how many of Plato’s works Copernicus read directly. It is even possible that he had read some of the dialogues already in Cracow.53 Note that Copernicus’s apparent reference to Timaeus in De revolutionibus referring to heaven as a visible god does not come from the passages cited by Bessarion. The passage (Timaeus, 93c) would hardly have strengthened Bessarion’s argument in behalf of Plato’s orthodoxy and utility for Christian theology. As argued in the introduction, we have strong reasons for believing that Copernicus read Plato’s Parmenides; first, a reminder about the copy of Ficino’s translation used by Copernicus.

53 For a careful, thorough, and authoritative review of Copernicus’s acquaintance with Ficino’s translation, see Knox, “Ficino and Copernicus,” 399–418. On 403, Knox lists the editions printed prior to 1543, and on 405–406, he adds that the Jagiellonian Library in Cracow holds four complete copies of the 1484 edition, annotations in which show that they were available there by 1490. Callimachus, a friend of Nicholas’s Uncle Lucas, may have received a copy as early as 1485. See Birkenmajer, Stromata, 80–81. Cf. Biliński, Alcune considerazioni, 14–15.

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Both the library at Frombork and the episcopal library at Lidzbark owned copies of Ficino’s translation. The old catalogues do not always inform us which editions or about the provenance, but Collijn says that the entire collection at Frombork was taken to Sweden in 1626. This cannot be the copy that Brachvogel lists among those from the catalog of 1633.54 In Commentariolus there are no clear references to any of Plato’s works. The catalog of 1633 shows that the episcopal library of Lidzbark owned a translation that Brachvogel identifies as the 1484 edition in two parts. We cannot be certain that a copy was in Lidzbark between 1503 and 1510, but it seems likely that had the library acquired the book much later, it would have been a more recent edition. The copy from Lidzbark has evidently completely disappeared.55 As mentioned above, the scholars who have examined the copies in Uppsala are uncertain about attributing the annotations in them to Copernicus.56 After a careful examination of the two parts, I concluded that Copernicus wrote some of the annotations in Part I, but the annotations in Part II remain doubtful.57 In De revolutionibus, Copernicus refers to Timaeus twice explicitly (I, 10, and V, Introduction) and five times indirectly (Preface; I, Introduction; I, 5; I, 10; and I, 11), and to Laws once (I, Introduction).58 The first two indirect references to Timaeus in the Preface and repeated in 1, 5, is to 40b, which some readers took to report an axial rotation of the Earth at the center of the cosmos. Copernicus was certainly acquainted with sources that attributed this view to Plato.59 The third 54 Collijn, Katalog Uppsala, 477. On the library in Lidzbark, see Brachvogel, “Bibliothek,” 329, no. 296, which he took from the catalog of 1633, listing both Part I and II. The Swedes plundered the collection in the winter of 1704–1705; hence, this copy of Ficino’s translation is not the copy at Uppsala. See Czartoryski, 382, no. 49; cf. Goddu “Annotations,” 220. At Uppsala, Part I is catalogued as Copernicana 31, but Part II is catalogued as Uppsala 32:82. On the collection at Frombork, see Kolberg, “Inkunabeln,” 116. Kolberg’s conclusion is based presumably on the ownership mark in Part I, but Kolberg does not distinguish the two parts, because the catalog makes no mention of two parts. For a summary of the history of the libraries in Varmia, see Brachvogel, “Bibliotheken,” 35–44. The first and still fundamental description of the collections is by Hipler, “Analecta.” See also Barwiński, Sprawozdanie; Birkenmajer and Collijn, Nova copernicana; Collijn, Katalog Uppsala; and Birkenmajer, Stromata. 55 Brachvogel, “Bibliothek,” 329, no. 296. 56 Collijn, Katalog Uppsala, 315, No. 1235, and for the provenance of each part, see 475 and 477–478. 57 The details with photographic evidence are in Goddu, “Annotations,” 215–220. 58 The Introduction was suppressed in the 1543 edition. See Gesamtausgabe 2: 487–488. 59 Knox, “Ficino and Copernicus,” 405.

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(already mentioned) is to heaven as a visible god, an expression that comes from the end of the dialogue (93c). The first explicit reference (I, 10) is to Timaeus 38d about the ordering of Mercury and Venus above the Sun. This is followed almost immediately by the fourth indirect reference (Timaeus 39b) about the planets reflecting sunlight. The fifth indirect reference (I, 11) is actually in the autograph, a passage that Copernicus deleted.60 The second explicit reference (V, Introduction) is a mistake, indicating that Copernicus did not check the original.61 The reference to Laws is from 809c–d and 818c–d.62 In Ficino’s translation, both Timaeus and Laws are in Part II. My evaluation of the annotations in Part II has not settled the question whether Copernicus annotated that part.63 Czartoryski and his team included both Part I and Part II among the works that remain uncertain. Dilwyn Knox reports that Grażyna Rosińska examined Part II, and concluded that the annotations are uncertain and probably not by Copernicus.64 As I asserted above, the annotation to Parmenides is genuinely Copernican. The annotation reads: “quid aduerti oporteat circa hyppotheses,” a comment on the text between 135e–136b.65 With only one comment to guide us, we can hardly draw certain conclusions about Copernicus’s reading of the entire dialogue, let

60 See Rosen’s translation, 25. Plato’s remark referring to only a few who mastered the theory of the heavenly motions comes possibly from Timaeus 27a–d, and Knox, 404, suggests 38d–e. As Rosen points out, 361, however, Copernicus may have depended on Bessarion here. 61 Rosen’s commentary, 416–417, suggests that Copernicus was familiar with Chalcidius’s Commentary on Plato’s Timaeus, where the same mistake appears possibly accounting for the misattribution to Timaeus in V, Introduction. But Knox, 404, n. 23, is unconvinced and proposes that Copernicus consulted the original Greek version of pseudo-Plutarch’s Placita philosophorum. The problem will be addressed in the section on Giorgio Valla, who partially translated what he thought was a genuine text by Plutarch. 62 Rosen’s commentary, 344 and 355. 63 Knox, 406, n. 28. 64 Knox, 406, n. 28. See Goddu, “Annotations,” 219–220. Although I lean towards authenticity on holistic grounds, for example, the fact that some annotations in Timaeus occur at astronomical passages, as noted also by Rosińska, there are problems with several of the letters that are difficult to explain away. 65 Goddu, “Annotations,” 208–215, analyzes the annotation in detail. Note that Bessarion quoted passages from around this text at 1: 5 (59): 137c–e; I: 5 (67): 135d– 136c, and 2: 4 (89): 137e–142a. For the relevant passage in Ficino’s translation see Appendix IV.

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Plate 1—Detail of annotation from Uppsala, Copernicana 31, fol. sig. e5ra.

alone other dialogues.66 Copernicus reacted to Plato’s advice about hypotheses. His comment is on a text in which Parmenides challenges Socrates to examine all of the consequences of a hypothesis taken both affirmatively and negatively, and to repeat the process for a variety of hypotheses. Parmenides characterizes the process as an exercise. Below I will suggest how such an exercise contributed to the formulation of the postulates in Commentariolus. Copernicus’s views about hypotheses, I shall argue in the last section of this chapter and more extensively in chapter eight, reflects his reasons for rejecting Ptolemaic hypotheses as unsound because they are irrelevant and unconfirmed by the observations.67 In sum, we do not know with certainty when Copernicus read Ficino’s translation. We have concrete reasons for believing that he read Parmenides. His references to Timaeus and Laws suggest that he either read them or quoted them from another source. There are numerous problems here that we cannot completely sort out or neglect. It seems clear that Copernicus relied on some commentaries on Plato’s works or citations of them (Bessarion is one example). Second, his citations are from that part of Ficino’s translation that has been lost. Third, he makes no explicit reference to the text that he did annotate from Part I. It is little wonder that we have to be cautious about his reading of Plato.

66

For a review of the modern scholarly debate over interpretation of Parmenides, see Turnbull, Parmenides, 189–199. Cf. also Plato, Parmenides, tr. Gill and Ryan. On Ficino’s commentary, see the remark of Turnbull, 189. Compare Malmsheimer, Platons ‘Parmenides’; Farndell, Evermore, vii–viii and xv–xxxix. Rheticus, Narratio prima, Rosen tr., 162–165, provides another analysis and interpretation of hypotheses and Plato, but he refers to a work, Epinomis, a title that does not appear in the table of contents of Plato’s works that Ficino translated in the 1484 edition. Rosen, 165, n. 198, points out as well that Rheticus used Simon Grynaeus’s revision of Ficino’s translation of Gorgias. 67 In an alternative and thought-provoking essay, de Pace has argued for a reading of De revolutionibus I, 10, based on Copernicus’s supposed following of Plato’s Phaedo, supplemented by a passage from Republic. See de Pace, “Copernicus,” 77–115.

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Of utmost importance, however, is the fact that Copernicus’s understanding and use of Plato and Aristotle are consistent with Bessarion’s interpretations and with the Neoplatonic tradition in general. From his reading of Bessarion and Plato he certainly was moved to a high regard for mathematics, but it is still not clear that he had yet adopted the strong realist position that many scholars have attributed to him. Indeed, as we shall see in chapter ten, it is dubious that he ever adopted such a robust realism about mathematical models. In any event, there is nothing in his reading that indicates that he had arrived at such a strong position prior to 1506. 5. Plutarch, Pseudo-Plutarch (Aëtius) and Giorgio Valla Neoplatonic and Stoic sources or traditions also influenced Copernicus. He drew on many authors to support his departures from Aristotelian doctrines, and either to transform Aristotelian concepts and principles or to propose alternative solutions and theories. In this section I examine his reliance on other ancient sources that we know or strongly suspect he used. Scholars have identified several passages in De revolutionibus that apparently derive from Plutarch and pseudo-Plutarch as translated by Giorgio Valla, and even some evidence that Copernicus consulted Plutarch in the original Greek. Valla’s translation was published posthumously in 1501, and there is evidence that Copernicus consulted it for Commentariolus. This would mean that he consulted it already in Italy and at Lidzbark. The catalog from Frombork lists Valla’s name but not which work. Collijn’s catalog does not list Valla’s De expetendis in the collection at Uppsala. There is also some evidence that Copernicus knew of another translation of Greek works by Valla that was published in 1498.68 We do not know whether this work was available in either Lidzbark or Frombork. In addition, Edward Rosen has shown that Copernicus used Valla extensively for descriptions of astronomical facts and some of his numerical values in De revolutionibus.69

68

Rosen, Revolutions, Commentary, 368. Rosen, Revolutions, Commentary, 368–382. Rosen refers to Valla’s translation of a text by Cleomedes. 69

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My brief summary of these works focuses on issues that would have contributed to Copernicus’s arguments, and on texts that may have stimulated his mind to consider the motions of Earth. Valla’s enormous book included a translation of pseudo-Plutarch’s De placitis philosophorum, which Valla and Copernicus thought was an authentic work.70 It is an odd collection of ancient opinions, but it provides a handy, if often inaccurate, summary of ancient views. De placitis consists of five books that Valla translated as Books 20–21 in De expetendis. It begins with a division of the sciences, discusses nature, its principles and elements according to several pre-Socratic authors, Plato, Aristotle, the Stoics, and Epicurus. From Book I, Copernicus would have found the views of these authors on questions dealing with the uniqueness of the universe, its eternity, matter, form, cause and effect, the nature, shape, characteristics, and divisions of bodies, on void, place, space, time, and motion. Book II assembles opinions on the universe, its shape, whether animate or inanimate, its eternity, its center, and order. These opinions are followed by discussion of void, the heavens, the number of spheres, the stars and their shapes, the names of the planets, the motions and nature of stars, the Sun, Moon, and periods of revolutions. Book III takes up issues that the ancients included under meteorology, and it discusses Earth, its shape, location, and views about its motions. Book IV turns to matters involving psychology and sensation, and Book V treats matters that fall under biology and medicine. For my purposes we may focus here on passages that concern the order of the heavenly spheres, and the shape and possible motions of Earth. In general, it is important to recognize that late antique authors noted the major disagreement between Platonists and Aristotelians about nature as a product of divine rationality and nature as an eternal and self-sufficient source of order. Scholastic Aristotelians, we may note, “Platonized” or “Christianized” Aristotle’s conception.71 Pseudo-Plutarch reports the opinions of Plato, Aristotle, the Stoics, and Epicurus on the natures of corporeal bodies. Plato is said to have

70 On the genuine author, Aëtius, see Daiber, Aetius Arabus, 1–2. Nobis and Schmeidler, citing Diels, in Zinner, Entstehung, 591, attribute the work to Theophrastus. They also refer to the 1516 editon as present in Frombork, evidently unaware of Valla’s translation from 1501. On Valla, see Heiberg, Beiträge, 385–390. On dialectic according to Valla, see Vasoli, “Nota,” 69–92. Cf. Gardenal, “Cronologia,” 93–97. 71 De placitis philosophorum I: 1; I: 36–39; and II: 3.

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regarded bodies as neither naturally heavy nor light absolutely but only relatively, that is, in relation to similar bodies and accordingly acquire heaviness or lightness. Aristotle held that earth is simply and absolutely heavy, fire simply and absolutely light, with air and water relative to earth and fire. The Stoics considered air and fire to be light, and earth and water to be heavy. What is light is carried from the middle, and what is heavy towards the middle. For Epicurus, all bodies are heavy and are moved by deflection, and of bodies that move upwards some move as the result of collisions, and others as the result of throwing.72 Pseudo-Plutarch also attributed to Aristotle the view that void can exist only outside the world (I, 18), a view that, as we saw in chapter four, some later scholastics adopted. Plato regarded place as a receptacle, and Aristotle as the extremity of the containing body (I, 19).73 In reporting views about the world and its shape, pseudo-Plutarch says nothing of Plato and Aristotle. Pythagoras was the first to refer to the universe as “world” on account of its order, for the Greek word kósmos means “order” and “world.” Thales and his followers were of the opinion that there is one world, whereas Democritus, Epicurus, and Metrodorus argued that there are infinite worlds. The Stoics adopted a distinction concerning “universe” and “whole.” The universe including void is infinite, but the world is separate from the void, so that “world” and “whole” are not identical.74

72

See De placitis I, 12, where I take “compulsio” for “collision,” and “repercussio” as referring to projectile motion. See Valla, De expetendis, f. sig. kk4v, lines 3–11: “Plato autem quod neque grave, neque leve suapte natura est cum suum tenet locum, at si in alieno sit, tum vim habere ad nutandum, ex nutu porro momentum fieri, vel in gravitatem, vel in levitatem. Aristoteles simpliciter terram esse gravissimam, tam aquam, ut levissimum ignem et aerem alias aliter. Stoici ex elementis quatuor bina levia ignem et aerem, reliqua duo, aquam et terram gravia. Leve siquidem est quod natura suapte in suo non nutat medio si ab eo absit, quod autem ad medium grave. Grave non est medium. Epicurus autem incomprehensibilia ait esse corpora, esseque prima simplicia quae vero ex illis concretiones. Cuncta porro esse gravia, moverique individua, alia quidem ad perpendiculum, alia vero declinare, quaedam sursum versus moveri per complosionem, percussionemque, et per tremorem.” 73 Valla, f. sig. kk 4v, lines 37–39, corrects “Plutarch” here: “Aristoteles extra mundum dumtaxat esse inane ut caelum respiret, ut Plutarchus inquit, quod tamen nusquam meminimus dixisse Aristotelem, sed extra mundum dumtaxat nihil esse habere, namque vim igneam Aristotelem testatum perhibet, utcumque nunc satis non liqueat.” 74 Valla, f. sig. kk5r: Book 21 and Physiologiae secundus [De placitis II: 1 and 3]; lines 43–51: “De mundo. Cap. i. Pythagoras primus ob absolutissimam quae in ipso est seriem, universique compraehensionem mundum fertur appellasse. Thales et qui Thalem secuti sunt mundum unum esse. Democritus et Epicurus eiusque discipulus

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The Stoics, we are told, regard the world as a sphere, others as coneshaped, and still others that it has the shape of an egg, that is, oval (II: 2, 1).75 The order of the world addresses the primacy of the elements. Plato chose fire as the first element, next aether, then air, water, and finally earth. Sometimes he connected aether with fire. Aristotle posited aether as the first, for as the fifth body it is incapable of passivity. Then in order subject to their dispositions come fire, air, water, and earth. He assigned circular motions to the heavenly bodies, upward motion to the light and downward to the heavy (II: 7, 4–5). The Pythagoreans believed that there is void outside the world. Aristotle denied that a void exists (contrary to what we read earlier), and Plato also denied void either outside or inside the world (II: 9). Aristotle, we are told, regarded heaven as composed of the fifth body, fire, or a mixture of hot and cold (II: 11, 3).76 Some ancients regarded the stars as aetherial, others as fiery. Plato for the most part considered the stars to be of a fiery nature, but such that they receive parts of the remaining elements as if glued in place (II: 13, 6). The Stoics regarded the stars along with all heavenly bodies and Earth to be spherical. Plato ordered the planets from the stars down as follows: Saturn, Jupiter, Mars, Venus, Mercury, the Sun, and then the Moon. Some mathematicians followed Plato, but others placed the Sun in the middle, presumably meaning between Saturn, Jupiter, and Mars above with Venus, Mercury, and the Moon below (II: 15, 4–5).77 Metrodorus infinitos mundos in infinito in omnem circunstantiam. Empedocles solis conversionem mundi circumscriptionem idque eius finem. Seleucus mundum infinitum. Diogenes universitatem quidem infinitam mundum terminari. Stoici porro totum et universum interse differre volunt, quod totum quidem cum inani sit infinitum universum autem absque inani mundum, et perinde non esse idem totum et mundum.” The text seems garbled for the point seems to be that “universe” and “whole” are identical, and that “world” is separate from the whole, and so have I interpreted it. 75 See f. sig. kk5v [De placitis II: 2 (reverses II: 2 and 3)] lines 6–8: “De figura mundi. Cap. iii. Stoici globosum mundum, alii conicae figurae, alii ovi figurae, Epicurus nihil affirmat, contingere namque omnia et globosum esse et aliis figuris contineri.” 76 Perhaps these conflicting accounts of Aristotle’s views are the result of some garbling of the texts, or perhaps they reflect differing views among Aristotelians. Valla, however, notes such discrepancies: f. sig. kk5v [De placitis II: 2, 4–11]; “ De caelo quaesit eius essentia. Cap xi.” And lines 54–55: “Aristoteles ex quinto corpore igni, aut ex calidi frigidique mixtione, ut Plutarchus nos, tamen non ita.” 77 Valla, f. sig. kk6r [De placitis II: 12–20]; lines 23–31: “De ordine astrorum. Cap xv, . . . Plato post non vagarum positionem primum phaenonta quem Saturni sidus vocant. Secundo loco Phahethonta, Iovis. Tertio pyrohenta Martis. Quarto Luciferum, seu vesperuginem quem hesperum latine vesperum versa aspirationis nota indigamma

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As for their motions, Plato and the mathematicians assigned the same period to the Sun, Venus, and Mercury, that is, once a year through the zodiac (II: 16, 4). Pseudo-Plutarch also suggested that while Aristotle made a complete distinction between celestial and terrestrial bodies with the stars lacking nothing, Plato and the Stoics thought that their illumination entails that the stars get their “fuel” from themselves (II: 17, 3–4). The Sun has a fiery nature, according to Plato, but is an aetherial sphere, according to Aristotle (II: 20, 4 and 6).78 Philolaus the Pythagorean described the Sun as a glass-like disk that receives the resplendence of earthly fire and returns it as light to us. The Sun has three features: heavenly fire, its resplendence and the reflecting mirror, and rays that are dispersed across our Earth by the reflection from its mirror. We call that reflection the “Sun,” as the reflection of a reflection (II: 20, 7). As for the Moon, the Stoics said that it is a mixture of fire and air. Plato thought its essence derives from an abundance of fire.79 There were a variety of explanations of eclipses, but the prevailing view was that the Moon and Earth do not produce their own light and hence can block the light of the Sun. Some concluded that Earth shines just as the Moon does (II: 25–31). Finally, the periods of revolution were determined to be thirty years for Saturn, twelve for Jupiter, two for Mars, twelve months for the Sun, Venus, and Mercury, and thirty days for the Moon (II: 32).80

aeolicum, Veneris. Quinto loco stilbonta Mercurii. Sexto Solem. Septimo Lunam. Mathematicorum quidam ut Plato, plurimi vero omnium medium Solem. Anaximander et Metrodorus chius et Crates supremum omnium solem, post ipsum Lunam, sub quibus non vagantes et vagas posuere stellas.” 78 Valla, f. sig. kk6r: lines 31–35: “Cap. xvi, De astrorum ambulatu motuque. Cap. xvi . . . Plato et mathematici cursus esse aequalis solem, Luciferum et stilbonta quem Mercurium diximus appellari.” And lines 36–39: “Unde lumen stellae habeant. Cap. xvii . . . Aristoteles caelestia ait nutrimentis neutiquam egere, quod minime corruptibilia sint, verum sempiterna. Plato et Stoici ut universum mundum in astra persese nutriri.” 79 Valla, f. sig. kk6v, lines 28–31: “De Lunae essentia. Cap. xx . . . Stoici mixtionem ex igni aereque. Plato ex copia igni abundante.” It is not clear that Valla understood that Plato regarded the Moon as Earth-like, according to pseudo-Plutarch, although the element fire belongs properly to the sublunar world. 80 See Valla, f. sig. kk7r, lines 4–6: “De anno quotus cuiuslibet planetae magnus sit annus. Cap. xxxii . . . Annus Saturni quidem annorum ambitus triginta, Iovis autem duodecim, Martis duorum, Solis duodecim mensium, iidem Mercurii et Veneris cursus namque perhibentur aequalis.” In Commentariolus, Copernicus evidently did not notice the discrepancy with the earlier figure of twenty-nine months for Mars, i.e. two years and five months, the number that Copernicus got from Valla, Book XVI,

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Most, but not all, judged Earth to be spherical and located at the center of the universe (III: 10–11). Philolaus the Pythagorean placed fire at the center, positing an Earth and an anti-Earth, assigning to it an orbit around the fire in the manner of the Sun and Moon (III: 11 and 13).81 These are the sorts of authors and notions that Copernicus would have found in De placitis philosophorum, most of which he could have obtained from Valla’s paraphrase; however, some of Copernicus’s quotations and comments show that he consulted the Greek original. Edward Rosen speculated that Copernicus may have noticed the comment in Plutarch’s De facie quae in orbe lunae apparet, namely, that Aristarchus of Samos was accused of impiety for having proposed the annual orbit of an axially rotating Earth around the Sun.82 Valla’s

f. sig. bb7v, lines 6–18: “Cum autem / non errantium syderum numerum esse conveniat infinitum, quae errantes dicuntur sint ne plures quae sub / visum non cadant in certum, septem certe in nostram devenere cognitionem, quorum altissimus quidem / esse videtur phoenon Saturni stella vocitata a quibusdam nemeos triginta ferme annis cursum suum confi/ciens, sub hoc est Iovis, quae etiam phahethontis dicitur, ab aliis osiridis intra xii annos suum peragens cur/sum. Tertio loco pyrois quae Martis est stella, quam herculis quidam vocant minus ordinatum videtur aliis habere motum, quod ubi illae stellae unam stationem faciunt et regressum. Mars duplicem faciat, hic duobus / annis et quinque mensibus suum orbem conficit. Martem Sol sequitur, quem persae Mithram vocant annuus / eius est motus cuius motu dies et horae deprehenduntur. Solem Venus sequitur eiusdem ferme cursus antecedens solem phosphorus, latine lucifer, solem occidentem sequens hesperus, latine vesperugo nominatur, sunt quae hanc Iunonis stellam vocent, sub Venere est stilbon quae Apollinis a quibusdam dicitur. Mercurii sacrum vocari etiam tradit Aristoteles cursus fere idem qui et veneris. Ultimo loco Luna quae quod evidentissime lumen a sole admittat a lumine luna dicta a latinis, a graecis selaene.” Notice as well that from this text Copernicus could have gotten the Greek phosphorus as the name for Mercury. Compare Knox, 404, note 23. 81 Valla, f. sig. kk7v, lines 50–55: “De motu terrae. Cap. xlv . . . Quidam ac fere omnes stare terram volunt. Philolaus autem pythagoreus circa ignem circumferri per obliquum circulum simili modo quo Sol et Luna. Heraclides ponticus et Ecphantus pythagoreus terram quidem movent, nec tamen transitive at rotae modo revolutam ab occasu inortum circa suum centrum a principio quidem vagatam terram ait Democritus ob exiguitatem levitatemque, condensuisse porro longo post tempore et gravatam constitisse.” 82 Rosen, Revolutions, Commentary, 360–361. Rosen’s note is convoluted. He first notes (25) in commenting on a passage from the manuscript deleted from the first four editions of De revolutionibus that prior to the recovery of the autograph, Copernicus’s acquaintance with Aristarchus of Samos was unknown. Next, Rosen cites a passage from Valla’s De expetendis XXI: 24 that mistranslates pseudo-Plutarch’s statement about Aristarchus’s placement of the Sun, which may have been reason enough, Rosen adds, for Copernicus to delete any reference to Aristarchus. Then comes the speculation about Plutarch’s De facie. At this point Rosen says: “If Copernicus noticed this statement on page 932 of Plutarch’s Opuscula LXXXXII, from page 328 of which he excerpted the Greek passage in his Preface, he may have decided to dissociate

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huge book does not contain a translation of this treatise, hence Copernicus would have had to consult a Greek edition. Fritz Krafft has argued more extensively that De facie was Copernicus’s source for some features of his account of gravity.83 Rosen’s suggestion and Krafft’s argument prompt me to consider what else he may have read in that dialogue. Before we do so, however, we must proceed cautiously and consider other Greek works that Copernicus evidently consulted. Dilwyn Knox has produced evidence that Copernicus relied on the Greek edition of De placitis philosophorum for one comment, because its details show that he could not have relied exclusively on Valla’s translation.84 Copernicus quoted a Greek passage from De placitis in the Preface to De revolutionibus. Of course, he may have read the Greek and Latin texts in parallel, checking the one against the other. Knox also argues, however, that Copernicus may have consulted the Suidae lexicon, claiming that some of Copernicus’s annotations in his own Greek-Latin lexicon appear to derive from the Suda, and, Knox believes, that Copernicus may have read some entries that influenced his doctrine of the elements and their motions.85

himself from Aristarchus.” What Rosen is referring to we can find on 342 of his commentary, clarifying 5, line 1, a quotation from Plutarch that Copernicus cited in Greek. Rosen explains that the Greek text was printed for the first time at Venice in 1509, and that Copernicus must have had access to it because he quoted the passage on 328 from that edition. As Rosen adds, the edition “omits two key words (alla treptikos), which were omitted by Copernicus too.” Finally, Johannes Kepler, Optics, also refers to Plutarch, and notes a parallel to Copernicus, but he does not say that Copernicus consulted Plutarch. See 267: “Therefore, the peripatetics should stop being angry at Plutarch because he dragged the earth up into the heavens, that is, gave it out that the moon’s body is earthlike, when they see it established by the most reliable experience that in the sharing of light, such as in fact the moon acquires shall have come from this our earth. But finally, where Plutarch, where Maestlin, shall have been received with unprejudiced ears, then Aristarchus, with his disciple Copernicus, may well begin to hope.” 83 Krafft, “Copernicus Retroversus II,” 65–78, esp. 69–71. 84 On the other hand, as pointed out above, Copernicus may have gotten the name for Mercury from Book XVI, not pseudo-Plutarch, and that is where Copernicus evidently got his figure for the period of Mars, namely, twenty-nine months. Incidentally, Rosen, Commentariolus, note 48, cites the incorrect folio number. The correct number is bb7v. Of course, the reference to phosphorus still does not explain Copernicus’s attribution of these names to Plato in Timaeus. 85 As we noted, the copies of Suidae lexicon at Uppsala, however, are not from Poland, and the Frombork and Lidzbark catalogs do not specify that particular dictionary. See Knox, “Ficino, Copernicus,” 333–366; and Knox, “Ficino and Copernicus,” 415–418. In correspondence, Knox has pointed out cases where Copernicus apparently corrected Crastonus’s dictionary by consulting the Suda. I should note, at

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As for Plutarch’s Moralia, also referred to as Opuscula, we do not know of any Greek edition at Lidzbark or Frombork.86 Now, Edward Rosen’s comment does not mean that Copernicus read De facie in its entirety. He could be interpreted to mean that Copernicus looked through it, perhaps searching for proper names, and noting only select passages. He evidently quoted a passage in Greek from De placitis, perhaps relying on Valla’s translation to guide him, but was he competent enough in Greek to read Plutarch’s dialogue without Valla’s translation to guide him? We cannot answer that question confidently. He could not have read it any earlier than 1509. Nevertheless, on the possibility that he may have read De facie, I summarize its content and some of its more stimulating ideas in Appendix V.87 Had Copernicus read this dialogue, he clearly would have found much of interest in it. Aside from the comment about Aristarchus, however, the provocative nature of its comments alone would have discouraged him from citing it explicitly. If he did know it, we cannot say that he used it for the composition of Commentariolus, for Copernicus avoids details of natural philosophy in that text. Valla’s translations and summaries of ancient authorities also showed the influence of later developments, especially in his reliance on scholastic authors for his summary of Aristotelianism. Although later much maligned, Valla’s book represented an encyclopedia of all knowledge. Copernicus may also have been familiar with some of his other translations published in 1498 before Valla’s death.88

his request, that he is cautious about his claims, and modest about his discoveries, but I find the evidence persuasive. See Knox, “Copernicus’s Doctrine.” 86 Brachvogel, “Bibliothek,” 329; Collijn, Inkunabeln . . . zu Uppsala, 318. 87 Knox, “Copernicus’s Doctrine,” provides a detailed summary and critique, concluding that Krafft’s case is flawed. Knox’s critique is persuasive. 88 Rosen, Revolutions, Commentary, 368, pointed to a correction that Copernicus made that may have been based in part on the edition of 1498. This speculation is not very persuasive, and there is a similar passage in De placitis, neither of which is sufficient to explain Copernicus’s correction. See Schmeidler, Kommentar, 145, who says that the source is not known. Cf. Knox, “Ficino and Copernicus,” 404–405, where Knox suggests the original Greek text.

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6. Pliny’s Natural History and other Ancient Authorities Copernicus annotated a copy of Pliny’s Naturalis historia that belonged originally to Caspar Salionis Cervimontani. Ludwik Birkenmajer concluded that Caspar came from Jelenia Góra (Hirschberg in German) in Silesia, but conceded that Caspar’s identity is uncertain.89 The copy belonged to the chapter library in Frombork, and several of the annotations in it are unquestionably Copernican. Copernicus read, used, and cited Pliny’s book throughout his lifetime, both for astronomical matters and other matters concerned with meteorological and medical topics. He even borrowed expressions and phrases from it. That said, I acknowledge that it is difficult to evaluate its significance for the development of his thought, or even its utility in helping him to construct his arguments. It was a source for some of his “facts,” and as such must we consider its importance.90 For Copernicus in particular the book contributed to his effort to establish accurate observations and resolve problems of nomenclature and classification. As several commentators, editors, and translators of De revolutionibus have pointed out, Copernicus borrowed several expressions and notions from Pliny’s book.91 For example, Copernicus’s talk of the whole universe as “resembling the infinite” in I, 12 comes from Natural History II, I, 2.92 89 Birkenmajer, Kopernik, 567–568. The location is supported by Grässe, Orbis latinus, 89. Birkenmajer speculated that Caspar might have been the Caspar of Hirschberg contained in the records of Cracow University. 90 The number of annotations varies, depending on what one counts as an annotation. Sometimes scholars include underlining or marks in the margins. I have included only words or comments, all in the margins. There are about sixty annotations in the 1487 edition. Of these, twenty-one are definitely in Copernicus’s hand, two are definitely not his, and the remainder must be classified among the doubtful. The authentic annotations are scattered throughout the book. Dilwyn Knox may undertake a more systematic analysis of Pliny’s influence on Copernicus, which will probably necessitate a re-evaluation, but my immediate concern is with Copernicus’s argumentative strategies. For commentary and interpretation, see Naturalis historia; and Naas, Projet. 91 Blair, Theater, 68, characterizes Pliny’s book appropriately as following “a pattern that resembles a topically driven method of commonplaces.” It seems that Copernicus used it as a source of commonplaces. 92 The passage was in the manuscript, and the Warsaw edition restored the text. See De revolutionibus I, 12, Opera, 2: 24, lines 27–31. In Gesamtausgabe 2: 490, 5–8: “Vae ex philosophia naturali ad institutionem nostram necessaria videbantur tamquam principia et hypotheses. Mundum videlicet sphaericum, immensum, similem infinito. Stellarum quoque fixarum sphaeram omnia continentem immobilem esse.

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Copernicus’s claim that natural philosophers have not achieved consensus on the extent of the universe in I, 8 echoes Pliny’s about inquiries into what is outside the world in II, I, 3–4. Pliny in II, VI, 32–35 confirmed Copernicus’s views about the ordering and periods of the superior planets, and Pliny is an example of an ancient author who placed Venus and Mercury below the Sun (II, VI, 36–40).93 Pliny may also have been one of Copernicus’s sources for the teleological definition of gravity, namely, the notion of gravity as a natural appetite or desire implanted in the parts so that they would join themselves into unified wholes in the form of a globe.94 We will examine some of these more substantive issues in chapters nine and ten. On the basis of annotations, comments, and the like, scholars have assumed that Copernicus also had access to works by Cicero, Macrobius, and Vitruvius. He annotated Ptolemy’s Geography, and either read Martianus Capella’s De nuptiis philologiae et Mercurii (in the 1499 edition from Vicenza or the 1500 edition from Mantua) or relied on some description of its geo-heliocentric account of Mercury and Venus.95 In Part III of this study we examine his knowledge of Aristotle in detail, noting here that we have discussed in chapter four standard scholastic commentaries that Copernicus would have heard as a student in Cracow. 7. Achillini Of the books we consider in detail, I turn now to a work by a professor teaching at Bologna while Copernicus studied there. Alessandro Achillini was an Averroist Aristotelian who attacked Ptolemaic

Caeterorum vero corporum caelestium motum circularem, sumatim recensuimus.” (Italics added). In Revolutions, Rosen placed the text in I: 11, 26, lines 37–42. 93 See Rosen’s index in his commentary to Revolutions for references to Pliny. 94 De revolutionibus I, 9; Pliny, Natural History II: 2. I owe this observation to Knox, “Copernicus’s Doctrine,” 189–193. 95 Goddu, “Annotations,” 204–206 and 222, identifies the correct copy of Ptolemy’s Geography in Uppsala, now catalogued as Copernicana 45. Copernicus’s annotations indicate that he used it, but it does not appear that it made an obvious contribution to arguments, although they explain why he was circumspect in his comments about the circumference of the world based on ancient calculations. The facts that he cites are used to support the conclusion about Earth’s sphericity, obviously an important fact related to its capacity for circular motion. On Martianus Capella, see Rosen, Commentariolus, n. 327; and Birkenmajer, Kopernik, 24. 267, 339, 560, and 565. One possible source is Macrobius, In somnium Scipionis I, 19.

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models, and argued for a strictly concentric astronomy. It is possible that Copernicus may have known him and his work De orbibus libri quattuor (1498). I summarize its contents briefly, noting passages that might have influenced Copernicus because some scholars think that Copernicus must have attended his lectures and known his work. The summary also indicates my doubts about these conjectures.96 In the four books of De orbibus, Achillini treats the matter, form, composition, and accidents regarding the heavens, all in scholastic style with many citations of Aristotle and Averroes. Book I considers three principal questions, whether there is matter in heaven, whether a star is specifically different from its orb, and whether there are eccentrics and epicycles. Book II treats intelligences and whether they undergo change. Book III asks whether heaven takes its being from intelligence, whether it undergoes change, whether it is actually finite in extent, and whether there is only one heaven. Book IV asks about the sphericity of heaven, whether it is essentially luminous, whether its motion is eternal and natural, and about what effects the celestial motions have on inferior bodies. Before we look at some details, we should observe the difficulty of distinguishing arguments that can be attributed specifically to Achillini from the views found in Averroes. In other words, we would have to find some distinctive expressions in Achillini that Copernicus echoes to conclude that he influenced Copernicus. My summary is selective, as it must be, focusing on the objections to eccentric and epicycle models, and selecting other passages that might have influenced Copernicus. The first objection to eccentrics is that the world has a unique center.97 The emphasis on this point is contradicted

96 Di Bono, Sfere, 62–64; idem, “Copernicus,” 153, n. 72, where he asserts that Copernicus “would have had to follow the lessons of Alessandro Achillini,” citing F. Barone’s edition of Copernicus’s Opere (Turin, 1979). I have been unable to obtain this edition and evaluate Barone’s evidence. See also Barker, “Copernicus,” 349–350. Granada and Tessicini, 433–435, on the other hand, seem to be less persuaded, emphasizing the deficiencies of Achillini’s work in astronomy, citing di Bono, Sfere, in support. 97 Achillini, De orbibus (1498), Book I, Dubium tertium, f. 10ra–b, and the argument concludes thus: “Contra quos ponuntur hec conclusio. Nullum corpus caeleste est excentricum et est conclusio Averrois 12 Metaphysice commento 45: excentricum autem et epiziclum dicere est extra naturam epiziclum autem est impossibile, ut sit omnino et secundo Caeli commento 32. Ex hoc apparet quod dicunt mathematici de excentricis est impossibile idem commento 35 et in suo libro Almagesti. Item secundo Caeli commento 62. Motus quos ponit Ptolomeus fundantur super duo fundamenta que non conveniunt scientie naturali excentricum et epiziclum quorum utrumque est falsum.” Barker, “Copernicus,” 357, n. 25, cites a form of this text from the 1545 edition.

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directly by Copernicus in his first postulate from Commentariolus. Does his first postulate, then, mean that he was responding to Achillini or Averroes, or that he had already accepted the need for eccentric and epicycle models, and, consequently, recognized that the motions of the celestial bodies have multiple centers? We will analyze the postulates in Commentariolus in more detail in the next section, but suffice it here to say that Copernicus seems to reject concentric models out of hand. There is no indication that he ever took them as a serious candidate for restoring astronomy. He may have considered them seriously on mathematical grounds later when more technically competent attempts became available, but it rather appears that he formulated his first postulate to dismiss concentric theories because he had already accepted the need for eccentric and epicycle models, not because he was responding to Achillini.98 There is evidence in Achillini’s text that he knew about Novara’s observation of the declination of the arctic pole.99 Evidence that they knew one another or one another’s work does not prove Copernicus’s direct acquaintance with Achillini’s work, but could rather indicate that Novara informed Copernicus of Achillini’s views. Over the next few folios, Achillini attempts to defend Averroes’s speculation about spherical models that generate a gyrational or spiral motion, rejects explicitly the metaphor about the Sun as a king in the middle, and also rejects any suggestion that the motion of the heavens moves other bodies by force or violence.100 In this context he cites the opinions of Eudoxus and Callippus, and defends Averroes as another author who tried to preserve the principles of Aristotelian natural philosophy.101

98 Granada and Tessicini, 435, focus on Achillini with respect to Commentariolus, and argue that Copernicus recognized the existence only of eccentric-and-epicycle astronomy at that time. It is true that there was not yet a technically competent concentric rival, but Copernicus seems to have been prejudiced by the failure of the ancient versions. 99 De orbibus I, 3um, f. 12vb. Birkenmajer, Kopernik, 516, also cites the text. 100 De orbibus, ff. 13r–15v. Achillini cites Averroes’s De substantia orbis (f. 14v), and also indicates familiarity with De sphaera, f. 14vb: “Patet etiam motuum caelestium catenationem esse nobilissimam et naturalissimam sine corporeis ligamentis sine raptu sine violentia a principio vitali naturaliter ligante corpora mobilia et ea ex desiderio rationali movente.” The rejection of raptus might also indicate that he influenced Capuano da Manfredonia whose commentary on De sphaera appeared in 1499, or the dependence of both on Sacrobosco or Averroes’s De substantia orbis. 101 De orbibus, f. 16vb.

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The kinds of expressions that Achillini uses, however, are not so specific to him as to confirm a connection with Copernicus. In the concluding section of his arguments regarding eccentric and epicycle models (ff. 15v–19v), Achillini launches into a skeptical attack against the reliability altogether of the observational basis of Ptolemaic astronomy. Pointing out the inaccuracy of observations is one thing, but attacking the reliability of the tradition of observational astronomy altogether is another matter. He argues against judgments about distances in principle,102 and about variations in the speed of the Sun during the course of a year,103 referring to perceptual distortions, visual errors, imprecise instruments, atmospheric variables, the deception of the senses, the falsity of measurements of the bounded elongations of Mercury and Venus, and the illusory observation of retrograde motion.104 Recall that Brudzewo had refuted Averroes’s objections and affirmed the basic reliability of the observations on which eccentric and epicycle models are based.105 If Copernicus read or heard Achillini’s arguments, it is hard to imagine a reaction other than shock and dismay. Achillini was right, of course, that there are observational difficulties, and, (Copernicus would have agreed) that we need to account for the observations in a natural way, but Achillini’s point, following Averroes, is that the observations are not to be explained but rather explained away.106 Of course, Copernicus read authors whose views he 102 De orbibus, f. 17rb: “Sed distantia et propinquitas non est sensibile proprium. . . . Ideo iudicare de propinquitate vel remotione per sensum exteriorem in valde magnis distantiis quales sunt in proposito non est certum iudicium de distantiis neque de aliis.” 103 Ibid. f. 17rb: “Preterea solis motus velocitatis celeritatemque vix orde explicatur quisquam potest, et tamen sensibilem temporis partem aponit postquam se nobis manifestari caepit.” 104 Ibid. f. 17rb–18ra: “Propter quam non firmum est etiam mathematicorum iudicium de quantitate diametri solis sive per instrumentis capiatur sive per eclipses et earum quantitates. . . . Ad primam confirmationem concessum est corpora caelestia aliquando apparentur maiora, immo luna nova arcualiter illuminata respectu visus nostri aliquando apparent cornua exire partem lune obscuram, ideo necesse est sensum decipi in istis casibus. . . . Et dicamus solem suo motu regulari quartas zodiaci in equaliter pertransire absque excentrico aut epiziclo aut inequali eius distantia a polis proprie spaere.” 105 As mentioned in chapter five, Świeżawski, “Matériaux,” in documenting references to Averroes in Cracow sources of the late fifteenth and early sixteenth century enumerated 213 citations to Averroes by comparison with 161 to Giles of Rome and 128 to Thomas Aquinas, for example. 106 Ibid. f. 18rb–19ra: “Tertio principaliter arguitur planete aliquando sunt stationarii et aliquando directi aliquando retrogradi quod non est possible sine excentricis et epiziclis. . . . Tertio illa sunt ponenda que longo tempore et infallibiliter sunt observata sine quibus apparentia salvari non possunt, sed epizicli et excentrici sunt huiusmodi. . . . Ad tertium negatur quia apparentium alias causas reddidimus, neque astronomi

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rejected, and in the early 1520s took the trouble to defend Ptolemy’s observations at the request of a friend (Letter Against Werner), but there is no indication of a reaction to Achillini’s attack on the observational basis of astronomy. In Book IV, possibly another book that Copernicus consulted, Achillini returns to more cosmological questions that we can assume would have interested Copernicus. They concern questions about the nature of heavenly spheres and their movers. In fact, these are the sorts of discussions that may have contributed to Copernicus’s reluctance to address or answer questions about the nature of spheres, the causes of their motions, the finiteness of the universe, and the like. These are, perhaps, the discussions that he had in mind, which in De revolutionibus he characterizes as exercises in logic, yet when he makes that comment, he refers specifically to Aristotle.107 All of that said, and despite my skepticism, I also urge a careful reading of Achillini’s treatise, and more consideration of his possible influence on Copernicus, even if dialectical. Copernicus knew the Averroistic objections to Ptolemaic astronomy, and at this point in his career tended to dismiss concentric approaches without much reflection. It could be that Achillini’s diatribe prejudiced him against concentric hypotheses, but that would still leave us to explain his use of models in Commentariolus that appear to derive from mathematical solutions developed to address objections to Ptolemaic models. It is clear that Copernicus had available to him summaries and translations of the opinions of ancient authorities. There can be little doubt that these are the works that he scoured to find predecessors, alternative views, and even arguments that may have inspired him to formulate the geokinetic hypothesis. They provided him at the very least with arguments in support of the hypothesis once he formulated it. Some experts have inisisted that strictly astronomical and mathematical considerations led him to the heliocentric theory, but formulating the geokinetic hypothesis explicitly required a virtually simultaneous dialectical re-evaluation of geocentric assumptions.108 To the extent that we can separate these steps or moments, we maintain

excentricos aut epiziclos demonstrant aliquo genere demonstrationis secundo caeli commento 35 et 62, quia non a priori videlicet neque a posteriori.” 107 De revolutionibus I, 8. 108 The most important representative of the technical, mathematical route to heliocentrism, of course, is Swerdlow, “Derivation,” 423–511.

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that qualitative (not technical) mathematical issues led him to adopt heliocentrism with its geokinetic consequences. Those consequences, however, entailed a refutation or, at least, critical evaluation of geocentric principles. In other words, his major innovation was cosmological (heliocentric and geokinetic), for which only qualitative mathematical considerations sufficed. All of the above steps (astronomical, mathematical, heliocentric, and geokinetic) necessarily occurred before he wrote Commentariolus, but can we establish with any certainty exactly when he read which text for the first time, whether before Commentariolus or later before he composed Book I of De revolutionibus? 8. Commentariolus In this section I will argue that the date of the composition of his earliest work should be set in or around 1510, hardly a risky or original conclusion inasmuch as several experts have settled on that year as well. I offer further circumstantial evidence in support of that conclusion. I will further argue that Copernicus relied certainly not only on Regiomontanus’s Epitome but also Bessarion’s In calumniatorem, Valla’s De expetendis, and Pliny’s Natural History, and very probably on Part I of Ficino’s translation of Plato’s Works. He probably also used Part II, but we have no compelling reasons for thinking that his acquaintance with the dialogues in that part were indispensable for the writing of Commentariolus. We begin with a brief summary of Commentariolus. Copernicus began Commentariolus controversially with “petitiones” that he also called “axioms.” If we set aside the personal attacks by some commentators, the experts agree, even if inadvertently, that he did not mean the word “axiom” in the sense of self-evident principles but rather in the sense of assumptions or common notions.109 As Copernicus himself made abundantly clear, the rest follows only if the seven postulates or assumptions are granted him. It is evident that he arrived at these seven propositions by working his way back to them as the ones necessary and sufficient from which to derive the remaining propositions. In the version later owned by Tycho Brahe from which two other copies derive, Commentariolus is very brief, written on twelve folios, 109 Rosen, Commentariolus, 92; Swerdlow, “Derivation,” 437; and Schmeidler, “Leben,” 11–17, esp. 12. See Knorr, “Notes,” 203–211, for additional comments and reflections.

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recto and verso.110 We may think of it as a first or working draft—there is no evidence that Copernicus intended it for publication. Its character and style are similar to what we find in the Theorica literature, so perhaps he intended Commentariolus as his brief version of the more popular and less technical works like Peurbach’s Theoricae novae or Albert of Brudzewo’s Commentariolum, both of which could be used as texts in university instruction. There were evidently at least two copies, a fact that suggests that he distributed or had it distributed for comment. If it was to serve as an outline for a complete work intended to replace Ptolemy’s Almagest, he abandoned that notion by 1515.111 The publication of the Latin Almagest in 1515 made it possible for him to model the complete work on Ptolemy himself. His annotations in the copy of the 1515 edition that he used show that he spent a lot of time correcting it and trying to sort out the corruptions and confusions. It seems that this process went on for several decades, probably not completed until he received a copy of the Greek edition. The introduction of Commentariolus sets out a brief and sketchy history of the work of his predecessors. They assumed a large number of celestial spheres to account mainly for planetary motions by means of the principle of uniformity. Heavenly bodies that are perfectly spherical should move uniformly. By linking and combining uniform motions, they hoped to account for the apparent motions of the bodies.112 In a few lines Copernicus reports that Eudoxus and Callippus tried to construct an account by means of concentric circles, but such models

110 Rosen, Commentariolus, 75. See Goddu, “Reflections,” 37. See also Dobrzycki and Szczucki, “On the Transmission,” 25–28. 111 It was probably in 1515 that Copernicus made the relevant observation. See Birkenmajer, Kopernik, 78, on the observation of 1512 as setting the tempus ante quem, which would move the date up two years from the documented fact of its mention in the collection of Matthew of Miechów in 1514. Schmeidler, “Leben,” 12–14, seems to agree that observations begun in 1512 indicate that Commentariolus was completed, and that Copernicus was starting to work on the observations needed for the promised full-length study with demonstrations. See also Biskup, Regesta, 58, No. 76. But see Swerdlow, “Derivation,” 430, for a correction. I accept 1514 as the tempus ante quem for reasons stated below. 112 In summarizing and paraphrasing the text, I have consulted both the Rossmann Latin edition that was reprinted in Copernicus, Das neue Weltbild, and Prowe’s edition in Coppernicus, 2, but I followed Rosen’s translation except in cases noted. Zekl did not use Rosen’s emendations, but at this time the critical editions have yet to appear.

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failed, leading others to construct eccentric and epicycle models, the solution adopted by most scholars. The latter is the system associated principally, of course, with Ptolemy. His models were consistent with the numerical data, but a number of difficulties remained. The eccentric-epicycle models do not work without adding an equant model on which the planet (or center of the epicycle) moves with uniform velocity. But that means that the planet is not moving uniformly on the deferent sphere or on its own epicycle relative to the center of the epicycle, but to some other point. To Copernicus this adjustment was neither sufficiently absolute nor sufficiently pleasing to the mind.113 These defects, he says, led him often to consider a more reasonable arrangement of circles that would account for every apparent irregularity and that would move uniformly as required by the rule of perfect motion. It was a difficult and almost insoluble problem, but after some time (at length) he hit on a suggestion that could solve the problem by means of fewer and much more suitable constructions than those put forward by his predecessors if some “petitiones” were granted him. As we all know, Copernicus accepted, indeed, insisted on the ancient principles of uniform, circular motion. The equant model, he implies, was the first indication that something was seriously wrong. But how he got from that realization to his solution is hidden in the expression “at length.” How long? By means of what additional steps? What else or what other problems or difficulties did he recognize or encounter? Can we reconstruct those steps? We will work towards answers to those questions. Here are the “petitiones”:114 1. All of the celestial orbs or spheres do not have one unique center. (To anyone familiar with the inadequacy of concentric models and with the eccentric-epicycle models, this might appear to be self-evident, but some astronomers continued to pursue concentric solutions.)115

113

Commentariolus, Rosen tr., 81. Rosen translates “petitiones” as “postulates,” Zekl uses the German word “Forderung,” which connotes “claim.” Swerdlow also uses “postulate.” I have usually followed Rosen and Swerdlow here, but occasionally “claim” strikes me as the appropriate sense. 115 For example, concentrists and Paduan homocentrists, about whom more below. As we saw in chapters four and six, the first postulate was commonly held at Cracow, and it appears in the Epitome, but Copernicus was evidently the first to interpret it 114

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2. The center of Earth is the center of gravity and of the lunar sphere; it is not the center of the universe. (Ptolemaic astronomers adopted a physical system of spheres or orbs in which eccentric-epicycle models were embedded, and thereby constructed a compromise that seemed to preserve both eccentrics and Earth as the center of each of the total spheres and the center of the starry vault.) 3. All of the spheres go around the Sun, which is near the center of the universe and, hence, is in the middle of them all. (This does not contradict postulate 1, but it seems little more than a solar version of the geocentric compromise rejected in postulate 2.) 4. The distance between Earth and Sun is imperceptible in relation to the distance between Earth-Sun and the stars. (It is as if the distance between Earth and Sun were reduced to a point in relation to their distances from the stars. The absence of stellar parallax is a result of this relatively small distance between Earth and Sun.) 5. Earth’s daily axial rotation causes the observed apparent daily motions of the stars, thus leaving the stars immovable. 6. Likewise, the motion of Earth on its sphere around the Sun causes the observed apparent annual motion of the Sun. (A sphere moves Earth annually around the Sun, hence Earth has more than one motion. Copernicus is not explicit here about a third motion of Earth.) 7. Earth’s orbital motion causes the observed apparent retrograde motions of the planets. The motions of the planets, then, are always direct. The motion of Earth suffices to explain many apparent irregularities in the heavens. (Note that Copernicus is not explicit here about the bounded elongations of Mercury or Venus, or about the ordering of the planets according to sidereal periods.) From these postulates, Copernicus proposes to show to what extent the uniformity of the motions can be saved in a systematic way. The mathematical demonstrations will appear in the larger work that he plans to write. Here the lengths of spherical radii or semidiameters will suffice to indicate to competent mathematicians how well his arrangement of circles agrees with the numerical data and observations.

as an assumption that together with other assumptions leads to the conclusion that Earth orbits the Sun.

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He distinguishes his effort from that of the Pythagoreans because their assertions about the motion of Earth are not based on mathematical considerations but rather belong to natural philosophy. Natural philosophers, however, base their conclusions about Earth’s immobility for the most part on appearances. But if Earth’s immobility is caused by an appearance, Copernicus implies, only a mathematical analysis can reveal the cause. Notice here that Copernicus is aware from the start that he must refute geocentric assumptions. He does not, however, say that the mathematical analysis has to be technically detailed; indeed in Commentariolus, the mathematics is of a more qualitative nature, relying primarily on estimates of orbital radii. Then follows without further preparation his announcement of the order of the spheres, beginning with the outermost sphere of the fixed stars. In providing the ordering according to sidereal periods, Copernicus supplies a number for Mars that he took evidently from Valla’s De expetendis XVI, 1.116 In the following section on the apparent motion of the Sun another notable peculiarity is Copernicus’s restriction of axial rotation to Earth alone. The spherical nature of other bodies did not lead Copernicus to ascribe an axial rotation to them, probably because he had no observational evidence of such rotations. As spheres they would be capable of axial rotation; however, as Copernicus’s training in logic had taught him, “a posse ad esse non valet consequentia,” that is, an inference from possibility to actuality is invalid. As is well known, Copernicus concluded that Earth has three motions, motivated by his aim to show which apparent celestial motions can be replaced by motions of Earth. As for the apparent motion of the Sun and fixed stars, the Sun’s annual motion, the universe’s daily rotation, and precession of the equinoxes can be replaced by respectively three motions of Earth.117 Then Copernicus notes explicitly for the first time disagreements in measurements and observations, namely, for the length of the tropical year based on the interval from vernal equinox to vernal equinox. The variation based on reliable observations leads inevitably to error.118 As

116 Rosen, Commentariolus, 94, n. 48. The exact reference in Valla, contrary to Rosen, is f. sig. bb7v, lines 12–13. 117 Rosen, notes, nn. 38, 56, 66, and 83. 118 In other words, because the different observations are reliable, the differences are not due to faulty observations. This is the sort of statement that supports my suggestion that Achillini’s skeptical critique of observations would have appalled him.

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a result of differences and what Copernicus believed to be a variability in the precession of the equinoxes, he proposed a derivation of the solar year from the fixed stars as more accurate, that is, the sidereal year as opposed to the tropical year.119 Finally in this section, Copernicus asserts that the apsides maintain a constant position among the stars. This claim will lead him to propose models that he later abandoned after he realized, probably around 1515, that the apsides move relative to the stars.120 For the Moon, Copernicus describes a double-epicycle model as “truer” than Ptolemy’s in accounting both for its non-uniform motion and its variations in distance. Copernicus’s first objection to Ptolemy’s theory was that the Moon’s epicycle center moved uniformly relative to Earth but non-uniformly relative to the eccentric’s center.121 Regiomontanus pointed out the problem with the variation in distance resulting from Ptolemy’s model in Epitome V, 25.122 The three outer planets have similar models, that is, double-epicycle models on a concentric deferent. Their spheres enclose the sphere on which Earth moves with its Moon. Copernicus implies that the observation of their retrograde motions is an optical illusion caused by the motion of Earth relative to the motions of the outer planets, the fourth appearance explained by one of Earth’s motions.123 Furthermore, their retrograde arcs increase in size according to their nearness to Earth. Accordingly, the arcs for Saturn are the smallest, and the arcs for Mars the largest.124 In accounting for variations in latitude, Copernicus says that the Earth’s motion “causes” the apparent latitudes to change for us. He imagines an oscillating motion along a straight line, a motion that can be produced by a combination of two spheres.125 119 Several attributions show that Copernicus relied on Epitome III: 2 for an incorrect statement, although Copernicus seems to have misread or misinterpreted Regiomontanus in part. See Rosen, Commentariolus, n. 93. 120 On the observation and the calculation, see Biskup, Regesta, 65, No. 98; p. 66, No. 102 (a calculation made in 1516); and Swerdlow, “Derivation,” 430. See also Rosen, Commentariolus, n. 110. See Birkenmajer, Kopernik, 78, for the emphasis on the observation of 1512; compare Schmeidler, “Leben,” 12–14. See also Goddu, “Reflections,” 47, n. 6. 121 Rosen, Commentariolus, n. 136; and Swerdlow, “Derivation,” 461. 122 Albert of Brudzewo, Commentariolum, 54–56 and 67–69, points out other defects in Ptolemy’s lunar model, but not this one. See also Rosen, Commentariolus, n. 140. 123 Rosen, Commentariolus, n. 192. 124 Copernicus expresses these numbers in terms of the ratio of the great orb’s semidiameter to the semidiameters of the respective planetary spheres. 125 See Rosen, Commentariolus, n. 233, on the so-called Tusi couple.

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Finally on the superior planets, Copernicus compared the sizes of a planetary sphere to the fixed length of the great orb’s eccentricity, twenty-five units.126 If Copernicus thought that the epicycles are also spheres, then it is apparent that spheres do penetrate one another, for the secondary epicycle penetrates the space occupied by the primary epicycle, and the primary epicycle penetrates the space occupied by the deferent sphere. Of course, if Copernicus regarded the spheres as the spaces in which epicycles move, then we must suppose that the epicycles represent only circles on which planets move with these circles somehow “attached” to or “embedded” in the sphere.127 Before attempting solutions to numerous textual and historical problems, we complete the essential parts of the summary. Copernicus’s description of the motions of Venus, unaccompanied as it is by either figures or geometrical demonstrations, is challenging. For our purposes, we may merely note that he accounts for its bounded elongation and its retrograde motion as appearances caused by Earth’s motion on its great orb outside of Venus’s orb. Again he resorts to a double-epicycle model to account for motion in longitude.128 Similar to the outer planets, he resorts again to an oscillating motion along a straight line as produced by a combination of two concentric spheres with oblique axes to account for its motion in latitude.129 Mercury poses the most serious problems for a mathematical astronomer. Copernicus proposes another double-epicycle on a concentric deferent, but difficulties arise in accounting for motions both 126 Rosen, Commentariolus, n. 169. Cf. Swerdlow, “Derivation,” 426–429; idem, “Summary,” 201–213, esp. 203 for the explanation of Copernicus’s rounding off the solar eccentricity of 26;28 to 25 units. The references are to the “Uppsala Notes,” for which see Czartoryski, “Library,” 366, item 2c. The “Uppsala Notes” are in Copernicana 4, Uppsala University Library, folios 270r-285v, esp. fol. 284v (fol. 15v of the “Notes” themselves). The notes are sometimes foliated separately with the folio in question numbered 15v, but in the codex it is folio 284v, as one can plainly see in the photograph. A detailed analysis with plates and tables appears below. 127 Compare Rosen, Commentariolus, nn. 172 and 174; Swerdlow, “Derivation,” 470– 478. See also Rosen, n. 200, where Rosen shows dependence on Pliny’s Natural History II: 59. Rosen questions whether Copernicus had yet read or studied Epitome XII: 1–2. See Swerdlow, who claims that the proposition dealing with an eccentric model for the second anomaly leads to the heliocentric theory. Compare Goldstein, “Copernicus and the Origin,” 221–222; Goddu, “Reflections,” 39–41; see also Rosen’s very long note 200, esp. p. 113. Apollonius’s theorem is the issue here, namely, a method that determines the stations and the length of the retrograde arc between them by the planets’ moving either on an epicycle or on an eccentric. The details appear below. 128 In De revolutionibus V, 20–25, he will replace these with an eccentreccentric. 129 Rosen, Commentariolus, 88 and n. 274.

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in longitude and latitude. Unlike the other four planets Copernicus here resorts to an oscillating motion by two small interlocking spheres to account for the planet’s approach and withdrawal in longitude. Similarly, its deviation in latitude also requires a combination of two concentric spheres with oblique axes. Commentariolus concludes with an enumeration of the circles sufficient “to explain the entire structure of the universe and the entire ballet of the planets.”130 Some questions will be reserved for later chapters, that is, technical philosophical details are left to Part III, where I will treat Copernicus as logician, natural philosopher, and mathematical cosmologist. Through enormous industry, and often with brilliant insights, previous scholars have laid the groundwork for what follows. My effort to reconstruct Copernicus’s path to the heliocentric theory in this section identifies the assumptions and establishes the conclusions that Copernicus would later strengthen with the arguments presented in De revolutionibus. Where there is substantive overlap between Commentariolus and De revolutionibus we may assume that the fundamental principles were already at hand as he wrote Commentariolus.131 Here I focus on Copernicus’s sources to try to reconstruct his steps to the heliocentric theory in its first form. Part of this discussion requires engagement with the secondary literature. I hope thereby to produce the likeliest account of the following issues—the method by which he arrived at his postulates, the decision to adopt double-epicycle models, the source of his models to account for planetary oscillations, and the year in which he completed his draft. Scholars have provided evidence that for the composition of Commentariolus Copernicus used the Epitome of Regiomontanus, Giorgio Valla’s De expetendis, the Almanach perpetuum of Alfonso de Corduba Hispalensis, the so-called “Uppsala Notes,” Cicero’s De natura deorum, Pliny’s Natural History, and Martianus Capella’s De nuptiis philologiae et Mercurii.132 To these I propose to add Plato’s Parmenides. There are apparently additional sources that no one has yet identified or found.

130

Rosen, Commentariolus, 90, and nn. 319–324. The question of “solid” spheres is treated in chapter ten, as well as questions about the reality of spheres, orbs, and circles. 132 Goldstein, “ Copernicus and the Origin,” 223–231, also considers Aristotle’s De caelo, Averroes’s commentary, Proclus (in Valla), and Vitruvius. See also Rosen, Commentariolus, nn. 326–327. On Cicero and Pliny, see Knox, “Copernicus’s Doctrine of 131

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It is, of course, possible, even plausible, that Copernicus arrived at his postulates last. That is to say, once he decided what he wanted to “prove” or “demonstrate,” he worked his way back from conclusions to the postulates that he would need to make the derivations work. Even though Copernicus does not provide precise mathematical demonstrations in this work, the conclusions and what details he supplies must follow from his assumptions. If we accept this, however, then that shifts the question to how he arrived at the conclusions. Copernicus himself tells us generally how, and it is in its essentials the same explanation he provides later in the Preface to De revolutionibus. In Commentariolus he tells us that he accepted the ancient assumption that the motions of the heavenly bodies are to be accounted for by using spheres that move uniformly. As anomalies arose, combinations of circles were introduced and became more complicated, and finally circles were postulated that violated the principle of uniform motion relative to its deferent sphere and even its own epicycle center. As a consequence, he began to search for a more reasonable arrangement of circles that would account for every apparent irregularity without violating the principle of uniform motion with respect to a sphere’s or circle’s proper center. At this point, his account becomes vague, informing us that somehow he hit on models that worked better, provided one accepted his seven postulates. He adopted one fundamental assumption as self-evident—uniform circular motion of perfectly spherical celestial bodies. From that point on, he describes a dialectical process, the stages of which he learned as a student and that Plato’s Parmenides reinforced and guided at least in one crucial respect. For there Copernicus encountered the advice to “test” every relevant hypothesis both affirmatively and negatively. The “self-evident” assumption was adopted because its contradictory was deemed absurd. He compared uniform motion and non-uniform motion; circular motion and non-circular motion; concentric models and eccentric models; eccentric models with epicycle models, concentric models with double-epicycle models, and eccentric with epicycle and equant models; geocentric and heliocentric models; geostatic and geokinetic models.

Gravity,” 189–193. I also think it likely that Bessarion’s In calumniatorem Platonis inspired Copernicus to appreciate Plato’s dialectical method of inquiry.

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By a series of questions he was led to his postulates. Here I arrange the questions in the order corresponding to the postulates. Do the celestial spheres have one center or many centers? If many, then Earth cannot be the center of the universe but only of gravity and of the lunar sphere. Why are the models for all planetary spheres related to the position of the Sun? If their motions are relative to the Sun, then let us suppose that the planetary spheres encircle the Sun approximately in the middle of their motions. If Earth’s distance from the Sun is very small in comparison to the Sun’s distance from the stars, then could we perceive Earth’s motion relative to the Sun or the stars? If not, then which motions are merely apparent and due to Earth’s motions, and which are the proper motions of the spheres? Do the stars and the entire universe rotate once a day around Earth east to west, or does Earth rotate on its axis west to east? Does the Sun orbit Earth once a year or does Earth orbit the Sun once a year? Do the planets really move backwards and then forwards, or does Earth’s orbital motion account for these apparent irregularities? The conclusions that natural philosophers reach about the immobility of Earth rest on appearances, but Earth’s immobility is itself an appearance. When confronted with two appearances that contradict one another, by what principles, standard, or criterion shall we remove the contradiction? We have seen that the assumption of geocentrism has led to the violation of uniform motion relative to the deferent center and epicycle center, and accounted for irregularities in motions and distances by resorting to non-uniform motions. By means of his seven postulates, Copernicus claims that he can account for every apparent irregularity while keeping everything else moving uniformly. Above all he can determine the order of the spheres between the fixed stars at the periphery and the stationary Sun near the center according to sidereal periods with the Moon orbiting Earth between the spheres of Mars and Venus.133

133 Now, an objective reader would have legitimate objections about the claimed uniform circular motions. Copernicus’s resort to an oscillatory motion introduces rectilinear motions into the heavens, and he has made the terrestrial celestial. But compare with Rheticus, Narratio prima, Rosen tr., 130 and 138, who also emphasizes Copernicus’s achievement as establishing the perpetual and consistent connection and harmony of celestial phenomena, and that the order and motions of heavenly spheres agree in an absolute system.

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Noel Swerdlow’s critique of the postulates and their ordering is persuasive.134 I conclude that their order does not correspond to the dialectical process by means of which Copernicus arrived at the heliocentric cosmology. I have reconstructed the stages elsewhere;135 here I reformulate them as a series of questions that correspond to his reflections in De revolutionibus I, 4, conclusions in I, 10, and criticisms of predecessors in the Commentariolus and the Preface to De revolutionibus. Both texts have the following in common: acceptance of the axiom of uniform motion, rejection of the equant model as a violation of the axiom, and the recognition that each of the heavenly motions has a proper center. That is to say, taken singly the heavenly motions do not have a single center. Taken together, however, the heavenly spheres rotate around one center. In following the Platonic advice to examine dichotomies, Copernicus in his statements suggests that the following questions led him to propose the motions of Earth. 1. Why are the planetary spheres ordered around Earth according to two different principles—sidereal periods for Mars, Jupiter, and Saturn; a zodiacal period of one year for Mercury and Venus? Should not the heavenly spheres rotate around one common center according to one common principle? 2. Why do some authorities place Mercury and Venus above the Sun (Plato), around the Sun (Martianus Capella), and below the Sun (Ptolemy)? Why are Mercury and Venus subject to bounded elongation and hence move with the Sun in one year? 3. Why does Mars have such a conspicuously large epicycle, such a large retrograde arc, and such great variations in distance by comparison with the other superior planets?136 134 Swerdlow, “Derivation,” 437–438. See also Martin Clutton-Brock, “Copernicus’s Path,” 197–216. 135 Goddu, “Reflections,” 41–46. 136 Ptolemy rounds the ratios in the Almagest off to 7 : 1 for Mars, and 104 : 16 for Venus, as compared with 88 : 34 for Mercury, 37 : 23 for Jupiter, and 7 : 5 for Saturn. The same gaps are reflected, of course, in the cosmological distance scale in Planetary Hypotheses, the results of which were available in the theorica literature known to Copernicus and in the Epitome. The variations in distance are about the same in Copernicus’s system. From Copernicus’s statements it is often very difficult to distinguish a clue from an afterthought. I have sometimes suggested that the variations

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4. Why does Venus along with Mercury fill such a large space between the Sun and the Moon, and why is Venus’s retrograde arc larger than Mercury’s? My claim is that starting from his assumptions and by answering these questions consistently, Copernicus was led by a process of elimination to his conclusion that the Sun is the cosmological center of the heavenly spheres, that the Earth with its Moon orbits the Sun, and that Earth rotates on its axis leaving the very distant stars at rest. If the planetary spheres are ordered around the center according to one principle, than Earth cannot be the cosmological center of their motions. Some experts speculate that Copernicus anticipated a Tychonic arrangement that he would have rejected because of the interpenetration of the spheres of the Sun and Mars.137 In fact, the spheres of Mercury and Venus, even in the Capellan arrangement, penetrate the sphere of the Sun, yet Copernicus says nothing about it.138 He refers to Martianus Capella merely to cite a predecessor who put at least two planets in motion around the Sun. Copernicus, I contend, never got as far as a Tychonic arrangement, because the Capellan arrangement proposed two centers (Sun and Earth) with necessarily two different principles of arrangement, which would not have answered the first

for Mars and Venus were a clue, but perhaps after he imagined the Earth in orbit, Copernicus realized that it would explain retrograde motion, eliminating the need for epicycles to account for that observation. Earth’s motion explains in part the large variations in distance, and renders the large epicycles for Mars and Venus superfluous. The only functions left for epicycles were to adjust the motions of the planets and to account for variations in latitude, for which epicyclets sufficed. 137 Swerdlow, “Derivation,” 478. 138 I owe this observation to Martin Clutton-Brock in a private communication. He believes that Victor Thoren was the first to notice this apparent result. Not even Tycho Brahe raised this objection, which leads me to suspect that he thought of the orbits of Mercury and Venus around the Sun as epicycles of the Sun, and probably did not regard them as spheres. Thoren does comment on the relation between the comet of 1577 and the penetration of the spheres of Mercury and Venus, and he says that Tycho seems to have realized this consequence only some years later. See Thoren, “Tycho Brahe,” 3–21, esp. 8. Compare Jarrell, “Contemporaries,” 22–32; Schofield, “Tychonic World Systems,” 33–44; and Schofield, Tychonic World Systems. For an illuminating discussion of the alternatives, see Gingerich and Westman, Wittich Connection.

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question satisfactorily.139 Copernicus clearly assumed that there should be one center with one principle of arrangement.140 The Capellan arrangement did suggest an arrangement around the Sun as center. This is very likely the suggestion that inspired Copernicus to imagine Earth with its Moon in orbit around the Sun, necessarily outside the orbit of Venus, filling the large space between the Moon and Sun, and inside the orbit of Mars, thus explaining the large retrograde arcs of Venus and Mars, the large Martian epicycle and variations in distance, and all the planetary spheres ordered around the Sun, after some calculation,141 according to sidereal periods. By drawing on the consequences of the dichomoties and questions, he arrived eventually at a heliocentric, geokinetic system with eccentric-epicyle models as preserving the principles of uniform and circular motions while accounting for observed non-uniformities in motion and variations in distance. The double-epicyle models in Commentariolus constituted an intermediate stage. The Platonic method of examining dichotomies likely led him to resolve other questions in principle, although he does not address these in Commentariolus. The universe is either a whole or it is not. If not, then it is disordered, an unacceptable consequence, hence it must be an ordered whole. The elemental motions are natural or violent. If violent, then the elements would be disordered, also unacceptable. If the spherical body on which elements exist has a circular motion, then the natural motion of elemental bodies must also be circular. The rectilinear motion that we observe in the case of a falling body must be a compound motion. A rectilinear falling motion cannot be unnatural, hence such motions are an expression, as it were, of a natural tendency in such bodies to be united with their whole, and the most rapid motion is rectilinear. In De revolutionibus Copernicus

139 In the Tychonic arrangement, all of the planets can be ordered from the Sun according to sidereal periods, but they are still ordered zodiacally (Mercury and Venus) and sidereally (superior planets) from Earth. One could calculate the mean distance of the planets from the Sun, but the mean distance of each planet from Earth is necessarily the Earth-Sun distance. 140 Goldstein, “Copernicus and the Origin,” 220–222; Goddu, “Reflections,” 40–41. 141 For a reconstruction of the computation, see Goldstein, “Copernicus and the Origin,” 230. Copernicus calculated the sidereal priods from the synodic periods, the numbers for which he probably derived from Regiomontanus’s Epitome. See Table 3 for a simple modern computation of Mercury’s and Venus’s sidereal periods from their synodic periods.

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compares their condition while falling or striving to be united with the whole as a condition of sickness compared to their healthy condition when united with the whole. Sickness, on this view, is natural, tending towards health. I will address the logic in chapter eight, natural philosophy in chapter nine, and cosmological details in chapter ten; here I simply remark that the annotation in Parmenides fits Copernicus’s argumentative strategies developed to support the greater probability of his hypotheses over those of his geocentric, geostatic predecessors and contemporaries.142 The decision about which hypotheses to accept or reject requires a thorough evaluation of all of the consequences. It was, I suggest, Plato’s Parmenides that emboldened him to undertake the dialectical inquiry with its mathematical details and that led, in Commentariolus, to the rearrangement in the form of seven postulates. Admittedly, this suggestion extracts a great deal from one annotation, but the reconstruction illuminates the sort of reasoning that guided his treatment of hypotheses. The comment, brief as it is, reflects the impression that the text made on him. The same criticisms of predecessors with the same assumptions we find once again in De revolutionibus.143 As in his later qualitative account in De revolutionibus, Book 1, Copernicus leaves detailed exposition for later. As expressed in the Commentariolus, the motions of Earth cause the regular non-uniformities and variations in distance, thus eliminating or explaining some of the most peculiar non-uniformities. Even when he agrees that the motions of heavenly bodies are circular or composed of circles, he is anticipating Earth’s motions. Earth’s rotation on its axis eliminates the diurnal rotation of the entire universe. Earth’s annual motion around the Sun explains the regularity of the seasons, the direct motions of all of the planets, and the planets’ varying distances from Earth. In short, he is far from mentioning the complications of the geometrical models but is rather content to insinuate the Earth’s motions as providing an initial approximation of the solutions and explanations of the observed non-uniformities. 142 Rosen, Revolutions, Commentary, 359. Knox, “Ficino and Copernicus,” 413– 418, and idem, “Copernicus’s Doctrine,” discusses Copernicus’s doctrine of elemental motion and its sources. Again, Rheticus, Narratio prima, Rosen tr., 131, presents Copernicus’s discovery as the end of a critical inquiry, the results of which compelled him to assume other hypotheses or theories. 143 In chapter ten, I explain how in De revolutonibus I, 4–10, Copernicus completed his analysis of spheres, orbs, and their arrangement.

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To summarize the observational data, then, we need refer only to the following. The sizes of the retrograde arcs and distances of the planets from Earth vary. For the planets that move with the Sun in the geocentric system, the retrograde arc for Venus is greater than Mercury’s retrograde arc. For the planets seen in opposition, the variation and the size of the retrograde arcs are greater the closer the planet is to Earth.144 In other words, Mars exhibits the greatest variation and Saturn the least. Next, Copernicus knows that the Capellan arrangement explains the observation of bounded elongation. By calculating the sidereal periods of Mercury and Venus from their synodic periods, he realizes that Venus’s sidereal period is more than Mercury’s and less than the Sun’s. When he places Earth where the Sun is, the entire system falls into place. Even geocentrists had concluded that Mars, Jupiter, and Saturn follow the distance-period principle, yet the periods for Mercury and Venus were measured by the zodiacal period of the Sun, one year. That is the case if one places the Sun in the middle between the inferior and superior planets. But if one places Earth between the inferior and superior planets, then all of the planets follow the same principle. The reason for the variations in distance, in the sizes of the retrograde arcs, and the sizes of the planetary epicycles in the Ptolemaic system becomes clear. Earth is a planet, and the planets are arranged according to their sidereal periods. Most of the details and the principal conclusions I have provided elsewhere, but here for the sake of completeness I include a photograph of the crucial folios (Plates 2 and 3) from Copernicus’s “Uppsala Notes” (referred to as U).145 The first shows the verso of the last printed table in Copernicana 4, on which Copernicus began to write the results of his calculations. For reasons that we do not know for sure, he stopped writing and turned to a later folio, on which he repeated the first word and completed writing the results. That folio reports the calculations used in Commentariolus. Following Plate 3 are tables summarizing Copernicus’s calculations (Table 1), a comparison between Ptolemy and Copernicus on linear distances (Table 2), and a modern computation of Mercury’s and Venus’s sidereal periods from their synodic periods (Table 3).

144 Those facts alone might suggest that Earth is closest to Venus and Mars, as Copernicus emphasizes near the conclusion of De revolutionibus I, 10. 145 Following Swerdlow, “Derivation,” 426–429.

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Plate 2—Detail of Uppsala, Copernicana 4, folio 269v.

Plate 3—Uppsala, Copernicana 4, folio 284v, also identified as folio 15v of the “Uppsala Notes,” referred to as U.

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Table 1—Copernicus’s Calculations in Uppsala Notebook In Uppsala Notebook, f. 284v (also identified as f. 15v of the notes themselves), Copernicus calculated the radii (semidiameters) of the planetary spheres according to two units. At the top of the folio he used 10,000 units to represent the radius of a planetary sphere, and compared it to the size of the planet’s eccentricity, that is, the Earth’s orbital radius relative to the planet’s orbital radius. In the bottom half of the folio he compared planetary orbital radii to Earth’s orbital radius scaled to 25 units. Scaled to 10,000 units, the planet’s orbital radius to the eccentricity of the planetary model or Earth’s orbital radius:

Scaled to 25 units, the planetary orbital radius to Earth’s orbital radius:

Mars = 6583 Jupiter = 1917 Saturn = 1083

Mars = 38 Jupiter = 130 Saturn = 230 5/6

10,000:6583 = 1.52 10,000:1917 = 5.22 10,000:1083 = 9.23

38:25 = 1.52 130:25 = 5.2 230.833:25 = 9.23

[Copernicus reversed the ratio for the inferior planets.] [Venus = 7200 7200:10,000 = .72]* Venus = 18 Mercury = 376[0]** 3760:10,000 = .376 Mercury = 9 2/5

18:25 = .72 9.4:25 = .376

The eccentricity of the planetary model is in the left-hand column. In Copernicus’s system the eccentricity is equivalent to Earth’s planetary orbital radius scaled to 10,000. Note that the ratios correspond approximately to the ratios of the orbital radii in Copernicus’s system with Earth’s orbital radius set at 1: Mercury = .376, Venus = .723, Mars = 1.523, Jupiter = 5.203, and Saturn = 9.234. * Venus is omitted at the top of the folio. ** The folio records two different numbers for Mercury’s “eccentricity,” 2256, but in the left-hand margin appears 376. The first number is normed to 6,000, a variation of Regiomontanus’s Tabella sinus recti. The number in the margin is normed to 1,000, which I have changed to 10,000 for the sake of consistency. (Sources: Copernicana 4, containing Tabule Alfonsi regis (Venice, 1492), Tabula directionum perfectionumque (Augsburg, 1490), Tabella sinus recti, and The Uppsala Notebook, ff. 270r–285v, Uppsala University Library; and De revolutionibus V, 9, 14, 19, 21, and 27.)

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Moon Sun Planet

Least Distance

Greatest Distance

33 Earth radii 1,160 Earth radii

64 Earth radii 1,260 Earth radii

Ratio of Greatest to Least Distance (rounded off )

Mercury Venus Mars Jupiter Saturn

88 : 34 104 : 16 7:1 37 : 23 7:5

(From Almagest, IX–XI. Approximately: (R – r – e) : (R + r + e) where R designates the deferent radius, r the epicycle radius, and e the eccentricity.)

Cosmological Distance Scale Least Distance Greatest Distance (Earth radii) (Earth radii) (minimum distance × ratio = maximum distance) Moon Mercury Venus Sun Mars Jupiter Saturn

33 64 166 1,160 1,260 8,820 14,187

64 166 1,079 1,260 8,820 14,187 19,865

(64 × 88/34 = 166) (166 × 104/16 = 1,079) (1,260 × 7 = 8,820) (8,820 × 37/27 = 14,188) (14,187 × 7/5 = 19,862)

(Source: James Evans, The History and Practice of Ancient Astronomy, 387–388.)

Copernicus’s Orbital Radii, Sidereal Periods, and Mean Distances of Planets in Terrestrial Radii Mercury .376 88d (.24 yr) 430 E.R.

Venus

Earth

Mars

Jupiter

Saturn

.723 225d (.616yr) 822

1.00 1yr 1142

1.523 1.88yrs 1736

5.203 11.86yrs 5960

9.234 29.46yrs 10,477

(The figures approximate the results in De revolutionibus V, 9–30; the mean distances are from Swerdlow and Neugebauer, Mathematical Astronomy, II: 539, Table 12.) The significance of Copernicus’s numbers, however, is not so much their differences from Ptolemy’s, but the explanation for the greater variations for Mars. The closer the orbits of two planets are, the greater the variations in distance between them.

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Table 3—Calculation of a Sidereal Period from a Synodic Period If Copernicus assumed that Mercury and Venus are inferior planets, then to determine their sidereal periods and which is faster, we can use the following formula with Sn standing for the synodic period of the planet and Sd for its sidereal period: 1 = 1/Sd – 1/Sn. We know from Regiomontanus’s Epitome that Copernicus could have calculated Mercury’s Sn at 115.78. Earth’s sidereal period, of course, is 1 year or 365.25 days; therefore, 115.78/365.25 = .317. (1) 1 = 1/Sd – 1/Sn. (2) 1 = 1/Sd – 1/.317. (3) 1 = 1/Sd – 3.16. (1/.317 = 3.16) (4) 1 + 3.16 = 1/Sd. (5) 4.16 = 1/Sd. (6) 4.16 Sd = 1. (7) Sd = 1/4.16. (8) Sd = .24 years. (9) Sd = 88 days (.24 × 365.25 = 88) From Regiomontanus’s numbers for Venus, its Sn = 584.4 days. 584.4/365.25 = 1.6. 1/1.6 = .625; therefore, Sd = 1/1.625. Beginning at step 7 as above: (1) Sd = 1/1.625. (2) Sd = .615. (3) Sd = 224.63 days (.615 × 365.25 = 224.63) In Commentariolus, Copernicus calculated Mercury’s Sd as 88 days, and Venus’s as 7 and 1/2 months (7.5 × 30 = 225 days).

One more issue requires our attention. Already in Commentariolus Copernicus adopted something like a Tusi couple to account for planetary oscillations. In chapter five, I proposed that he might have developed his solution independently of Arabic sources by relying on suggestions that he could have encountered in Poland. Such a possibility, in my view, is supported by Mario di Bono’s critical evaluation of the literature that assumes that Copernicus must have been acquainted with Maragha models. Here is the appropriate place to consider the technical details at least sufficiently to understand the solution at which Copernicus arrived.146

146

See di Bono, “Copernicus, Amico,” esp. notes 1–7 for the scholars who have

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Because Giovan Battista Amico (1536) used this device, Noel Swerdlow suggested that the transmission of the model came through Italy. Hieronymus Fracastoro (1538) provided a demonstration of a similar reciprocation device.147 Di Bono’s critique is based on the way in which modern mathematical translations can obscure important differences and exaggerate marginal similarities.148 The Tusi device has one circle carrying a second circle whose radius is half its size and that rotates in the opposite direction at twice the velocity of the first. The initial point of contact (for example, at the top of the first circle) will generate a straight line (the diameter of the first circle) down to the opposite point and back to the original point.149 The 1:2 ratio is crucial, as we will see later. Furthermore, a description of the device as a circle that “rolls inside another twice its dimension” obscures the fact that the physics of that era precluded such a rolling in reality because there is no void in the heavens.150 Despite such objections, Tusi’s mechanism is a physical, not a simple, geometrical construction. Arabic asronomy attempted to find a physical structure for the Ptolemaic system that reconciled the mathematical constructions and physical reality.151 Di Bono goes on to describe three different versions of the device. The first is called a “rectilinear version,” which di Bono calls, more precisely, “the spherical version with parallel axes and radii in the ratio of 1:2.”152 This version is designed to solve those problems dealing with the non-uniform motion of the deferents of the Moon and the planets, that is, the problem of the equant. See Figure 1. The second version, called the “curvilinear version” and “spherical version,” di Bono, again more precisely, describes as the “spherical

made contributions to this topic. According to di Bono, n. 2, Dreyer seems to have been the first (1906) to show that Copernicus’s theorem was already known to Nasir al-Din al Tusi. Di Bono, n. 74, rejects the Cracow connection. 147 See di Bono, nn. 3–4, for the details. Cf. Swerdlow, “Aristotelian Planetary Theory,” 36–48, esp. 37. 148 In addition, Aristotle rejected the very idea that a rectilinear motion can be compared with, let alone composed by, circular motions. See di Bono, n. 14. 149 See di Bono, 134, figure 1. He adopted the figure from Saliba, “Astronomical Tradition,” 67–99, esp. 79. 150 This is, of course, another Aristotelian objection. 151 Ragep, Nasir al-Din al-Tusi’s Memoir, 1: 41–53. 152 Di Bono, 135–136. Compare Ragep, “Two Versions,” 329–356. Di Bono took his first figure from Saliba, “Astronomical Tradition,” 68–69 and 74–81.

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Figure 1—Tusi’s device: spherical version with parallel axes and radii in the ratio of 1:2. (From Saliba, p. 79)

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version with oblique axes and equal radii.” This version is designed to generate an oscillation between two points on a great circle arc (not a straight line). This device solves problems such as deviation in latitude, variable precession, and variation in the obliquity of the ecliptic.153 See Figure 2. George Saliba then identified a third version called “the plane version with equal radii.” This version of the device is composed of two identical circles in a single plane, one of which “rides” on the circumference of the second and moves in the opposite direction at a uniform speed that is twice the speed of the second. This version solves the problem of motion in latitude, not the problem of the equant for which the Tusi device (first version) would later have to be applied. See Figure 3. Di Bono’s description of Copernicus’s devices is complicated by obscurities in the texts and differences between Commentariolus and De revolutionibus.154 Di Bono says that the version Copernicus used in Commentariolus for deviations in latitude for the superior planets and Venus is the spherical version with oblique axes and equal radii (that is, the second version). The result, then, would be an oscillation on a great circle arc.155

153 Di Bono took the figure from Saliba and Kennedy, “Spherical Case,” 285–291, esp. 288. 154 We might also add that it is complicated by Edward Rosen’s commentary to Commentariolus, which is often a lengthy, running attack on Swerdlow’s translation and interpretation. Di Bono apparently ignored Rosen and followed Swerdlow, although di Bono’s reading concludes (140) with a paradox about how to interpret the solutions in Commentariolus. 155 Rosen’s translation, 87–88 and nn. 227–254. In fact, Copernicus says that the motion of libration or the oscillatiing motion occurs “along a straight line.” See Zekl, 24–26: “Accidit etiam motu telluris in orbe magno latitudines visibiles nobis variari, ita sane propinquitate et distantia visibilis latitudinis angulos augente et minuente, sicut mathematica ratio exposcit. Siquidem hic motus librationis secundum lineam rectam contingit, fieri autem potest, ut ex duobus orbibus huiusmodi motus componatur, qui cum sint concentrici, alter alterius deflexos circumducit polos et inferior contra superiorem duplici velocitate polos orbis epicyclos deferentis, et hi quoque poli tantam habeant deflexionem a polis orbis mediate superioris, quantum huius a polis supremi orbis. Et haec de Saturno, Iove et Marte ac orbibus terram ambientibus.” If he was thinking of plane circles, then the result is a straight line. But if he was thinking of spheres, the result is an oscillation on a great circle. But see Swerdlow, “Derivation,” 488–489, who interprets the equal radii as “degenerating” an ellipse into a straight line. Di Bono evidently follows Swerdlow’s interpretation, whereas Rosen takes Copernicus at his word that the oscillating motion occurs along a straight line, not an arc, because the “orbs” are functioning in a plane.

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Figure 2—Tusi’s device: spherical version with oblique axes and equal radii. (From Saliba and Kennedy, p. 288)

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Figure 3—Tusi device: plane version with equal radii. (From di Bono, p. 137)

Copernicus then introduces the “spherical version with parallel axes and radii in the ratio of 1:2” (that is, the first version) to account for variation in the distance of Mercury from the center of the deferent.156 In his account, di Bono then shifts to the devices as described in De revolutionibus. First, he describes a plane version with two circles of equal radii, the second turning in the opposite direction and at twice the velocity of the first. By means of this device, a point will oscillate back and forth along a diameter of the larger circle that contains both of the smaller circles. Their oscillation is rectilinear. This is clearly the 156 Di Bono, 138–139. This is what Rosen takes to be a variation in longitude. See Rosen, 89 and n. 293. Again, Copernicus says that by composite motion “the centers of the larger epicycle are carried along a straight line, just as I explained with regard to the oscillating latitudes.” Copernicus seems to have focused on a plane version, and he apparently saw no difference between the version with oblique axes of equal radii and one with parallel axes of unequal radii. What is more, he suggests “solving” the latitude problem for Mercury in the same way as that of the other planets.

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third version, and this is the version that Copernicus demonstrates in De revolutionibus III, 4. See Figure 4. Why did Copernicus change from spherical versions to the plane version in De revolutionibus? Di Bono concludes from III, 5, that because the “differences between the arcs and the chords in the cases under consideration are minimal,” Copernicus used the plane version with equal radii, not the spherical version with oblique axes, to account for all variations. That is, the plane version accounts for variability in precession, variability in the obliquity of the ecliptic, the variations in latitude of all planets, and the variation in longitude for Mercury.157 After describing devices in texts of Amico (eds. 1536, 1537, and 1540) and Fracastaro, di Bono takes up the question of transmission or re-discovery. First, he asserts, the claim that the drawings in Tusi’s Tadhikira (in Ms. Vatican, Greek 211) and De revolutionibus are identical is false. The first version of the device (1:2 ratio) is in Tadhikira and the third (equal radii) is in De revolutionibus. Second, contrary to the claim, the letters in the figures are not identical, and even where they are, such a coincidence can be explained by mathematical conventions of nomenclature in geometrical figures. In any case, the drawings are different. As far as De revolutionibus is concerned, it is possible that Copernicus relied on Proclus (published in 1533). But for Commentariolus he either would have had to see a manuscript, or he might have encountered among Paduan homocentrists the idea of a reciprocation device as a variation of the hypothesis of Eudoxus and Callippus.158 Copernicus may have seen some manuscript with the Tusi device, but that would explain his use of the first version in Commentariolus for Mercury, not his use of the second version for the latitudes of the planets. His demonstration and use of the third version in De revolutionibus suggests independent elaboration. Di Bono advances a second hypothesis:

157 So do I interpret di Bono’s remark, 141: “Our opinion is that he does so in all other cases including Mercury.” This conclusion may explain why Rosen interpreted the examples in Commentariolus as plane versions generating a rectilinear motion. In addition, Swerdlow, “Derivation,” 489, states the condition under which the line generated will be a straight line, namely, a case where the angle between a point on the circumference of the lower circle and the point on the circumference of the upper circle is small enough so that the point on the upper circle generates a straight line. Swerdlow goes on to point out problems with this supposed solution. 158 Copernicus pointedly says in Commentariolus that their concentric circles failed. Di Bono, n. 74, dismisses the possible Cracow sources as too different in content and purpose to have inspired Copernicus to his solution.

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Figure 4—Reciprocation mechanism in Copernicus. (From holograph of De revolutionibus III, 4, Opera omnia I, fol. 75r) Copernicus, starting from criticisms of the Ptolemaic system (among them the problems of the equant and uniform circular motion, which were certainly known to him and which his stay at Padua would have reinforced) and working on the solution of the double epicycle, found himself in practice starting from the same presuppositions, and operating with the same objectives and the same methods, as the Arab astronomers. This being so, it is by no means remarkable that he obtains results very similar to those of his predecessors—leaving out of consideration the fact, which is not at all cosmologically irrelevant, that the Arab models maintained the immobility of the Earth. From this viewpoint, the reciprocation device, even if prompted by the discussions with the Paduan Aristotelians, could equally well have derived from an independent reflection on these same problems.159 159

He goes on to discuss Amico and Fracastoro, arguing for a revival of the hypoth-

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With that comment I conclude my summary of di Bono’s critique. If Copernicus did arrive at the first two versions independently, and showed no awareness of the third version in writing Commentariolus, then the question comes down to what could have prompted him to hit on a reciprocation device. Di Bono thinks that discussions with Paduan Aristotelians may have prompted him, but he concedes that independent reflection on problems with the equant and uniform circular motion may have led him to his solutions. If independent, however, then we must also consider any source that described a geometrical solution, for the problem emerged, as we encountered it in Commentariolus, in accounting for deviations in latitude of all planets and, additionally, in longitude for Mercury. By that time Copernicus had already committed himself to solving all of the problems by use of uniformly moving circles alone. Any oscillation model using spheres or circles, regardless of content, context, and purpose, would have been a suitable candidate for solving the problem. In other words, scholars should again look at the Cracow sources through “Copernican eyes.” There he may have encountered an oscillation model, whatever its source and whatever its purpose, that he later adapted in the forms in Commentariolus and De revolutionibus.160 * * * While still residing in Lidzbark, Copernicus did record at least two astronomical observations—one in 1504 and the other in early 1509, at least one of which was on the Cracow meridian, suggesting that Copernicus was either in Cracow or Frombork, not Lidzbark.161 Later when he wrote De revolutionibus, Copernicus referred all of the observations

esis of Eudoxus, a characteristic feature of Paduan homocentrism. Schmeidler, Kommentar, 184, decisively rejects Copernicus’s direct knowledge of Arabic works: “Die von Swerdlow und Neugebauer vorgebrachten Vermutungen, daß Copernicus direkte Kenntnis von Originalschriften islamischer Astronomen gehabt haben könnte, sind wenig überzeugend.” 160 See Appendix VI for an excursus on transmission and suggestions for a reconstruction based on late medieval sources at Cracow. 161 Rosen, “Biography,” 333. Copernicus observed the conjunction of Saturn and Jupiter on 12 May 1509, an observation not recorded by Biskup, Regesta, 46–47. Biskup, 52, no. 59, records the lunar eclipse of 2 June 1504 on the Cracow meridian, also in Rosen, “Biography,” 334. Rosen based his comment about the conjunction of 1509 on a report by Marcin Biem of Olkusz in a marginal note to his copy of John Stöffler’s Ephemeris. There was correspondence between Martin and Copernicus about the event. The letter was lost, but Starowolski testifies to having seen it. See Hilfstein, Starowolski’s Biographies, 87, and Hilfstein’s comments, 55–58.

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that he made in Frombork to the Cracow meridian because he believed Frombork to lie on the same meridian as Cracow.162 Evidently Copernicus did visit Frombork on occasion before he moved there permanently in 1510. It does not appear that Copernicus used any of the observations recorded during the period in Lidzbark prior to 1509 in De revolutionibus. This suggests that he had not yet decided to compose a major mathematical work with models and tables that required being checked against observations. He was still at an early stage where he was making observations to compare them against the predictions in current ephemerides, as Rosen suggested. If that judgment applies to the observation of early 1509, then this leads me to conclude that Copernicus had not yet arrived at the resolution to compose a major work on astronomy, and that he had not yet begun to write Commentariolus.163 In 1510 Copernicus came to the conclusion that he could not follow Uncle Lucas’s plans for the advancement of his ecclesiastical career any longer. He would continue to perform his duties as a canon and remain engaged, at times heavily, in the administration and even defense of Varmia. Were he to become a bishop, however, all hope of completing a major and arduous reformation of astronomy would have been futile. By the autumn of 1510 Copernicus was transferred from Lidzbark to the cathedral chapter at Frombork. It seems that he was far enough at work on the Commentariolus to realize the need for a thorough reworking of Ptolemaic astronomy, such that would require years of calculations and observations to complete. He may have already completed the text in 1510, or shortly after the move to Frombork. The break with his uncle probably caused him some anguish, but it was sweetened by the knowledge that he had helped his uncle through a serious illness and, most of all, by a sense of relief from the burdens of higher church office. As for the selection of Frombork, it was the site of the chapter, its library especially with his additions was better

162 Modern geographers place Cracow at 50.04N and 19.57E, Frombork at 54.21N and 19.40 or 19.41E, and Lidzbark at 54.08N and 20.35 or 20.34E. Compare Times Index-Gazetteer, 441 for Kraków and 276 for Frombork, with Oxford Atlas for the alternate coordinates. 163 See Rosen tr., 82, where Copernicus alludes to his intention to write a larger work.

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stocked than Lidzbark’s for his purposes, and from the observations made there already he probably recognized its superiority as a place for relatively undisturbed observations. In brief, it was superior as a workplace in most respects.164 He remained involved in the business of the chapter and in Varmia, but he had escaped a potentially allconsuming job for the comparatively lighter duties of a canon and its sufficient income.165 He may also have wondered about his freedom to pursue a controversial project as a bishop. Even under the circumstances he delayed as long as he could, and perhaps would never have published De revolutionibus but for Georg Joachim Rheticus’s intervention. Judging from some annotations in his copy of Pontanus’s works and Bessarion’s defense of Plato, we perceive a figure who cherished the solitude and leisure to indulge his taste for the contemplative life. These were inclinations that he probably began to form as a young student. They were deepened by his contacts with humanists and academics at Cracow, and confirmed in Italy. Uncle Lucas had evidently seen promise in Nicholas at an early age, but little did he suspect that he had helped to form an intellectual, not a full-time administrator. In 1510, then, he informed his uncle that he could not follow his wishes. Could he have made such a personally difficult decision—one that he knew would disappoint his uncle—unless he had already recognized the absolute necessity of a break with him? I conclude, then, that he began to write Commentariolus after May 1509 and completed it in 1510. To sum up yet another long chapter, we have concluded that Copernicus acquired and developed the philosophical assumptions and techniques that he deployed for the remainder of his life in reforming ancient astronomy by 1510. His education and the books

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This is not to say that Copernicus made extensive observations in Frombork. In fact, his instruments and the visibility from his tower were limited, and Frombork is very far north and also affected by fog from the lagoon. See Hamel, 177–184, for the limitations under which Copernicus labored. With some justice it may be said that Copernicus did not fully appreciate the need for new and more accurate observations to the extent that Regiomontanus and, later, Tycho Brahe did. As we shall see in the concluding chapter, even Rheticus was dismayed by Copernicus’s willingness to settle for inaccurate observations. 165 In fact, Copernicus was extremely busy administering church property, participating in the struggles against the Teutonic Knights, making himself available for medical advice, and engaging himself in economic and monetary policies, as a glance at Biskup’s Regesta demonstrates.

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that he acquired and used allowed him to formulate the fundamental assumptions and conclusions that he had reached by means of the qualitatively astronomical, mathematical analysis that led him to the heliocentric and geokinetic hypotheses. In U and in Commentariolus we see the first efforts to transform Ptolemy’s geocentric models into heliocentric, heliostatic ones. We turn now in Part III to the elaboration of Copernicus’s philosophy.

PART THREE

COPERNICUS AS PHILOSOPHER

CHAPTER EIGHT

COPERNICUS AS LOGICIAN 1. Introduction In an earlier effort to uncover the logical principles behind Copernicus’s arguments in De revolutionibus, I focused attention on his likely education in logic at Cracow. Because an examination of his arguments indicated that he had been trained in logical reasoning and argumentation, it was plausible to assume that he learned logic and dialectic as an undergraduate at Cracow.1 Today the formal study of logic has been relegated to mathematical technicalities and its practical study reduced to exercises in critical thinking. We can hardly appreciate the extent to which medieval universities trained their students in logic, devoting about twenty percent of courses to the study of works on logic. Accordingly, I described the instruction in logic at Cracow in the 1490s, and tried to show how his teachers influenced Copernicus to develop the arguments presented in the Preface and Book I of Revolutions. I stand by the analysis and principal conclusions of the articles that appeared in 1995 and 1996. My subsequent examination of Copernicus’s education in law at Bologna and his reading of Neoplatonic supporters of Plato and of some Platonic dialogues, however, has led me to a deeper appreciation for Copernicus’s attention to indispensable methodological principles and his participation in the reform of ancient astronomy.2 By 1510 he formulated his answers to the principal foundational questions, and concluded what issues required a definite solution and which questions he could leave for others to answer. There is already sufficient evidence in Commentariolus to identify Copernicus’s argumentative strategies. However, he did not articulate them more fully until the 1520s in Book I of Revolutions 1

Goddu, “Consequences,” 137–188; idem, “Logic,” 28–68. The details are in chapters three, four, and seven. Earlier scholastics introduced a doctrine rejecting the paradoxes of strict implication that in practical disciplines like law was applied to evaluate conditional propositions. Even so, some Cracow logicians gave the doctrine a peculiar emphasis by stressing relevance as a condition of validity. 2

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and even later (1542) in the Preface. As far as strictly philosophical, dialectical, and methodological issues and argumentative strategies are concerned, Copernicus resolved the principal issues well before 1520. We turn from a chronological examination of his intellectual development to analyses of Copernicus as logician, natural philosopher (chapter nine), and mathematically trained cosmologist (chapter ten). Around 1546–1547, Giovanni Tolosani alleged that Copernicus was ignorant of logic and natural philosophy.3 We do not have a detailed critique from Tolosani, but we may surmise that he possibly had two issues in mind. First, Tolosani was probably referring to Copernicus’s obscure statement in the Preface to Pope Paul III about the relationship between hypotheses and conclusions. Copernicus’s statement suggests that by 1542 he may have thought that he was leaning on Aristotle. “If the hypotheses assumed by them were not false,” he says, “everything [that] follows from their hypotheses would be confirmed beyond any doubt.”4 According to a standard scholastic formula (cited in chapter three), the true agrees with the true and cannot follow from the false.5 Among other standard scholastic accounts, however, Tolosani seems to have ignored the view of Thomas Aquinas that results may follow from hypotheses that we cannot demonstrate are true. In other words, they may be false, yet we can derive the appearances from them.6 Second, Tolosani may have been referring to Copernicus’s overturning of the traditional relation in the arts between mathematics and natural philosophy.7 This is the sort of criticism made by Luther 3 Tolosani, Opusculum quartum, 31–42. See Garin, Rinascite e rivoluzioni, 283–295, esp. 288. I treat Tolosani’s complete argument in the conclusion in the context of the reception of the heliocentric theory. Compare Lerner, “Aux origins,” 681–721, which provides another edition with French translation. 4 On the Revolutions, tr. Rosen, 4. 5 Perhaps it was Rheticus who reminded Copernicus of this formula. In Narratio prima, tr. Rosen, 142–143: “Aristotle says: ‘That which causes derivative truths to be true is most true’. Accordingly, my teacher decided that he must assume such hypotheses as would contain causes capable of confirming the truth of the observations of previous centuries, and such as would themselves cause, we may hope, all future astronomical predictions of the phenomena to be found true.” As Rosen notes, the quotation from Aristotle is found in Metaphysics I minor, 993b26–27. The relevant Latin passage in Rheticus, Narratio prima, ed. Hugonnard-Roche, 58 reads: Aristoteles inquit: Verissimum est id quod posterioribus, ut vera sint, causa est. As pointed out in chapter three, Aristotle used similar language in Nicomachean Ethics I, 8, and in Prior Analytics II, 2–4. 6 Thomas Aquinas, Summa theologiae IaIae, q. 32, art. 1, reply to objection 2. 7 Tolosani, Garin ed. 35–36. See Epilog for the text. Notice that in addition to criticizing Copernicus for his ignorance of Scripture and the potential theological danger

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about 1541 and that is echoed in Andreas Osiander’s “Letter to the Reader.”8 The first objection, expressed in modern terms, has come to be known as the problem of induction. The problem, of course, can be traced to Aristotle, and in modern philosophy of science it is linked with the intractable logical dilemmas of the hypothetico-deductive method.9 The consensus among philosophers is that induction and hypothetico-deductive method are not compatible with classical logic. In classical logic it is not possible to show that evidence confirms a hypothesis, because even irrelevant consequences follow just as logically from an antecedent. Some logicians have proposed relevance as a condition of validity and, accordingly, have attempted to develop a relevance logic that is otherwise just as formally valid as classical logic.10 The response of scientists seems for the most part to go on with their work, ignoring the objections of logicians. In effect, what they have adopted is some form of relevance logic, even if intuitively, and they have left it to the logicians to argue among themselves about the validity of relevance logics.11 A careful reading of Copernicus’s texts shows that he too adopted relevance between consequents and their antecedents (hypotheses) as a condition of validity for astronomical hypothetical propositions. In the previous publications mentioned above I showed that Copernicus could have encountered discussions by philosophers at Cracow, who held just such views about relevance. Furthermore, their use of

of his work, he especially emphasizes the point that there is no arguing with those who deny the first principles of a science. Tolosani adds that an inferior science receives its principles by which its conclusions are proved from the superior science. 8 Copernicus, Revolutions, XX, translated by Rosen as “Foreword by Andreas Osiander.” 9 The comments by Johannes Kepler in this regard are instructive. See Kepler, New Astronomy, II, 21: 294, “Why, and to what extent, may a false hypothesis yield the truth?” I will return to Kepler in my conclusion. Here I quote only the first sentence of Kepler’s remarks: “I particularly abhor that axiom of the logicians, that the true follows from the false, because people have used it to go for Copernicus’s jugular, while I am his disciple in the more general hypotheses concerning the system of the world.” 10 The literature on these topics is vast. For an introductory orientation, see Goddu, “Consequences,” 140–152. For more recent discussions of the logical issues, see Waters, “Relevance Logic,” 453–464; Achinstein, Book of Evidence; Koutras, “Aristotle,” 153–160; and Read, “Formal and Material Consequence,” 233–259. 11 Achinstein, Book, 86–94, for instance, does not find relevance either necessary or sufficient to meet his criteria for veridical evidence.

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traditional topics to support relevance corresponds closely to Copernicus’s arguments in De revolutionibus. Subsequently, however, I discovered that as a law student at Bologna, Copernicus would have encountered the very same doctrine about relevance in legal dialectic. Chapter six summarizes that doctrine, which now leads me to suggest that experts in their disciplines modified the rules of formal classical logic defended by some philosophers. They adopted relevance as a condition of validity for inferences in their professional domains partly as a matter of common sense based on assumptions about causal connections or, when causal connections were uncertain, other relationships based on topics, such as part and whole. In short, as an undergraduate at Cracow and a law student at Bologna (and perhaps as a medical student at Padua),12 Copernicus took it as a matter of course that relevance between hypotheses and consequences is a condition of validity, and irrelevance provides a justification for rejecting alternative hypotheses. In addition, the discovery of Copernicus’s annotation to Plato’s Parmenides in Ficino’s translation of that dialogue further confirms Copernicus’s attention to philosophical and logical issues regarding hypotheses.13 The annotation is very brief, but its context suggests that the advice to consider hypotheses thoroughly from both constructive and deconstructive points of view influenced Copernicus’s consideration and evaluation of hypotheses in astronomy as a methodological principle. His familiarity with topics provided the logical tools for the construction of his arguments. This reading is consistent with the view, supported by Copernicus’s explicit statements, that he regarded his hypotheses as more probable than those of his predecessors, and

12

His education in Padua, however, seems to have consisted mostly of gathering information about medications, drugs, regimen, and their effects with little concern about methodology. See chapter six for the details. 13 See chapter seven. We may also note here that in his annotation, Copernicus replaced Ficino’s word “suppositio” with “hypothesis.” See Goddu, “Copernicus’s Annotations,” 208 and Plate 42. In Narratio prima, Rheticus (Rosen tr. 162–165) confirms Copernicus’s reflection on hypotheses and reliance on Plato for his approach to hypotheses, but he does not refer to Parmenides. In Rheticus’s reconstruction, he refers to the Epinomis, a title, however, that does not appear in the table of contents of Ficino’s translation of Plato’s works in the 1484 edition. See Goddu, “Copernicus’s Annotations,” Plate 41. Rheticus is at pains here to emphasize Copernicus’s reliance on divine guidance; the reference to Epinomis confirms Rheticus’s emphasis.

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that he recognized that he had no strictly demonstrative proof of the Earth’s motions.14 Here I focus on the principal topics used by Copernicus to support his arguments. Plato’s advice in Parmenides about how to treat hypotheses provided Copernicus with methodological guidelines that we can articulate and exemplify. I discuss the logical issues involved in his use of mathematics and astronomy to justify the instances where he proposes mathematical grounds for arriving at conclusions in natural philosophy. In this regard I will consider the views of Luther and Osiander about the liberal arts. Finally, I examine the logical issues in my reconstruction of Copernicus’s “discovery” of the heliocentric theory. I follow the problems that he identified in the theories of his predecessors. His critique led him to propose the Sun’s stability and Earth’s motions as the solutions to the problems that prevented his predecessors from accounting for the observations on the assumption that the celestial bodies move uniformly in circles. In chapter seven I argued that he arrived at his theory from the recognition of various centers and varying distances. I showed that his grounds were partly aesthetic, but more importantly, he made epistemic claims supporting the greater likelihood of his hypotheses as compared with those of his predecessors. 2. The Sources of Dialectical Topics, 1490–1550 During the period of Copernicus’s formal university education and the publication of his major treatise, 1490–1543, humanist critics of scholastic logic placed such emphasis on rhetoric that the arguments of early modern authors are sometimes dismissed as little more than emotional appeals for a new ideology. The greater emphasis on rhetoric obscures the extent to which humanists included logic and dialectic in their broader and more comprehensive understanding of rhetoric. This chapter analyzes Copernicus’s discourse in a way that shows how

14 Thus, I reject an alternative interpretation by de Pace based on a speculative reconstruction of Copernicus’s supposed reading of Plato’s Phaedo, according to which Copernicus did have a demonstration of the heliocentric theory based on his interpretation of Plato. The method in Phaedo corresponds roughly to that in Parmenides, emphasizing generally accepted opinions and the need to test theories, adopting the theory that seems the soundest, and achieving truth insofar as the human mind can attain it.

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he took full advantage of the new rhetorical strategies by discovering arguments that made extensive use of dialectical topics. The vast majority of arguments in most disciplines are dialectical or probable. Although demonstration is undoubtedly the ideal that all strive to achieve, only some proofs in mathematics and logic start from premises that have the self-evidence, primacy, immediacy, necessity, and universality requisite to the construction of a strict demonstration in the Aristotelian sense. Other arguments even in mathematics and logic and nearly all arguments in other disciplines start from hypothetical assumptions or from the opinions generally accepted by the experts in that field, and whatever results emerge from them, the conclusions have only the degree of probability or plausibility and the persuasive force that characterize the premises. The connections between premises or hypotheses and conclusions may be necessary, that is, the conclusions may follow necessarily from the premises or hypotheses, but as long as the premises or hypotheses remain at best probable or plausible, then so do the conclusions that follow from them.15 As we saw in chapter three, techniques of dialectical, probable, and plausible reasoning have a long history in the west. By examining arguments against the background of the teaching of dialectical topics, we will find, I believe, that the authors whom we read were trained in techniques of argumentation, and that they were trained in their specialized disciplines to use and develop the assumptions, warrants, and backing that the community of scholars in their disciplines used as a matter of course. What we also find is that scholars adapted or changed traditional warrants to support new conclusions, developed new warrants, and also rejected some traditional warrants as irrelevant.16 Copernicus’s education and his writings were influenced by late medieval and Renaissance contexts. There is abundant evidence that the ancient and medieval traditions of dialectical argumentation continued to be transmitted and developed throughout the Renaissance.17 Although humanists had generally nothing good to say about scholas-

15 For excellent summaries of the background and explanations of the terminology, see Moss, Novelties, 1–23; Serene, “Demonstrative Science,” 496–517; Jardine, “Humanist Logic,” 173–198. 16 On the terminology, see Toulmin, Uses of Argument, and Bird, “Rediscovery,” 534–540. In chapter three, see section 1. See also Spruyt, “Peter of Spain,” 3. 17 Risse, Logik.

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tic logic, their criticisms were often consistent with the views of late medieval scholastic authors who viewed logic and argumentation in terms broader than demonstration and the syllogism. When authors like Lorenzo Valla (1407–1457) and Rudolf Agricola (ca. 1443–1485) shifted emphasis from the syllogism and formal validity to a variety of techniques for settling a matter that is in doubt, they were continuing trends that reflect late medieval thinking about topical invention.18 The humanist revival of rhetoric and the tendency to blend rhetorical with dialectical topics has contributed to the impression that the humanists had little regard for logic, and that they were only interested in persuasion by appeal to the emotions. Although some scholastic authors overreacted to humanist critiques by returning to emphasis on the syllogism and formal validity, others accorded dialectical topics a very important role in the construction of arguments. The evidence of their teaching suggests as well that their views exercised an important influence on students, even students, who, we know, responded positively to the new humanist dialectic and rhetoric. Copernicus was one of those students, and as we turn to him, we may focus briefly on the sorts of texts that were available to him during the period of his formal education (1491–1503) and of his major writings (1510–1543). As we also saw in chapter three, the standard sources for teaching dialectical topics to students were Aristotle’s Topics and Peter of Spain’s Tractatus better known as the Summulae logicales.19 I summarize briefly the main relevant points of chapter three here. When Copernicus entered the University of Cracow in 1491, the leading and most influential teacher of logic there was John of Glogovia. Copernicus very likely attended lectures and exercises on logic taught by John or by a colleague whom John had trained. The relevance of these considerations to Copernicus’s major work is relatively straightforward. In his commentaries on texts of Peter of Spain, John of Glogovia rejected the paradoxes of strict implication (from the impossible anything follows and the necessary follows from anything), and in his analysis argued that the validity of consequences

18 On Valla and Agricola, see Jardine, “Lorenzo Valla,” 253–286. On Agricola, see Mack, 227–256. 19 Some scholars also returned to Boethius, who again became popular in the early modern period. I owe this observation to Jennifer Ashworth. In fact, Johannes Caesarius is an example of an author who evidently did return to the texts of Boethius. See below for a summary of Caesarius’s version of topics.

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depends on rules of reasoning supplied by dialectical topics. We do not know whether Copernicus ever read or used the commentary by John. As we shall see below, however, the use of dialectical topics as rules evaluating consequences and as warrants for discovering arguments, and John of Glogovia’s reasons for rejecting the paradoxes of strict implication fit Copernicus’s argumentative strategies perfectly.20 Other important sources of dialectical topics that would have been available to Copernicus are Rudolf Agricola’s De inventione dialectica written around 1479 but first published in 1515, and Johannes Caesarius’s Dialectica first published in 1520. There were also other texts, but those of Agricola and Caesarius were widely influential and published in many editions. Both of these works applied Cicero’s topics as well, and would, therefore, have been complementary to the education in law that Copernicus received at Bologna between 1496 and 1501.21 Agricola studied at Erfurt and Cologne in the 1450s, but his major work on dialectic, De inventione dialectica, was evidently influenced more by his studies in Italy.22 Although the work is often disparagingly classified among works of rhetorical logic, the title clearly suggests that it is a topics-logic treatise. Agricola’s work was an effort to put Valla’s innovations into a textbook form.23 As such, it depends on the use of topics to construct arguments, and it assigns a subsidiary role to syllogistic argument as artificial and not suited to practical arguing and persuasion. If we were to locate Agricola’s work in the scholastic debates of the Middle Ages, we would include it among those approaches that viewed logic as an art rather than as a science. Accordingly, it stresses informal reasoning over formal inference, practical uses over theory, and persuasion over formal validity. It is a work that employs topics in the discovery of arguments for the purpose of securing or confirming belief about something that is in doubt.24 Expressed in that way, the purpose of Agricola’s work is consistent with the Boethian tradition of dialectical topics.

20 See chapter three. See Boh, “John of Glogovia’s Rejection,” 373–383; Goddu, “Consequences,” 152–163; idem, “Logic,” 36–61. 21 Rosen, Copernicus, 65–75; and see chapter six. 22 Jardine, “Lorenzo Valla,” 257. 23 Mack, 244–250, but also notes fifteen ways in which Agricola departs from Valla, showing how Agricola accepted the basis of Aristotelian metaphysics. 24 Jardine, “Humanist Logic,” 181–184; Mack, 233–237. Cf. Green-Pedersen, Tradition, 330; and Ashworth, Language, 10–14.

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Among the authors influenced by Agricola and who contributed to the popularity of Agricola’s approach to dialectic after 1530 was Johannes Caesarius. His Dialectica was published in over thirty editions between 1520 and 1579, and it became one of the most popular textbooks at Cologne, where it was first published, and subsequently in Cracow, Erfurt, Tübingen, and in Italy. Following the lead of Agricola, Caesarius argued for a revival of the approach to philosophy that places dialectic as the art of invention at the heart of the philosophical enterprise. Be that as it may, the work begins with a summary of standard Aristotelian and scholastic topics—predicables, predicaments, propositions, syllogism, demonstration, and definition and division. In the treatises on the categorical syllogism, hypothetical syllogism, and consequence, Caesarius considered disputations, topics, and dialectic argument, drawing a close connection between dialectical arguments and enthymemes. Treatise IX on dialectical topics draws on Boethius and Rudolph Agricola to emphasize the importance of topics for constructing arguments to secure belief about something that is in doubt. Caesarius’s influential textbook provides another example of a manual intended to teach students how to use dialectical topics to construct plausible arguments, and it does so in a way that makes Agricola’s new emphasis consistent with Aristotelian logic. As we did for Peter of Spain’s Summulae in chapter three and Appendix I, we may set down Caesarius’s scheme or list of topics as presented in the Dialectica. Caesarius divided topics into maxims and differentiae, and he divided the differentiae into intrinsic, extrinsic, and intermediate.25 (I) Intrinsic topics are further divided into (A) from the substance: (1) from the definition, (2) from the description, (3) from the interpretation of the name; and (B) from things that accompany the substance of the thing: (4) from the whole, (5) from the part, (6) from the cause, (7) from the effect, (8) from generation, (9) from corruption, (10) from uses, and (11) from concomitant accidents.

25 Caesarius, Dialectica, ff. X 7v–Bb3; the scheme is presented on f. Y 8v. Compare with Green-Pedersen, Tradition, 46–54, for Boethius’s list. Compare with the list from Peter of Spain above in chapter three. See Appendix I.

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(II) Extrinsic topics: (12) from authority, (13) from similar things, (14) from equal or equivalent things, (15) from proportion, (16) from what is less, (17) from what is more, (18) from opposites, (19) from contradictory opposites, (20) from transumption, and (21) from changed proportion. (III) Intermediate topics: (22) from inflections, (23) from coordinates, and (24) from division. The differences between the lists of Peter of Spain and Caesarius can be easily explained in most cases. Where Peter distinguished the intrinsic topic from the whole into six subspecies, Caesarius simply mentioned one, “from the whole.” Peter distinguished “from the cause” into the four Aristotelian causes, and he distinguished “from opposites” into four types, not just two. These differences suggest that Caesarius used the list as it appears in Boethius. On the other hand, Caesarius introduced “from equals or equivalents” and “from changed proportions,” which suggest mathematical examples. It does not seem that Caesarius’s list was as useful as Peter’s. In fact, one gets the impression that Caesarius merely summarized, in a schematic way, categories and distinctions with which everyone was already familiar. Peter of Spain’s Summulae, Agricola’s De inventione dialectica, and Caesarius’s Dialectica are representative texts of the Copernican era. They all drew on Aristotle and Boethius; Agricola and Caesarius borrowed directly from Cicero as well. In reading the arguments of an author like Copernicus, we can reconstruct the rules or warrants on which Copernicus relied by asking ourselves how his arguments are structured and how they depend on dialectical topics. The dialectical topics cited below are mostly what we could call commonplaces, that is, the standard sorts of rules that any well-educated person of the era would have known. Experts in the fields of natural philosophy and astronomy would have known the topics specific to those fields. In some instances, we can see that Copernicus is clearly and deliberately challenging some of the commonly held assumptions of his era. Even as he does so, however, he tries to persuade the reader by critiquing the commonly accepted view while at the same time arguing for the plausibility or reasonableness of his alternative. The last strictly logical source that we may mention is the teaching of legal dialectic at Bologna. As we saw in chapter six, Pietro Andrea Gammaro, a student of teachers at Bologna who taught at the univer-

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sity during the period that Copernicus attended the university, wrote an important work on legal dialectic. Although he probably learned logic as an undergraduate in Cracow, Copernicus would also have learned how to apply dialectical techniques to the analysis of legal cases. Legal dialectic of the era was dominated by the concept of topics as the seat of arguments. Topics from similitude and from authority were the most applicable and used in law, but legal dialecticians also emphasized the topic from the whole. What is remarkable about legal dialectic is the way in which jurists routinely assumed connection or relevance as a condition of validity for consequences. In other words, it is altogether possible that Copernicus’s intuition here was a common view in specialized disciplines where scholars either assumed the need for restrictions on logical theory or ignored the technicalities defended by some experts in logic. They no doubt viewed such technicalities as theoretical and not practical or applicable to the real cases with which they were concerned. Because of the unique importance of one topic in particular, from an integral whole, I beg the reader’s indulgence as I turn to yet another summary, this one devoted to part/whole relations in the western tradition.26 3. Mereology—Logic and Ontology Up to this point I may have given the impression that ancient and medieval discussions of logic were completely free of ontological assumptions or commitments. That is a false impression as the following discussion illustrates. “Mereology” is a major subject of discussion in late antique and medieval philosophy.27 Derived from the Greek méros (part), mereology is the “science” of part/whole relations. Medieval thinkers analyzed relationships between parts and wholes with great acuity.28 The first

26

Much of what follows is in Goddu, “Copernicus’s Mereological Vision.” Liddell and Scott’s Greek-English Lexicon (Oxford, 1883) lists “part” as only one of the many meanings of méros. Varzi, “Mereology,” 1–5, provides a variety of meanings for “part” and “whole” in both technical senses and in ordinary language. 28 King, “Medieval Mereology.” The bibliography on mereology is extensive and can be found in the following: Henry, Medieval Mereology; Burkhardt and Dufour, “Part/Whole I: History”; Simon, Parts. 27

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explicit analysis of part/whole relations in western thought appears in Plato. In Parmenides (137a–145e) Plato pursues the consequences of contrary assumptions. If being has parts, then what is the relation of the whole to the parts? Is the whole just the collection of the parts or more than the sum of the parts? In Theaetetus (202e–205e) Plato notes the difference between a syllable and the letters in it. A syllable is formed from letters yet is distinct from them, for it has its own peculiar form or arrangement. Plato also concludes that there is a difference between a sum and a whole.29 In other words, an arithmetical sum is not the same as a whole that possesses unity (hólon or súnolon). Aristotle took up these issues in several texts, too many to summarize briefly.30 I select texts essential for the results that follow, namely, those regarding integral whole and parts and the texts where Aristotle draws conclusions about the order of the universe and the natural motions of bodies. Although Aristotle did not discuss part/whole relations in a systematic way, his discussion of concrete wholes in Topics (VI, 13, 150a22–b36) forms the basis for the later dialectical topics from an integral whole and from an integral part: “The whole perishes when the parts do, but the parts do not necessarily perish when the whole has perished.” This assertion is the basis for the consequences, “If the whole is, then the part is; if the part is not, then the whole is not.” But the following are not valid: “If the whole is not, then the part is not; if the part is, then the whole is.”31 Aristotle adds that a whole compounded of parts in a particular way is not just a totality, sum, or collection of parts. In other words, a quantity (posón) is not what he understands by a composite whole (súnolon). Metaphysics (V, 15–16) clarifies this qualification by using the word “total” (hólon) to describe a quantity the parts of which can change

29

Additional texts from Plato: Phaedrus 265d-266b, Philebus 16c-17a, Sophist 260e261d. Burkhardt and Dufour, “Part/Whole,” 663–664; King, “Medieval Mereology,” 2. 30 Topics V, 5; VI, 11, 13–14; Physics I, 1, 4; II, 4; III, 5–6; IV, 5; De caelo I, 3; II, 14; Metaphysics I, 5; IV, 2, 5; V, 2–3, 23, 25–27; VII, 2; VIII, 1, 6; X, 1; XI, 10; XII, 8, 10; and XIII, 8; Parts of Animals 640b1–5; 646a25–30; Rhetoric II, 24.2.1401a23–b5; and Poetics, 6 and 12. In the analytical indexes of technical terms in his translations of Metaphysics and Physics, Richard Hope provides many more references to méros, mórion (pars, particula), hólon (totum), and súnolon (a composite or integral whole, sometimes also rendered totum in Latin and totum integrale). 31 Rhetoric II, 24, 1401a23–b5 supports these qualifications, but also points out examples of syllogisms that are not genuine, for example, from a whole action that is wrong concluding that each part is wrong.

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position without affecting the aggregate. A total, in turn, is distinguished from organic substances composed of homogeneous parts such as tissue, flesh, and bone, thus generating the distinctions (Parts of Animals II, 1, 646a1–647b9) among three sorts of substantial composition: elemental, uniform (bone, flesh, and tissue), and non-uniform (organs). Things in which the whole is not like a heap or lump have some uniting factor (Metaphysics VIII, 6, 1045a8–12). Such texts are connected to the teleological dimension in Aristotle’s biological thinking but they have echoes in his cosmological views of Earth and the celestial spheres as primary beings—the world is a cosmos, a definite something, all things ordered together around a common center (Metaphysics XI–XII). We commonly divide the Aristotelian cosmos into two spheres (celestial and terrestrial), but Aristotle allows for many ways in which the celestial influences the terrestrial. For example, the motions of higher bodies are transmitted to lower bodies even down to the rotation of the upper terrestrial atmosphere, the Sun warms Earth, and many continued to believe in the astrological influences of the qualities and motions of celestial bodies. In Metaphysics IV, 5, 1010a28–32 Aristotle criticizes his predecessors for having attributed to the whole that which is true only of the part: We should add another criticism against those who hold these views: they have been reporting what they observe in only a few sensible things as if it were true of the whole cosmos. For it is only the region of what is sensible round about ourselves that is continually in process of destruction and generation; but this is, so to speak, not even a small part of the whole, so that it would have been more just to acquit this small bit because of the whole than to condemn the whole because of this small bit.32

Aristotle himself concluded that the heavens were made of an element different from the elements in the sublunar realm. For him, each simple body or element has only one natural motion, and the whole of an element, if united, and the part move naturally in the same direction, as, for example, the whole Earth together and a small clod (De caelo I, 3, 269b30–270a13). De caelo II, 14, 296b27–297a7 summarizes the argument succinctly:

32

Hope translation, 79–80.

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chapter eight If it is inherent in the nature of earth to move from all sides to the centre (as observation shows), and of fire to move away from the centre towards the extremity, it is impossible for any portion of earth to move from the centre except under constraint; for one body has one motion and a simple body a simple motion, not two opposite motions, and motion from the centre is the opposite of motion towards it. If then any particular portion is incapable of moving from the centre, it is clear that the earth itself as a whole is still more incapable, since it is natural for the whole to be in the place towards which the part has a natural motion.33

It should be noted, however, that constructive arguments from part to whole depend on the conception of a natural whole thing. By concluding that the heavens are made of a different fifth element, the aether, with a distinctive natural motion in circles around the center of the cosmos, Aristotle cut off arguments that the celestial motion follows the same patterns as terrestrial motion. Although they departed from Aristotle on their notions of the relation between God and the created world, Neoplatonic and medieval authors devoted much attention to part/whole relations.34 Their motives varied, but a number of puzzles caught their attention. For Neoplatonists like Proclus, the whole is hierarchically related to the parts, an idea that could be easily adapted to Aristotle’s arrangement of the spheres down to the center of Earth. Boethius, sympathetic to such schemes, summarized and interpreted Aristotle’s doctrines on topics and division. As we indicated above, he devised in particular the formulas that would be repeated down to the Copernican era. With regard to whole/part topics, Boethius organized the topics into rules for the discovery of arguments. He adopted Cicero’s division of topics, two of which are from the whole and from the enumeration of the parts. In discussing parts, Boethius distinguished between two ways: parts taken as species or as members. By “members” Boethius meant “real parts.” He discussed inferences from whole to parts and from parts to whole, often referring to examples of integral whole and integral parts.35 The scholastics adopted this category of topic, introducing a number of distinctions by way of ever more sophisticated examples. From the existence and non-existence of whole and parts, they devel33

Guthrie, tr. Aristotle on the Heavens, 245–247. King, “Medieval Mereology,” 2–3; Charles-Saget, L’Architecture. I owe the latter reference to Dilwyn Knox. 35 Stump, tr. De topicis differentiis, 37, 51–52, and 65; Boethius, De divisione liber, ed. and tr. Magee, 38–41. 34

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oped rules for valid and invalid constructive and destructive inferences respectively. Already implicit in Aristotle, who, however, had applications to organic substances pre-eminently in mind, the consequences that we owe to Cicero and Boethius are the ones found later in Peter of Spain with the typical example of the house:36 (1) (2) (3) (4)

If the house exists, then the parts (roof, walls, foundation) exist. If the house is not, then the parts are not. If the parts are, then the house is. If the part is not, then the house is not.

Everyone agreed that (1) and (4) are valid, although some authors added qualifications. For example, Abelard regarded an integral whole as identical with a unique set of parts including the arrangement that individual parts have. (2) is then qualified to read: (2´) If the house is not, then the parts-of-this-house are not (which in this form is valid). Although (3) remains invalid, in the following sense it is valid: (3´) If the parts-of-this-house are, then the house is potentially. Later scholastics emphasized integral wholes that are actually composed out of their parts, implicitly recognizing that not all parts of a whole (totum) are plausibly parts of an integral whole (totum integrale), otherwise a monster results. For example, cobbling together hands, feet, and a head does not make up a human being.37 The claim about unique arrangement of parts can generate other puzzles noted by medieval philosophers. If I repair a house by replacing some parts, is it still the same house? Some changes (renovation) may indeed produce a new, different house. Such considerations led medieval philosophers to a variety of solutions. Some distinguished between principal (or vital) parts and less principal (non-vital) parts, one consequence of which is that the destructive application from the integral part (If the part is not, then the house is not) holds only for principal parts. For things that change, move, grow, or diminish, the distinction provides a way of preserving identity over time and for distinguishing between principal and less principal parts.38 36

Peter of Spain, Tractatus, V, 64. King, “Medieval Mereology,” 16–18. 38 King, “Medieval Mereology,” 24; Henry, Medieval Mereology, 54–57, 82–84, 334–336; Simon, Parts, 198–204. 37

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Answers to questions about the composition of homogeneous and heterogeneous substances, and about continuous, contiguous, and discrete things often depended on how authors interpreted Aristotle. Aristotle thought the cosmos qua unified thing “has” a nature in the sense that the parts are ordered according to the substantial or qualitative forms that they possess as inferred from their observed motions and behaviors. Where Aristotle observed contrary simple motions (up and down), he concluded that the contrary motions must be due (aside from their generating cause) to contrary qualitative forms that account for a natural directionality in the things possessing those qualities. The observed circular motions of celestial bodies must be due to a form that has no contrary thus revealing a different substance the nature of which is to move in circles. Aristotle’s metaphysical analysis also led him to the existence of immaterial intelligences that are the cause of eternal circular motion. The contiguity of the celestial spheres is revealed in the way that the circular motions influence the motions of lower spheres down to comets in the upper atmosphere and even to the circular motion of the Earth’s atmosphere.39 To situate Copernicus’s dialectical strategies in this context, I focus now on simpler kinds of dilemmas. For example, the topics from an integral whole and from an integral part seem to imply that if, for example, Socrates loses a hand, then Socrates does not exist. One strategy for dealing with this apparently absurd consequent is to define an integral part as the kind of part that cannot be removed without destroying the whole. As we saw above, authors who applied this strategy made distinctions between vital parts (applicable only to organisms) and less vital parts, or between principal as opposed to less principal parts. Or, to put it negatively, a non-integral part is one that we can remove and still have the same individual. This criterion does not remove all ambiguity. We could attempt to find some nonarbitrary criterion, but we would obscure an important lesson from these examples. The answer that we would give to such a question reveals our view of what it is to be an individual and of what constitutes the identity of an individual. Copernicus’s mereological vision of the universe refers to an intuition about the universe as a composite or integral whole. By analyzing the intuition held by him and his followers, we can reveal features of

39

De caelo I, 2; Metaphysics XII, 7–9.

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their heliocentrism that otherwise remain obscure. We will also discover why they believed that their conclusions were more probable and likely than those of geocentrists. Finally, we will also appreciate (in the conclusion and epilog) why Michael Mästlin and Johannes Kepler found Copernicus’s answers persuasive, even compelling. 4. Logic in the Commentariolus In Commentariolus Copernicus proceeds in the following way: He follows a brief recitation of the principles of ancient astronomy and the failures of his predecessors with the postulates that, he claims, preserve the principles, and solve the problems that his predecessors were unable to solve. The first result that he announces is the order of the celestial spheres and of the planetary spheres according to sidereal periods. He then proceeds to treat the motions of the planets, providing a largely qualitative account that relies for the most part on the ratios of spheres and circles to convey the image of the harmonious cosmic ballet that results from the adoption of his postulates. I proposed in chapter seven that he arrived at the postulates initially by means of a dialectical exercise, identified conclusions, formulated the postulates that he needed to derive the conclusions, and then reorganized them. Copernicus asserts as his first postulate or claim that there is no one center of all motions. He no doubt regarded this claim as a premise for the conclusion that Earth is not the center around which all bodies revolve. The true Sun in his system is also not the unique center of all heavenly motions. There are several centers, and even for the motions of the planets’ epicycles it is the center of Earth’s orbit, not the true Sun, that is the center of their motions. The Moon accompanies Earth in its annual motion around the Sun, but the center of the Moon’s motion is Earth, not the Sun, and the center of the Earth’s motion is not the true Sun but the mean Sun. What Copernicus asserted as his first postulate seemed obvious to him indeed, not because of his heliocentrism but as the result of a review of Ptolemaic geocentrism. In that system all bodies circulate around Earth, but with exception of the Sun, they do so in epicycles, and in every model there are eccentrics and equants that serve as centers of circles. Copernicus concluded that it is obvious that there is no one center of all heavenly motions, hence he tried to persuade his readers to begin with that obvious fact and proceed to other claims or likely hypotheses.

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chapter eight 5. The Use of Topics in the Preface of De revolutionibus

This summary begins with the structure of the dedication to the Pope, and then suggests and makes reference to the standard dialectical topics that Copernicus seems to have used. The analysis used here is typically represented by the following scheme:40

W

G

according to these rules or principles

C support

The grounds

the claim.

As the scheme indicates, evidence is linked to a claim or conclusion by way of rules. The rules include standard and common logical relationships that one finds in Aristotle’s Topics or in the handbooks described above. Additional rules are supplied by the standard discussions in a discipline, that is, by what experts in the field regard as warrants in that field. In the analysis that follows, I will characterize the parts of the argument G (grounds), W (warrants), and C (claim) according to the above scheme. The scheme does have weaknesses. For

40 Note Spruyt’s formulation of the general idea, “Peter of Spain,” 3. The scheme and variations on it can be found in Toulmin, Uses, 99; and Toulmin, Rieke, and Janik, Introduction to Reasoning, 49. Some experts criticized Toulmin’s books severely, and objected that Toulmin’s scheme merely reintroduced Aristotelian syllogistic with premises in a way that is deficient from a formal perspective. See, for example, Booth, Colomb, and Williams, Craft, 90. I have not included the “qualifications” that often need to be inserted between the grounds or evidence and the claim. In general, Copernicus’s qualifications come in the form of statements where he characterizes his conclusions as more probable than those of his predecessors. Note Booth’s comments and his reference to Toulmin, 268, especially to Freeman, Dialectics, and to van Eemeren, Grootendorst, and Kruiger, Handbook. Defenders have countered that Toulmin’s scheme is less artificial and less formal from a stylistic perspective. In Appendix VII, however, I have provided syllogistic versions of the most important of Copernicus’s arguments, most of which have the structure of enthymemes requiring us to supply the missing premises.

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example, it is sometimes difficult to distinguish between grounds and warrants. In some cases, warrants are premises that provide a middle term linking two extreme terms as in a categorical syllogism. The warrants that serve as rules or principles cannot always be found among the strictly dialectical topics but come from principles of a specific discipline such as astronomy or natural philosophy. Finally, Copernicus occasionally adapts warrants involving metaphysical criteria such as ontological superiority or dignity. In what follows below I will specify in the footnotes which of the above corresponds best with Copernicus’s warrants.41 Before I analyze its logic in detail, however, I consider three important studies of the Preface. Robert Westman’s most important articles offer innovative and illuminating revisions of the standard approaches.42 The dominant note is about Copernicus’s appeal to and participation in reform (humanist, ecclesiastical, calendrical, and astronomical). The persuasive strategies that Copernicus adopted and the HorationErasmian rhetoric uncovered by Westman fit the clerical-humanist audiences that he was addressing. Following on Westman’s groundbreaking work, Peter Barker and Bernard Goldstein proposed an alternative interpretation that focuses on the intended patron.43 They argue that Copernicus’s original intention was to dedicate De revolutionibus to Duke Albrecht of Prussia. The argument rests largely on the role that Georg Ioachim Rheticus played in finally bringing the book out in print. I cannot repeat all of the details or evidence here, but the argument goes something like this. Although Rheticus addressed the Narratio prima to Johann Schöner of Nuremberg, the book concludes with a long encomium directed to the Duke of Prussia (Encomium Prussiae). As Barker and Goldstein see it, Rheticus and Copernicus’s friend, Tiedemann Giese, developed a strategy to secure the Duke’s support and remove Copernicus from a potentially damaging court case in Frombork. They conclude, then, that dedicating De revolutionibus to the Duke was part of the strategy. Why, then, did Copernicus dedicate it to Pope Paul III? According to Barker and Goldstein, Giese persuaded Copernicus to dedicate the work to the Pope without Rheticus’s knowledge. The

41

Critics of Toulmin’s scheme complained about all of these weaknesses. Westman, “Proof,” and idem, “La préface.” Compare with Westman, “Astronomer’s Role.” 43 Barker and Goldstein, “Patronage.” 42

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evidence supporting the reconstruction is partial for not all correspondence has survived. In my view, however, the story is implausible. They do not explain adequately the grounds that would authorize a dedication to the Pope. A dedication was not just the decision of the writer but a kind of negotiation. In other words, the writer required an intermediary through whom he could approach the Pope, and thus know that the dedication of the book would be welcome.44 Second, their account implies that Giese and Copernicus were duplicitous in their treatment of Rheticus. Now, there is some evidence that the failure to mention Rheticus’s role in the publication of the book had troubled Rheticus, yet Rheticus seems to have accepted Giese’s excuse that Copernicus was old and infirm when he wrote the dedication. There is no indication that he was surprised that it had been dedicated to the Pope.45 It also seems consistent with the facts in their account to suppose that Rheticus and Giese developed a strategy that from the start entailed the dedication of the Narratio to the Duke and of De revolutionibus to the Pope, precisely to cover both Protestant and Catholic interests. In the most recent important discussion of the Preface, Miguel Granada and Dario Tessicini raise similar objections to the account by Barker and Goldstein, and devote a good deal more attention to addressing the question of the intermediary between Copernicus and the Pope.46 One detail that they emphasize also ties their explanation to Girolamo Fracastoro’s homocentric models as an alternative to Ptolemaic astronomy. Contrary to his comments in Commentariolus where he dismisses concentric alternatives, Copernicus refers explicitly to

44 They argue, 358, that because Copernicus had become a client of Duke Albrecht, an approach to the Pope would be credible. What connection did the Duke have with the Pope? 45 Burmeister, Rhetikus, I, 57–62, and III, 55–59 (Giese’s letter of 26 July 1543) emphasizes the fact that Rheticus remained until his death Copernicus’s true disciple. Rheticus’s letter to Giese that prompted the response is not extant, but Giese was presumably responding to a remark by Rheticus, yet there is no indication in it that the dedication to the Pope surprised Rheticus. Burmeister also points out that in the Narratio, Rheticus refers to Copernicus consistently as “my teacher,” never by name. Burmeister suggests that later authors have invented a problem or exaggerated it, for there is not the slightest indication that Rheticus was inconsolable about the matter. Rosen, “Biography,” 400–402, implies that Rheticus knew about the dedication to the Pope, and says that it was Rheticus who omitted the Introduction. That suggests that Rheticus knew enough about the Preface to realize that the Introduction was no longer appropriate. 46 Granada and Tessicini, “Copernicus and Fracastoro,” esp. 437–447.

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homocentric attempts in the Preface.47 In the absence of an exhaustive examination of the texts from 1490 to 1540, it is difficult to evaluate the significance of the terms concentric and homocentric. If Granada and Tessicini are right, then they have pointed out an important difference between Commentariolus and De revolutionibus that suggests that part of the motive for the Preface involved eliminating a rival. In my opinion, it is far from clear that Copernicus ever took concentric or homocentric alternatives as a serious rival. He seems to have dismissed them out of hand in both texts as theories that cannot be made to fit the phenomena.48 They have, however, strengthened Westman’s case for the dedication to the Pope. All of that said, I must conclude that it is premature to draw any confident conclusions about the more speculative reconstructions. Westman’s argument, by contrast, is more secure. What emerges from it is a picture of Copernicus interested in reform of the calendar, concerned about objections to his theory based on Sacred Scripture, and motivated to frame his decision to publish such an unconventional cosmological proposal so as to address a clerical audience steeped in a humanist-artistic culture of reform. As Westman has shown in this and other contexts, Michael Mästlin’s later comments on De revolutionibus provide clues about Copernicus’s strategies. Although I had developed my arguments prior to noticing Mästlin’s observations, I introduce these comments here to emphasize the relation between rhetoric and dialectic. I will return to these themes explicitly in section six below and also in the conclusion of this work. Here I turn to the task of explaining the logical or dialectical features of Copernicus’s Preface. In the introductory section of the Preface to Pope Paul III, Copernicus’s rhetorical strategy is to anticipate rejection and acknowledge the outrageous nature of his proposals.49 This leads him, then, to explain

47 Westman, “Proof,” 179 and 198, n. 45, also noted “homocentrics” as a reference to Paduan Averroism. 48 Copernicus seems to have been unaware of Regiomontanus’s interest in concentric astronomy. See Shank, “Regiomontanus,” idem, “Regiomontanus and Ptolemy,” and Swerdlow, “Regiomontanus’s Concentric-Sphere Models.” 49 Westman, “Proof,” 167–205. Note Westman’s emphasis on poetics and its relation to Copernicus’s humanistic credentials. All of these devices support Copernicus’s claims as they relate to his character and the moral aim of achieving perfection. My relative neglect of these features of his arguments is due to the focus on strictly logical criteria.

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what led him to adopt the new ideas, beginning with the inadequacies of, first, narrowly homocentric astronomy and of, second, the Ptolemaic geostatic alternative. Aside from observational problems with the first (non-confirming results) and theoretical problems with the second (contradiction of first principles of uniform motion), the principal problem was that Ptolemaic hypotheses failed to elicit the “structure of the universe and the [commensurability] of its parts.” The principal criterion is that the method of Ptolemaic astronomers is unsound, for they “omitted something essential” or they “admitted something extraneous or wholly irrelevant.”50 To resort to the scheme sketched at the beginning of this section, the hypotheses (G) should yield by virtue of an essential relation or be relevant to (W) the structure of the universe and the commensurability of its parts (C).51 The warrants of essential relation and relevance suggest that Copernicus may have relied on the following standard, common topics to support the argument: W1: from an integral whole, which supports the inference from a composition of parts having quantity to the existence of the part in a quantitative relation to the whole, as Copernicus exemplifies by comparing a portrait in which the parts are taken from different individuals resulting in a monster with a portrait of a single individual; W2: from the description, inasmuch as the reference to an essential relation suggests that he is referring to essential properties.52

50 Copernicus, De revolutionibus, Gesamtausgabe 2: 4. The translation is, with one emendation, from Revolutions, tr. Rosen, Complete Works 2: 4. I will cite the translation, as in this case, by page number. The Latin expression used by Copernicus: “aliquid necessariorum, vel alienum quid, et ad rem minime pertinens, admisisse inveniuntur.” 51 This argument and all those following can be recast as a hypothetical syllogism. See Appendix VII, Example 1. The model for this version of the argument is in Slomkowski, Aristotle’s Topics, 53. Although Slomkowski’s is a controversial interpretation, the examples suggest how the arguments can be rendered syllogistically. 52 These correspond to the topics in the Summulae (as numbered in Appendix I) to I, B, 6 and I, A, 2 respectively; and in the Dialectica to I, B, 4 and I, A, 2 respectively. We noted in Chapter 3 that Peter of Spain simplified the logic of part/whole relations. Copernicus follows such a simplified version, and was evidently unaware of technical difficulties. Copernicus’s use of mereological (part/whole) topics requires a separate and detailed analysis. His intuitive view suggests a solution of a more precise question. I will indicate some consequences below, but see Goddu, “Copernicus’s Mereo-

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Although less likely and appropriate in my view, the topics from definition, from universal whole or genus, or from the formal cause may also have played a role here, but the above warrants seem to fit the best.53 The argument presented by Copernicus clearly possessed aesthetic and rhetorical appeal as well, and which he proceeds to exploit even more effectively in the next section of the Preface. Copernicus returns the reader’s attention to his state of mind by describing the frustration that he felt over the centuries-long failure to discover the true arrangement of the parts created by the “best and most systematic Artisan of all.” Copernicus relies here above all on the topic from efficient cause and its maxim: “that is good whose efficient cause is good as well.”54 He immediately uses this equally theological warrant as the explanation why he reread the sources to see if anyone had proposed any other motions of the spheres. The extrinsic topic from authority justifies the serious consideration of a heliocentric alternative, for some respectable ancient authors did so.55 Hence, Copernicus implies, he might not be insane after all, and when one considers the motion of the Earth seriously, otherwise incidental observations follow necessarily and naturally from the hypothesis. The structure of the argument is as follows: From the assumption that God is a systematic artist (G), we may conclude by virtue of the topic from efficient cause (W), that God arranged the parts of the world machine in a definite and unique order (C).56 Because God created the system for our sakes (G), we may suggest by virtue of the topic from efficient cause as well (W), that we are capable of discovering the definite and unique order in which God arranged the parts (C). Because God created us with a desire to know (G), we are permitted by virtue of the topic from authority (W), to consider alternatives proposed by the ancients (C). Because some ancient authors were free to imagine

logical Vision,” for the complete analysis. The Conclusion and Epilog summarize the results. 53 Compare Summulae, topics I, A, 1; I, B, 4; and I, B, 14; Dialectica, topics I, A, 1; I, B, 4; and I, B, 6. 54 Revolutions, 4. Cf. Summulae, topic I, B, 12; Dialectica, topic I, B, 7. 55 Cf. Summulae, topic II, b, 29; Dialectica, topic II, 12. 56 See Appendix VII, Example 2. There were several sources from which Copernicus might have adopted the expression machina mundi. In chapter seven, we noted Bessarion’s use of the expression. Baroncini, “Note,” 12–18, cites over a dozen relevant passages, including one from Lactantius, Divinae institutiones 2, 5, 7–37, a passage where Lactantius also refers to God as artifex mundi. Rosen, Commentary, 359, to 22:7, also refers to Lactantius for Copernicus’s expression visibilem Deum.

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any circles whatever (G), Copernicus contends by virtue of the topic from authority and, he implies, out of fairness (W), that he too should be permitted “to ascertain whether explanations sounder than those of [his] predecessors could be found for the revolution of the celestial spheres on the assumption of some motion of the earth” (C).57 By attributing certain motions to the Earth (G), by intense study, correlation of the motions of the other planets with the orbiting of Earth, and by computation (W), Copernicus finds that the otherwise incidental observations follow necessarily and naturally (C). The final argument of a substantive nature is this: Because “the order and size of all the planets and spheres, and heaven itself is so linked together” (G), by virtue of the topic from an integral whole (W), it follows “that in no portion of it can anything be shifted without disrupting the remaining parts and the universe as a whole” (C).58 After this argument in the Preface, Copernicus describes the order of De revolutionibus, in which he seems to be telling the reader that he adopted the topic from the whole, more specifically from an integral whole, as a model for the book:59 Accordingly in the arrangement of the volume too I have adopted the following order. In the first book I set forth the entire distribution of the spheres together with the motion which I attribute to the earth, so that this book contains, as it were, the general structure of the universe. Then in the remaining books I correlate the motions of the other planets and of all the spheres with the movement of the earth so that it may thereby determine to what extent the motions and appearances of the other planets and spheres can be saved if they are correlated with the earth’s motions.

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Revolutions, 5. Revolutions, 5. See Appendix VII, Example 3. 59 Revolutions, 5. On the importance of this topic at Cracow, see Chapter 3. Copernicus’s use of the topic from an integral whole is constructively valid and destructively invalid. His evaluation of from an integral part is constructively invalid and destructively valid. On the other hand, he does speculate that gravity is a tendency implanted in all bodies in the universe, a constructive application of part to whole. This is strong evidence for concluding that the whole, as Copernicus understands the cosmos, is a heterogeneous, not a homogeneous, whole. Furthermore, his conception of cosmos indicates that he regarded it as an integral and essential quantitative whole. As an artifact of the divine Artisan, the cosmos possesses as its foundation a design and an idea of construction. For details and precedents, see Burkhardt and Dufour, “Part/Whole I,” 663–673, esp. 669–671. 58

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He hopes that astronomers will examine his derivations, and he seems optimistic that if they do so, they will agree with him. He concludes the Preface with remarks suggesting why he dedicated the book to the Pope. It seems that Copernicus anticipated Scriptural objections, and was trying to fend off theological objections and perhaps even censure. He dismisses objections based on Scripture bluntly as incompetent, but he softens the blow by also suggesting that his work may contribute to reform of the ecclesiastical calendar. Copernicus was apparently aware that in the past some medieval authors had considered the motion of the Earth, but in the absence of observational proof and in the face of Aristotelian natural philosophy, they had allowed Scripture to settle the matter.60 In other words, passages in Scripture were admitted as legitimate warrants supporting the conclusion that the Earth is stationary at or near the center of the universe. In the conclusion of the Preface, Copernicus challenges the legitimacy of using passages from Scripture as warrants for conclusions in astronomy and natural philosophy. Passages from the Bible are irrelevant. To propose a major change in a discipline requires an author to use the warrants accepted by contemporary experts, but it is virtually impossible to propose such a change without also challenging the legitimacy or relevance of some warrants. Throughout the Introduction to Book I (analyzed in detail below), Copernicus uses some warrants in an uncontroversial way, but he also reinterprets others or applies them in an original way, and there are yet others that he replaces or dismisses altogether. He uses rhetoric to frame the argument, which itself relies on dialectical topics, the warrants acceptable in natural philosophy and astronomy, and the geometrical means available to mathematicians allowing them to show that the observations or results are consistent with the hypotheses. The discursive strategy adopted by Copernicus is to frame dialectical arguments in a rhetorically persuasive humanistic style. By means of rhetoric Copernicus provides the structure and motives for the arguments. In the arguments Copernicus arranges the objections, evidence, and warrants supporting the conclusion, in the first half of the

60 Nicole Oresme is the best-known example, but direct acquaintance with Oresme’s works, especially one written in French (Livre du ciel et du monde), is difficult to prove. On the other hand, Copernicus may have heard of Luther’s reaction to his proposal even before the work appeared. On Luther’s remarks, see Norlind, “Copernicus and Luther,” 273–276.

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Preface, that the Ptolemaic theory has failed to elicit the structure of the universe and the commensurability of its parts. That conclusion, in turn, leads to the more satisfying solution provided by the heliocentric view, according to which the observations follow naturally and necessarily from the observations with the parts arranged commensurately in the structure of the whole. Copernicus achieves this conclusion by the blending of rhetorical persuasion, poetic image, aesthetic pleasure, theological ethos, mathematical consistency, and the use of dialectical topics. Some have suggested that the aesthetic dimension of Copernicus’s arguments excludes epistemic claims.61 But this is a mistake. The aesthetic dimension involves structure and coherence, both of which provide Copernicus some justification for believing in the truth of his principal hypotheses. Furthermore, the claim that some observations follow naturally (not in an ad hoc manner) is an epistemic claim.62 The further study and understanding of Copernicus’s discourse requires attention to all of these techniques and strategies. 6. The Rhetorical Framework of Book I In the 1543 edition of De revolutionibus, Copernicus or Rheticus suppressed the Introduction that is found in the holograph. After Copernicus wrote the Preface in 1542, he and Rheticus may have felt that the Introduction was redundant, and perhaps also realized that its tone was not entirely consistent with that of the Preface. The aesthetic and moral appeals of the Introduction follow Ptolemy in part and seem almost pagan by comparison, whereas the Preface is clearly addressed to a clerical-humanist audience. Despite its suppression, I examine it here because it does reveal important motives at an earlier stage of composition.

61 Kokowski, Copernicus’s Originality, 8, tries to force an either-or choice between aesthetic criteria and epistemic criteria in support of his claim that Copernicus’s criteria were exclusively epistemic. 62 McMullin, “Rationality,” 55–78, esp. 70–75, where McMullin argues that “naturalness,” that is, coherence is epistemic, not aesthetic. In explaining his statement, however, he says that coherence is not just a matter of taste, suggesting that it is partly aesthetic but primarily epistemic, for the claim is that “a theory that makes causal sense of a whole series of features of the planetary motions is more likely to be true than one that leaves these features unexplained.” Compare with Kokowski, who cites McMullin to deny that coherence is aesthetic at all.

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Copernicus begins the Introduction by reminding the reader of the motives for studying astronomy—it is an appeal to the entire tradition of classical learning and its appreciation for mathematics and astronomy in the formation of the liberally educated individual. Copernicus portrays himself as part of this tradition, and he affirms his desire to continue this tradition, putting himself at the service of its noble tasks, which includes bringing astronomy closer to perfection and completion, not overturning and destroying it.63 As is well known and as we have tried to elucidate by focusing on the dialectical strategies adopted by Copernicus, he placed great emphasis on such criteria as harmony, symmetry, and commensurability. These criteria have been interpreted primarily as aesthetic in nature, and thus as appealing primarily to the emotions in a rhetorical fashion. As a result, Copernicus’s arguments tend to be dismissed as not strictly rational. The aesthetic role of ideals of harmony in astronomy has been a commonplace theme, but one of those commonplaces that we somehow have not adequately fathomed. The relation between ideas of harmony and science seems mysterious and even mystical, and so the connection has remained elusive, unpersuasive, and unsatisfying, at least from a modern scientific and secular point of view. By coming to grips explicitly with the rhetorical purpose of Copernicus’s turn to traditional ideals and his exploitation of aesthetic design, we can elucidate the role that dialectical argumentation plays in Book I. He used dialectic to persuade astronomers and philosophers that his proposals will achieve the goals set by Ptolemaic astronomers that their methods have failed to achieve. We mean many things when we refer to “aesthetics.” In using the term, we are usually referring to something that we regard as possessing beauty, elegance, and simplicity. We are also often thinking of the mental pleasure that comes from solving problems in an elegant way. By extension we may mean the realization, wonder, and recognition at having found some new understanding of what we always knew but had never quite appreciated completely, that is, the sense of having plumbed the depths of some vast mystery. At the same time, Copernicus claimed to have solved an age-old problem in a way that achieved its goal. We may also reflect on the peace of mind that may accompany the completion or perfection of a work, as if somehow

63

Compare with Moss, 49–51.

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a restless energy has found its fulfillment. It is, I think, fair to say that Copernicus was motivated to construct an astronomical system that was well composed and well organized, that mirrored the perfect, complete, and unified whole that is the universe, as a product fitting of a divine artisan.64 It is striking, by contrast, to read the opening paragraphs of the Introduction. While appealing to the liberal tradition of learning and reminding us of its goals, Copernicus seems anxious to allay the fears that his proposals would, he knew, engender. His solution was frightening to some. In an age of violent reform, even Luther of all people complained that Copernicus was just another innovator who would turn the whole art of astronomy upside down.65 To such, Copernicus’s ideas threatened destruction and fragmentation. His vision implied to many that the universe was possibly boundless and hence with no true center. In solving one major and long-standing problem, Copernicus was creating another that perhaps had no solution because the universe that emerged from his mind might be devoid of wholeness and meaning altogether. For Copernicus, then, it did not go without saying; rather, he had to affirm his continuity with the tradition, with the traditional vision of a finite universe that was a complete and unified whole, and above all with the fulfillment of traditional goals. Indeed, to judge by the recent standard accounts of the Copernican Revolution, Copernicus was entirely successful in his effort to persuade readers that his vision was traditional and conservative.66 By using such language, I do not mean to imply that Copernicus was insincere. His affirmation of traditional beliefs seems genuine. Still, the structure of his text reveals the following pattern: proclamation of traditional goals followed by enumeration of the shortcomings of Ptolemaic astronomy. The contrast could hardly be clearer. Throughout Book I, the pattern is agreement 64 As Danielson, First Copernican, 74–76, emphasizes, there is a similar tone in Rheticus’s Narratio linking the metaphor of harmony, poetic metaphors, and musical analogy to scientific models. 65 On Luther’s reaction, see Norlind. One can get a picture of the anxiety provoked by Copernicus’s proposal in the sixteenth and seventeenth centuries in Crowe, Theories, 174–188. 66 See, for example, Swerdlow and Neugebauer, Mathematical Astronomy, 1: 54–64 and 70–85. Of course, Swerdlow’s judgment reflects his understanding of the technical mathematics in Copernicus and his predecessors; still, such focus tends to minimize the broader cosmological impact of Copernicus’s hypotheses.

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with what is right in Ptolemy, compared with what has failed and does not fit. When he proposes his own solution, the contrast, then, is with what succeeds and does fit. The suggestions that follow are neither exhaustive nor exclusive of other explanations. They expose the logic of Copernicus’s arguments without excluding other readings and possible sources. They confirm that Copernicus was attentive to the logical strategies that could move a reader to assent. What we may observe is that many of the dialectical topics summarized above have counterparts among the rhetorical topics. This observation suggests that the differences between some dialectical and rhetorical topics depend on their purpose and function. Aristotle saw rhetoric as the counterpart of dialectic—rhetoric aims specifically at persuasion while dialectic provides the strictly logical arguments.67 Throughout the Rhetorica Aristotle refers the reader to the Topica.68 Later in Book I, Aristotle says of rhetoric that it is an offshoot of both dialectic and ethical studies.69 The context here suggests that because its aim is persuasion, the purpose of rhetoric is not only speculative but also practical. The division of rhetoric into political, forensic, and ceremonial seems advisory more than scientific, that is to say, someone writing a political speech, for instance, would do well to follow Aristotle’s advice. In analyzing a text, however, we may not find the same distinctions very helpful or illuminating. In whatever way we use the Rhetorica, we may observe that the lengthy enumeration of

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Aristotle, Rhetorica I, 1, 1354a1–15. For modern interpretations of Aristotle on the relation between dialectic and rhetoric and on enthymemes, see van Eemeren and Houtlosser, Dialectic and Rhetoric, 3–11. Note the editors’ comment related to Aristotle’s adoption of the term enthymeme to refer to rhetorical proof, 10. I paraphrase their very complicated formulation. Authors take a perspective that is primarily dialectical when they advance arguments in order to resolve a difference of opinion, and adopt a procedure to test the acceptability of the opinion at the core of the difference in terms of its tenability in the light of critical reactions. Authors take a perspective that is primarily rhetorical when they view the argument as aimed at achieving agreement by having the audience agree on the acceptability of the opinion. “In this way in the former case the resolution of the difference of opinion is firstly associated with the dialectical aim of valuing opinions and in the latter case with the rhetorical aim of creating consensus.” It is clear that Copernicus tried to achieve both aims. 68 There are at least ten explicit references to the Topica in the three books of the Rhetorica. 69 Rhetorica I, 2, 1356a20–30.

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twenty-eight topics in Book II is very reminiscent of several topics in the Topica, and so confirms the close relationship between the two.70 Although Renaissance authors like Valla and Agricola reacted against scholastic academic structures, in some respects they seem more faithful to the spirit of Aristotle’s reflections on rhetoric and dialectic. Their blending of the two suggests that they adopted a point of view similar to Aristotle’s, whether they saw themselves as Aristotelian or not. Later readers like Caesarius and Melanchthon, just to mention two prominent examples, found Agricola’s ideas on dialectic and rhetoric consistent with Aristotelian logic. In a similar way, Copernicus saw himself as an interlocutor in ancient traditions, Ptolemaic and Aristotelian. As he adopted their goals and methods, he simultaneously adapted them to new ends thus transforming the traditions to which he was contributing. 7. The Use of Topics in Book I As we proceed, then, to analyze Book I of De revolutionibus, we will suggest the topics that seem to link grounds and conclusions and the arguments themselves together, keeping in mind that they may serve a rhetorical function or a dialectical function or both. For the Introduction, I use the same scheme as I did for the Preface—ground (G), warrant (W), and claim (C). The ground and claim are taken from Copernicus’s text. Where the warrant is also in the text, it is in parentheses (W), but where I supply what appears to be the warrant linking the ground to the claim, it is in square brackets [W]. Because heaven is the most beautiful natural thing (G), by virtue of its position close to God and its nearly divine disposition [W], it is the most deserving to be known (C). Almost all of the other branches of mathematics support it (G), by virtue of the relation of function or purpose [W] astronomy represents the consummation of mathematics, the summit of the liberal arts, and the most worthy of a free man (C). Because all of the good arts serve to draw man’s mind away from vice and lead it to better things (G), by virtue of its higher position [W], astronomy can perform this function best (C). Because contemplation of the best stimulates one to do the best and to admire the

70

Rhetorica II, 23, 1397a7–1401a1.

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Maker of everything (G), by virtue of efficient cause [W], we achieve extraordinary intellectual pleasure and are made glad (C). Because mathematics and astronomy confer great benefit and adornment on the commonwealth (G), we may appeal to authority [W], where Plato commends it to keep the state alert and attentive to festivals and sacrifice, as necessary for the teacher of higher learning, and to become and be called godlike (C). Principles and assumptions (hypotheses) have been a source of disagreements, many observations do not agree with Ptolemy’s predictions, and the aids assisting our enterprise have grown with time (G). We may thus conclude from the progress that has been made [W], that we may still through our efforts bring astronomy to perfection (C). The warrants in the Introduction seem to be rhetorical for the most part. As we noted above, the assertions here are intended to assure readers of Copernicus’s conservatism. Copernicus draws on his reader’s belief in God, on recognition of the importance of mathematics for training the mind, on the traditional aim of perfecting the science over time, and on the relation of this activity to the achievement of self-perfection. He intends all of these appeals to make the reader sympathetic to his efforts. There is a hint of the idea that bringing astronomy to perfection may require a radical move, but for the most part the Introduction is reassuring, not threatening. Having established a reassuring mood, Copernicus maintains that mood for the next four chapters. He does so by following the structure of Ptolemy’s own introduction, drawing on the ideas in Ptolemy that Copernicus supports, again providing at best only a hint of how he will bend these to his own purpose. In concluding in Chapter 1 that the universe is spherical (C), Copernicus appeals, it seems, to common wisdom [W], in citing a variety of metaphysical, physical, and mathematical grounds. A sphere is the most perfect form and a complete whole, a sphere is the most capacious or efficient of geometrical solids, all have observed the universe to be of this shape, and wholes strive, as it were, to be circumscribed in a sphere (G). Chapters 2 and 3 confirm the conclusion that Earth is a sphere (C). The conclusion is based empirically [W] on well-known observations (G), for example, standard astronomical observations, observations of Earth’s curvature made on ships or of approaching ships as seen from a coast, the fact that water flows downward and forms a single sphere with Earth.

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There is a note of progress in Chapter 3 with respect to new geographical knowledge, but it is expressed so subtly as to be more re-assuring than alarming. Spanish and Portuguese explorers have corrected and added to Ptolemy’s Geography, which Copernicus uses immediately to support his conclusions: that land and water together press upon a single center of gravity; that the earth has no other center of magnitude; that, since earth is heavier, its gaps are filled with water; and that consequently there is little water in comparison with land, even though more water perhaps appears on the surface.71

It is, however, tempting for us to see in this correction of Ptolemy an additional (though suppressed) argument: If Ptolemy was wrong about the geography of Earth (an object close enough to us to test claims about it), then why could not Ptolemy be wrong about astronomy? Just as new explorations have added to and corrected Ptolemy’s understanding of geography, so, we may see Copernicus implying, can we add to and correct Ptolemy’s astronomy. After he draws his conclusions about Earth and water, Copernicus concludes Chapter 3 by listing and correcting all of the errors made by the most prominent ancients about the shape of Earth. Chapter 4 affirms Copernicus’s commitment to circular motion (C) as the motion most appropriate or proper to (W) a sphere and its form (G). There are several variables, such as direction, size, etc., with each sphere possessing a circular motion proper to its shape. In some cases, we must imagine circular motions compounded of several circles (C), because their “nonuniformities recur regularly according to a constant law” (G), which would not happen unless their motions were circular, “since only the circle can bring back the past” (W).72 Copernicus hints at some discomfort here, for he takes it as established that “a single heavenly body cannot be moved by a sphere nonuniformly,” and supports the commonly accepted view with a counterfactual argument. If there were such non-uniformity in the motion of a sphere, “it would have to be caused either by an inconstancy . . . in the moving force or by an alteration in the revolving body.”73 71

Copernicus, Revolutions, 10. Copernicus, Revolutions, 11. See Appendix VII, Example 4, for the general form of the argument. In this case the warrant appears to be a premise that links two extreme terms by means of a middle term. 73 Copernicus, Revolutions, 11. 72

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From these considerations (G), it follows from geometrical principles [W] that their uniform motions appear non-uniform to us (C). There can be by virtue of geometrical principles [W] two causes of this result (C), the circles of the heavenly bodies may have poles different from Earth’s or Earth is not at the center of the circles about which they revolve (G). Observation (G) shows us by measurement [W] that the distances of objects from the observer vary (C). This variation (G), in turn, makes their motions appear unequal in equal times (C) as a result of geometrical principles [W]. We must, then, examine the relation of Earth to the heavens carefully (G); otherwise we may make the error of attributing to the heavens what belongs to Earth (C) by violating the rule that permits only a negative inference from part to whole [W]. That is to say, the error here would be to attribute to the whole what belongs only to one of its parts.74 Copernicus, we may see in retrospect, is easing the transition to the idea that Earth moves. The structure of these chapters corresponds roughly to the first three postulates from his earliest known work on this subject, the Commentariolus. The first four chapters of Book I show us how Copernicus’s argument improved since that first effort from around 1510. With Chapter 5, Copernicus makes his first proposals about the motion and position of Earth. Earth is a sphere (G), so we must ask whether its shape as a sphere entails (W) its motion in a circle (C), and what place it occupies in the universe (C´). The reason, Copernicus seems to imply, is that spheres, as we have seen [W], can occupy any place in the universe (C). Copernicus knows, of course, what the common-sense view is, but he urges his reader to be open-minded to seeing that the problem has not yet been solved. On the correct answers to the questions about the Earth’s motion and position depends the correct explanation of what is seen in the heavens. The next paragraph reminds the reader of the familiar principle of relativity and applies it to the observation of daily rotation. Already here, Copernicus suggests that Earth’s rotation on its axis (G) would account for the observation of daily rotation (C). He challenges the reader to consider why motion should not be attributed to the enclosed

74 These are complex examples that involve a topic proper to natural philosophy (relativity of motion) and the topic from the part. See Appendix VII, Examples 5a and 5b. These arguments are linked together with the argument in Example 6 below.

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rather than to the enclosing [W], to the thing located in space rather than to the framework of space [W]. He cites several ancient authorities [W] in support of the hypothesis.75 In the previous arguments, Copernicus raised doubts about whether the part moves or the whole moves. With this argument he now provides a reason why we should attribute motion to the part rather than to the whole. The next question concerns Earth’s position in the whole universe and in relation to the Sun and planets. As for the sphere of the fixed stars, its distance is so great (G) as to make Earth’s distance from the center (C) insignificant by comparison (W). Earth’s variable eccentricity in relation to the Sun and planets (C) has been demonstrated observationally and mathematically (G) by measurement and geometrical reasoning [W], so the only serious question is whether the explanation is that only the planets approach and withdraw or that Earth approaches to and withdraws from them. In other words, the suggestion following from the above observations (G) is that aside from daily rotation, Earth would move as a planet among the planets (C), as the authority of Philolaus (and Plato) confirms (W).76 This argument now challenges the reader to accept Earth’s orbital motion as an explanation for the variation of Earth’s eccentricity and distances in relation to the Sun and planets. But many believe it possible to prove by geometrical reasoning [W] that Earth is in the middle of the universe (C), serving as a center, relatively speaking, and is motionless (C' ) because when a body rotates, the center remains unmoved and things nearest to the center move most slowly (G). With Chapter 6, Copernicus begins his refutation of the commonsense view by attacking the warrants or principles used to confirm Earth’s centrality. Because the universe is so immense and the size of Earth is a point in relation to it (G), it is impossible to say whether Earth is the exact geometrical center of the universe. If we cannot prove that it is the center (G), then we cannot prove that it is at rest in the middle.

75 See Appendix VII, Example 6. The warrant in this example appears to be a topic proper to metaphysics, namely, ontological superiority or dignity. 76 This argument now challenges the reader to accept Earth’s orbital motion as an explanation for the variation of Earth’s eccentricity and distances in relation to the Sun and planets. See Appendix VII, Example 7. The entire series of arguments appears to rely on the topic from the whole, a warrant that is proper to natural philosophy (relativity of motion, and an application of the principle of economy).

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That an immensely vast universe should rotate in twenty-four hours is more astonishing (W) than a rotation of a small body like Earth. Because they were unable to provide observational and mathematical proof, the ancients resorted to physical arguments to prove that Earth is at the center. Copernicus summarizes these arguments in Chapter 7. The arguments are standard Aristotelian claims based on the absoluteness of Earth’s heaviness and on the association between heaviness and simple rectilinear motion. The “natural” motion of a heavy body is rectilinear and downwards towards the center of Earth. Any motion of a heavy body contrary to rectilinear or down (upwards, sideways, circular) is contrary to nature or “violent.” The rotation or circular motion of a heavy body like Earth, then, would be violent and contrary to nature. Chapter 8 refutes these arguments and shows them to be inadequate. Copernicus’s response is a masterpiece of dialectical reasoning. If Earth does in fact rotate (G), reasons Copernicus, then surely someone would regard its circular motion as natural (C). What is natural has natural effects, namely, they are well ordered and preserve Earth in its best state (W). What is violent would have violent effects and eventually would cause disintegration. If Earth does rotate, and rotation is its natural motion, then Ptolemy need not have feared the consequences.77 The point here is that what is called “natural” depends on identifying or defining the nature of a thing correctly. If Earth in fact rotates, then rotation is natural to it. How Earth in fact behaves must be determined before we can conclude what its nature is and what is natural to it. Rather than worry about the motion of tiny Earth, Copernicus chides Ptolemy, why was he not more worried about the motion of the heavens? It must be very swift, so swift in fact that we would expect it to be driven by centrifugal action farther and farther to infinity and so would its speed, then, also have to increase to infinity. But, as we all know from Aristotelian physics, the infinite cannot be traversed or moved in any way (W), so it follows that the heavens must be stationary (C).

77 The warrant here appears to be the topic from the cause. See Appendix VII, Example 8.

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There are several other questions about whether the heavens and the universe are finite or infinite, which lead to more questions that are better left to natural philosophers to discuss. Copernicus seems to imply here that trying to answer empirical questions by reasoning alone does not settle the questions.78 We can perhaps settle questions about Earth. The principle of relativity shows us that the motion of Earth accounts for observations of the heavens. Can its motion account for other observations? The motions of clouds, air, or falling bodies would be affected by Earth’s axial rotation (G), but we can assume that objects close to Earth share in Earth’s motion and move with it (W). The motion of rising and falling bodies would be compounded of both circular and rectilinear motions (C). Rectilinear motion, far from being natural, is the motion that we attribute to bodies that have been thrust from their natural place: Therefore rectilinear motion occurs only to things that are not in proper condition and are not in complete accord with their nature, when they are separated from their whole and forsake its unity.79

Rectilinear motions are not simple, constant, and uniform, but change— accelerating or decelerating according to variable circumstances. Circular motions are uniform and eternal, but rectilinear motions vary and are limited, for when a body reaches its natural place, it is no longer heavy or light, and its motion stops. Circular motion belongs to wholes, rectilinear motion to parts, and they are relative to one another. Immobility is nobler and more divine than change and instability (G), and what has greater dignity should be the least moved (W), hence it makes more sense to attribute motion to Earth than to the universe (C). It is more absurd to attribute motion to the framework of space (G) or to what encloses the whole of space than to that which is enclosed and occupies some space (W), and so it makes more sense to attribute motion to Earth (C). Finally, the planets approach Earth and recede from it (G), which means that if Earth were the center, then the planets move at times

78 If this is what Copernicus meant to suggest here, it is an objection that could be raised against his own speculations. What is more, Copernicus dismisses or sets aside the physical questions as ones that perhaps can be settled only after the correct framework is adopted. 79 Copernicus, Revolutions, 17.

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away from and at other times towards the middle. Variations in distance argue against the Earth in the middle [W]. It makes more sense, then, to understand “motion around the middle” in a more general way, namely, as a motion that encircles its own center (C): You see, then, that all these arguments make it more likely that the earth moves than that it is at rest. This is especially true of the daily rotation, as particularly appropriate to the earth. This is enough, in my opinion, about the first part of the question.80

Because nothing prevents Earth from moving (G), we can consider in Chapter 9 whether it has other motions and can be regarded as one of the planets.81 Earth is not the center of all of the revolutions (G). The non-uniform motions and varying distances of the planets indicate this (W). There are many centers, a fact that leads us to ask whether the center of the universe is identical with the center of terrestrial gravity or with some other point (C). Gravity, in fact, seems to be a quality proper to all spheres (G), some tendency placed in them by God (W) that gathers the parts together into a unity and a whole in the form of a globe (C). The other observed motions are also relative. If Earth has an orbit around the Sun (G), then, according to the principle of relativity [W], the appearances of the daily rising and setting of the stars, Sun, Moon, and planets would be the same (C). The retrograde motions of the planets are not proper to them (C' ) but an effect of their proper motions (G) relative to Earth’s motion [W]. It will then be seen that the Sun occupies the middle of the universe (C" ). All these facts are disclosed to us by the principle governing the order in which the planets follow one another, and by the harmony of the entire universe, if only we look at the matter, as the saying goes, with both eyes.82

80 Copernicus, Revolutions, 17. See Appendix VII, Example 9. The warrant here is the fundamental hypothesis of ancient astronomy accepted by Copernicus. 81 In Narratio prima, Rosen tr. 148, Rheticus refers to Aristotle, De caelo II, 14: When one motion is assigned to Earth, it may properly have other motions. Aristotle was referring to the assumption of its orbital motion and its shared diurnal motion with the starry vault, and objects that its proper motion would then be along the ecliptic, not the equator. Despite the conclusion, Copernicus may have been leaning on Aristotle here in moving from consideration of one motion to other motions. 82 Copernicus, Revolutions, 18. See Appendix VII, Examples 10a and 10b.

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Copernicus’s procedure in using the available facts to answer the questions about Earth’s position and its motions is to analyze the order of the heavenly bodies and to use the available clues. He has assumed from the outset that a question about a part can be answered affirmatively only by establishing the order of the whole [W]. From the existence of the order of the whole we can infer the order of one of its parts.83 Everyone agrees that the fixed stars are the farthest, followed by Saturn, Jupiter, and Mars. The planets were arranged (C) according to the duration of their revolutions (G) on the assumption that duration corresponds to the size of the orbit (W). Therefore, those that take the most time are probably the farthest (C). With respect to Mercury and Venus, however, there are differences of opinion, because these planets exhibit bounded elongation from the Sun. Copernicus recounts the different arguments that have been proposed. Plato’s opinion is based on observational considerations, such as the failure to observe phases and eclipses, which support the opinion that Mercury and Venus must be above the Sun. Ptolemy’s opinion is based on the vast space that is left between the Sun and Moon if the first opinion were correct. Because such a space seems unfitting, Ptolemy placed Mercury and Venus between the Sun and Moon. The failure to observe phases and eclipses is explained by the following assumptions. These planets are not opaque and so would not exhibit phases and would not eclipse the Sun and, anyway, they are so small in comparison to the Sun, they are not visible against the bright light of the Sun. Even these conclusions, however, mean that Venus has a huge epicycle, which raises again the objection against a vast empty space. Ptolemy’s argument that the Sun must move in the middle between the planets that show every elongation from it (Saturn, Jupiter, and Mars) and those that do not (Venus and Mercury) is unpersuasive. The Moon too shows every elongation from the Sun, yet Ptolemy did not place the Moon in an orbit beyond the Sun. As for those who locate Venus and Mercury below the Sun in a different order around Earth, they violate the principle based on the

83 Although he expresses the point differently, Rose, Italian Renaissance, 127–129, also emphasizes the connection between the principle of uniformity and the idea of a well-ordered universe.

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duration of the orbits. If they are correct, then only two alternatives are left—either Earth is not the center of the heavenly spheres or there is no principle of arrangement. (Copernicus suppresses the conclusion here that because there is a principle of arrangement, then Earth cannot be the center of the heavenly spheres.) Copernicus turns to the Capellan arrangement (W) to support the notion that Mercury and Venus orbit the Sun, thus explaining the observations of their bounded elongations. If we link Saturn, Jupiter, and Mars to the Sun, and that they are nearest to Earth when in opposition to the Sun and farthest when in conjunction with the Sun (G), then the Sun seems to be the body around which all of the planets execute their revolutions (C).84 This arrangement also yields a vast space between Mars and Venus, which is large enough to contain both Earth and its Moon (G). Copernicus at last bites the bullet and proposes that Earth with its Moon makes an annual revolution around the Sun (C' ). Here Copernicus appeals to the principle of economy or simplicity (W)85 to argue for the conclusion that many of the observed motions thought to be proper to the stars, planets, and Sun can be reduced to the effects created by the motions of Earth (C" ). Copernicus realizing that the conclusion is shocking turns immediately to the first principle accepted by virtually everyone, namely, that the sizes of the spheres correspond to the durations of their revolutions (G). From that commonly accepted view he establishes their order beginning with the highest: the fixed stars, Saturn, Jupiter, Mars, Earth and Moon, Venus, and Mercury with the Sun near the center or, as he puts it, in the middle of everything (C). With the fixed stars and Sun immovable, the ordering principle is the sidereal period of the planets around the Sun (W). That principle establishes the order of the

84

Copernicus clearly recognized that the Capellan arrangement also explained the observation of bounded elongation, but it also would explain their retrograde motions. Copernicus’s models for the superior planets required small epicycles (epicyclets) to make them more accurate and to account for their motions in latitude, but his focus here is on the architectonic structure of the whole and the principle of arrangement of the whole, not on the possibility that an effect may be explained by introducing an ad hoc assumption. He does not use the epicyclets to account for retrograde motion. The planets move on the epicyclets in such a way as to generate a slightly oval orbit. For Venus and Mercury, in De revolutionibus, he uses eccentreccentrics rather than epicyclets. 85 He does not use the principle here to argue for a reduction in the number of circles or spheres.

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whole, from which we may determine the order of any part [W]. The ordering also enables us to explain (G), not just describe or merely account for, the observed retrograde motions of the other five planets and the observed bounded elongations of Mercury and Venus (C). Left with the failure to observe stellar parallax, Copernicus can only suppose that the fixed stars must be much farther than anyone had ever imagined before (G). This huge gap with its vast space is a problem, but as with the twinkling of the stars, he argues that there had to be a great difference between what moves and what does not (W) in order to distinguish the planets from the stars (C). “So vast, without any question, is the divine handiwork of the most excellent Almighty.”86 It appears that Copernicus accepted the view of numerous late mediaeval philosophers that the principle of economy does not necessarily apply to God and his creative activity. Elsewhere in Revolutions Copernicus also makes arguments and uses dialectical topics. Probably the most controversial involve claims about the truth of alternative models. In these cases he was relying on the topic from division, but in retrospect we can now see that he was optimistic to think that the alternatives were exhaustive. In fact, we shall see in chapter ten that Copernicus was not always certain which hypothesis or model was correct. 8. Hypotheses in Copernicus’s Method In chapter ten I will examine Copernicus’s hypotheses in the context of his cosmological principles and mathematical models. Here I focus briefly on the logical and methodological issues. Copernicus, I have argued, read and annotated Ficino’s translation of Plato’s Parmenides. That dialogue in particular impressed Copernicus with the method of dialectical inquiry regarding hypotheses. Genuine philosophers must test all of the main theories and hypotheses affirmatively and nega-

86 Copernicus, Revolutions, 22. See Appendix VII, Examples 11a and 11b. In these linked arguments Copernicus draws the connection between distances and periods by appealing to natural explanation as opposed to a merely ad hoc account of observations. See Rheticus, Narratio prima (Rosen tr. 138) for emphasis on the absolute system and (187) on Copernicus’s reluctance to depart from ancient philosophers except for good reasons and when the facts themselves coerced him. See also Rose, Italian Renaissance, 127.

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tively for all of their consequences, selecting only those that are sound and rejecting those that are inconsistent with the sound hypotheses. Copernicus understood that the ancients distinguished hypotheses that they believed to be true from ones they assumed for the purpose of demonstrating the appearances. The ancient principles and hypotheses that they regarded as fundamental and true include principles of uniform and circular motion, geocentrism, geostability, and the circular motion of the fixed stars. In his famous “Letter to the Reader,” Osiander in speaking of the “novel hypotheses” of Copernicus’s work referred explicitly to the Earth in motion and the Sun at rest. Osiander departed from Copernicus in conflating these hypotheses with mathematical models as all imaginary and fictitious. Osiander claimed to regard the geometrical hypotheses of the ancients as equally fictitious. Yet Osiander was silent about the geocentric hypothesis, which he implicitly took for granted, not on philosophical grounds, but on scriptural grounds, for only in revelation, he asserted, do we find anything certain.87 Copernicus accepted the principles of uniform, circular motion, but rejected the others as false because from those assumptions his predecessors failed to deduce the structure of the universe. Other hypotheses, however, clearly refer to the devices of the geometrical models. In geometrical contexts, Copernicus referred consistently to the hypotheses of circles by means of which the ancients demonstrated the appearances. In their demonstrations, he alleged, they omitted something necessary or essential and admitted something extraneous and wholly irrelevant. “The necessary and essential that they omitted” probably refers to one or more of the fundamental propositions of natural philosophy. The extraneous and irrelevant refer most likely to a mathematical model that violates a fundamental hypothesis. The word translated as “extraneous” is alienum, exactly the word he used to criticize the models that have the epicycle center moving uniformly on an extraneous circle (in circulo alieno). Although we have been chastised by modern mathematical experts for misunderstanding the technical issues here, Copernicus said and repeated on several occasions that the defect in the ancients’ assumptions was that their hypothesis of combinations of circles was neither suitable enough nor adequate (IV, 2). The principal example that he provides is always of the same sort,

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namely, while they claim that the motion of the epicycle’s center is uniform around the center of Earth or some other point, it is nonuniform on its own eccentric:88 Therefore, the epicycle’s motion on the eccentric described by it is nonuniform. But if this is so, what shall we say about the axiom that the heavenly bodies’ motion is uniform and only apparently seems nonuniform, if the epicycle’s apparently uniform motion is really nonuniform and its occurrence absolutely contradicts an established principle and assumption? But suppose you say that is enough to safeguard uniformity. Then what sort of uniformity will that be on an extraneous circle on which the epicycle’s motion does not occur, whereas it does occur on the epicycle’s own eccentric?

So here he refers explicitly to the violation of an axiom, an established principle and assumption.89 His solution is to propose another arrangement or system of circles that he claims does not violate the axiom. I will return to the technical issues in chapter ten with a discussion of Copernicus’s “hidden” equant, but I proceed here with the recitation of Copernicus’s comments. One of the principal achievements of Book V is to show how the motion of Earth and the motions of the planets account for retrograde motion better than the assumption of motion on an epicycle around a stationary Earth. Here again in recounting the ancients’ theory, he complains that the motion of the epicycle is not uniform around the deferent center but around an extraneous and non-proper center (V, 2: circa centrum alienum et non proprium). He refers explicitly to the case of Mercury, and adds the comment:90 I have already adequately refuted this result in my account of the Moon. These and similar consequences furnished the occasion to consider the mobility of the Earth and other ways by means of which to preserve uniform motion and the principles of the science and to render the account of apparent non-uniformity more constant.

We will have to complete the discussion of mathematical hypotheses and models when we turn to those issues in chapter ten. For now I emphasize the logic of Copernicus’s reasoning and arguments. He

88

Revolutions IV, 2: 176, lines 1–9. It is one thing to conclude that the resultant motion is noncircular and nonuniform but altogether another matter to conclude that the circular motions out of which it is composed are themselves non-uniform! See Revolutions V, 4. 90 My translation. 89

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adopted some hypotheses as fundamental, namely, the uniform, circular motions of the heavenly bodies. He examined and evaluated hypotheses such as geocentrism and geostability for their consequences or results, which, he concluded, were inconsistent with the fundamental hypotheses. That failure provided the license or warrant to consider alternative hypotheses, namely, the mobility of Earth and stability of the Sun. He claims that the results of these hypotheses are consistent with the fundamental hypotheses or principles, and he adds further consequences that provide natural explanations of observed phenomena. We will elaborate on other relevant details in chapters nine and ten, but here we may observe without deeper examination that his proposed hypotheses are natural-philosophical. Their justification depends on their consistency with the fundamental principles and hypotheses of astronomy (uniform, circular motions), and on the relation of the whole to the part. His reasoning depends on architectonic principles that subordinate natural-philosophical hypotheses to astronomical considerations. His argument from whole to part retains a dialectical character for it depends on the greater probability of his architectonic principles. 9. The Logical Issues in the Relation between Mathematics and Natural Philosophy In the previous section we alluded to the subordination of some natural-philosophical hypotheses to mathematical and astronomical hypotheses. When his contemporaries accused Copernicus of ignorance of logic and natural philosophy, and complained that his hypotheses threatened to turn the whole art of astronomy upside down and throw the liberal arts into confusion, they recognized that Copernicus had reversed the relation between mathematics and natural philosophy. Robert Westman has interpreted this reversal, rightly in my view, as the revolutionary move in the Copernican theory.91 I am not persuaded, however, that Copernicus intended this reversal as a general methodological principle. In other words, it was not his view that all natural-philosophical principles are to be subordinated to

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Westman, “Astronomer’s Role,” 105–147.

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mathematical ones. In this section, I explore the logical background of this reversal, and I propose to identify the limitations or qualifications that Copernicus adopted in selecting those cases in which the reversal was legitimate as opposed to those that were not. Again, the main idea here is that he examined hypotheses for their conformity with more fundamental and sound hypotheses, rejecting hypotheses whose consequences were not consistent with the more fundamental ones.92 We have briefly discussed the Aristotelian background in chapter four on the relation between mathematics and natural philosophy. Aristotle set restrictions on the transition from one discipline to another in the prohibition of illicit metábasis. Metábasis means “transition,” and Aristotle objected to an illicit transition in a proof from one genus or species to another, based usually on ambiguity, which leads to fallacious arguments. Aristotle considered most, but not all, instances of sliding from one field to another in a proof or demonstration as an example of illicit metábasis. The arithmetical proof of a geometrical proposition is an example that he cited, but he did allow exceptions. In cases where a discipline is concerned with the collection of empirical facts while the other is concerned with discovering the reason for the fact, Aristotle judged the transition to be licit. There are cases where two disciplines are hierarchically ordered, for example, when physics provides the fact and mathematics the reason for the fact.93 In other 92 Rheticus, Narratio prima (Rosen tr. 140) confirms that there was widespread acquaintance with the importance of hypotheses and theories to astronomers, and with the difference between a mathematician and a physicist. Rheticus emphasizes the point that the observations and the evidence of heaven lead to the results, suggesting that God and mathematics will enable us to face and overcome every difficulty. These are ideas that he and Copernicus may have derived from the Neoplatonic tradition in authors like Bessarion and Ficino, both of whom revived a version of the illumination theory. According to such an account, God illumines the human intellect making it possible for us to reach the highest truths and to discover truths about the universe. On Ficino, see Platonic Theology, 4, Books XII–XIV. 93 The usually cited examples, we must however point out, are trivial by comparison with the examples that we find in Copernicus and Galileo. One of the most cited examples is from Posterior Analytics I, 13, 78a31–38 that the distance of stars causes their twinkling and the nearness of the planets causes their non-twinkling. See also Aristotle, On the Heavens II, 8, 290a17–23. Copernicus, in fact, cited this example in his Letter Against Werner, tr. Rosen, Complete Works, 3: 146. The Letter provides more evidence of Copernicus’s acquaintance with Aristotle, primarily to Metaphysics, Physics, and On the Heavens. See Rosen’s comments in his introduction, 134. I have not analyzed this treatise for the logic of its argumentation, because it is a critique of Johann Werner’s treatise, “On the Motion of the Eighth Sphere,” in which Copernicus devotes most of his effort to defending the reliability of Ptolemy’s data. The topics discussed are primarily relevant to questions about Copernicus’s direct acquaintance

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cases, the two disciplines are equal, for example, a geometrical proposition provides the reason why circular wounds heal more slowly than other wounds. In other texts, however, Aristotle suggested that two disciplines remain separate, and that the apparent transition is actually a matter of considering a particular case as primarily physical or primarily mathematical. In the Physics he prohibited the comparison between circular and rectilinear motions as involving an illicit transition because “circular” and “rectilinear” belong to different kinds of things, just as the sharpness of a pencil and the sharpness of a musical tone are incomparable. He may have had the problem of squaring the circle in mind, but his view placed severe logical and ontological constraints on mathematical analysis. Among the most important critics of Aristotle’s prohibition was William of Ockham. Ockham interpreted Aristotle as allowing for the subordination of a mathematical analysis to physical considerations, the subordination of a physical analysis to mathematical considerations, and even the partial subordination of one science to another. The consequence is that Ockham subdued the logical and ontological restrictions on mathematics, making it a suitable instrument for analyzing any problem that can be quantified or clarified logically by means of mathematics.94 There was a time when I thought that Ockham’s critique had survived in late medieval sources that indirectly reached Copernicus. In fact, it appears as if Ockham’s critique, even if adopted by a number of fourteenth-century scholars, fell into neglect. This is not to say that Aristotle’s prohibition disappeared, but later medieval sources suggest that Aristotelians were influenced by developments in mathematics and by the revival of Platonism.95 This leaves us, then, to seek another explanation for Copernicus’s conclusion that some natural-philosophical propositions are subordinate to some astronomical-mathematical ones. The explanation, in fact, is already at hand. Copernicus adopted the assumption about uniform,

with Aristotle’s texts, especially the three mentioned which we discuss further in chapters nine and ten. 94 This argument is developed more extensively in Goddu, “Impact,” 204–237. 95 Wallace, Domingo de Soto, has cited Jesuit authors of the sixteenth and early seventeenth centuries who advocated the greater use of mathematics in natural philosophy. Wallace’s claims that these approaches can be traced back to Thomas Aquinas are unconvincing. See McMullin’s review of Wallace’s Prelude to Galileo, 171–173; and Wallace’s response in Philosophy of Science, 504–510.

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circular motions as fundamental. If he ever subjected that assumption to questioning, he dismissed the questions as contrary to the whole tradition of astronomy. He evidently concluded from the regularity of celestial events that the motions of celestial bodies must be circular, uniform, and, therefore, must be represented by circles and combinations of circles.96 Copernicus may also have found encouragement in the fact that Aristotle himself used mathematics as a paradigm of science, and subordinated physics to mathematics to some extent in the mixed sciences of astronomy and optics.97 The next step, as we showed in the previous section, was to subject other hypotheses to scrutiny, namely, whether they produced results in agreement with the fundamental hypothesis of uniform, circular motions. Where such hypotheses failed, he rejected them. In chapter seven, we provided an account of how he arrived at the hypotheses that he accepted. This step is complicated for it involved simultaneous rejection of geocentrism and adoption of geokineticism, rejection of the motion of the Sun and adoption of heliocentrism, and recognition of the results that agreed with the fundamental assumptions and further results that strengthened the greater likelihood of his hypotheses. As we can see, then, Copernicus had to adopt some hypotheses as fundamental, select secondary ones in conformity with these, and select models that would satisfy both the fundamental and secondary ones. The secondary included cosmological and natural-philosophical assumptions that had to be subordinated to the fundamental astronomical-mathematical assumptions. The selection of further mathematical hypotheses and models had, in turn, to be subordinated to the cosmological, natural-philosophical assumptions while preserving the fundamental astronomical-mathematical assumptions. We consider the acceptance of the secondary hypotheses in chapter ten. Although he went further than Aristotle in subordinating physics to mathematics, like Aristotle, Copernicus did not make a complete subordination of physics to mathematical astronomy.

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Revolutions, I, 4: 11, lines 10–15. For recent emphasis on these points, see Hussey, “Aristotle and Mathematics,” 217–229, esp. 217–218, and note Hussey’s careful qualification (225) that Aristotle did not make a complete subordination of physics to mathematics. 97

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10. The Logical Issues in the Discovery of the Heliocentric Theory As we have suggested in the previous two sections, Copernicus adopted a dialectical methodology. What we wish to clarify here are the logical steps in his reasoning from problems with geocentric systems to the adoption of an alternative system, leaving the details of his critique of geocentricism to chapter nine and of his discovery to chapter ten. There are principally two facts that led Copernicus to reject his predecessors’ efforts, the problem of saving uniform motion by resort to an equant and the problem of the variations in the distances of the planets from Earth. In both cases Copernicus concluded that the systems violated the fundamental principles or, if they satisfied them, they did so by introducing hypotheses that failed the test of relevance. In chapter three we referred to three Aristotelian texts as possible sources for Copernicus’s view about the relation between hypothesis and results. Nicomachean Ethics I, 8, 1098b11–12 (“with a true view all the data harmonize, but with a false one the facts soon clash”), Prior Analytics II, 2–4, and Metaphysics I minor, 993b26–27 (“that which causes derivative truths to be true is most true”) agree broadly with Copernicus’s controversial statement in the Preface to Paul III. Because the text from Ethics refers to data, it seems the most relevant, but of all of the alternatives, there are reasons for thinking that Copernicus knew the text of the Metaphysics best. Rheticus refers to it explicitly in Narratio prima.98 Copernicus’s friend Tiedemann Giese wrote a commentary on the Metaphysics in the form of glosses, but I have found no evidence in Giese’s copy at Uppsala that Copernicus knew the commentary. Of course, he might have discussed the text and especially this passage with his friend. It is possible that they knew each other as early as 1503, but Copernicus did not transfer until 1510 to Frombork where Giese was also a canon.99 Perhaps more significant, we know that Copernicus either garbled or deliberately changed Aristotle’s meaning in a passage from Metaphysics not far from the text about truth. At 993b12–15, just fourteen lines earlier, Aristotle expresses gratitude to those who have spoken superficially, for they too have made contributions to the powers of

98 99

Rosen tr. 142. On Giese, see Pociecha, “Giese,” PSB, 7: 454–456. Cf. Rosen, “Biography,” 340.

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thought. Copernicus either had a different version or he understood Aristotle to have been expressing gratitude to those who have committed errors for they too have contributed to the truth. Copernicus’s interpretation is not completely at variance with Aristotle’s dialectical method, but Giese’s commentary could not be the source for Copernicus’s interpretation.100 On the one hand, Copernicus’s comment suggests acquaintance with Metaphysics, but, on the other, it also suggests that he was relying on his memory in 1524. Hence, it seems likely to me that Copernicus knew all of the passages either from his teachers or his own reading prior to 1503. As he struggled with puzzles about the truth status of hypotheses in astronomy, he recalled them and arrived at his own strong views. His assertions in De revolutionibus, however, also demonstrate acquaintance with dialectical topics, a branch of philosophy that he learned in Cracow and probably reinforced in Bologna. In adopting the Aristotelian view about the relation of true premises to true conclusions, he expanded Aristotle’s criterion from causal (propter quid) demonstration to the somewhat weaker criterion of relevance. He further concluded that irrelevance was a ground for rejection of a cosmological theory on which Ptolemaic geocentric astronomy was based. Because their hypotheses introduced something extraneous and irrelevant, Ptolemaic astronomers failed to resolve the problems in accord with their own principles, and, consequently, failed to arrive at the true system of the world.

100 Copernicus, Letter Against Werner, Complete Works, 3: 145 and notes 11 and 12. I consulted Giese’s glosses on this text in Uppsala, Inc. 31:164, questions of Johannes Versoris on the Metaphysics with the complete text of Metaphysics (Cologne, 1493; Hain *16051). The book is annotated in several hands, but Giese owned the book, and there is no question that he wrote the comments on Metaphysics. On f. 13v, Aristotle’s text reads: “Non solum autem his dicere gratiam iustum est quorum aliquis opinionibus communicaverit. Sed his qui adhuc superficialiter enunciaverunt, etenim conservunt aliquid.” At the words “superficialiter enunciaverunt” Giese enters the comment “de veritate” between the lines. In other words, he interpreted Aristotle to be speaking of those who had spoken the truth but in a superficial way, not those who had spoken incorrectly. At the beginning of the chapter in question, Aristotle says that everyone says something true about the nature of things, and makes another striking comment just a little below it. At 993b7–11, he says: “Perhaps, too, as difficulties are of two kinds, the cause of the present difficulty is not in the facts but in us. For as the eyes of bats are to the blaze of day, so is the reason in our soul to the things which are by nature most evident of all.” It is hard to imagine Copernicus not being struck by such statements. I have again used the translation by Ross in Basic Works, 712–713.

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In the conclusion of this study, we will return yet again to the issue of true hypotheses. There is a problem with Copernicus’s view, yet he could hardly have been expected to see it. He had focused his attention on reforming astronomy within the confines of a natural philosophy and cosmology that were still broadly Aristotelian. In chapters nine and ten we articulate the consequences for Copernicus’s philosophy of nature and cosmology. In the conclusion we explain the momentous advance by Kepler about the understanding of hypotheses. 11. Concluding Remarks on Copernicus’s Relation to the Aristotelian Logical Tradition Copernicus became acquainted with Aristotelian philosophy in the context of late medieval schools of interpretation and transmission. Although we cannot prove that he attended classes in either Cracow or Bologna, his later treatises indicate that he had been trained in the techniques of dialectic, the means for discovering middle terms in syllogistic arguments. His arguments are, of course, not syllogisms, and he tried to model his style on humanistic or classical authors. There are, nonetheless, arguments, and they sometimes have the structure of enthymemes, leaving us to supply the warrants or premises on the assumption that his arguments are hypothetical syllogisms. In other, perhaps most, cases, his warrants are explicit. Aristotle regarded enthymemes as rhetorical proofs, but he also advocated analyzing them for their logical validity. In other words, we focus on dialectic to examine the logical validity of an argument, and on rhetoric to understand how the argument is supposed to move readers to assent.101 Copernicus’s views about hypotheses, however, derive from his reflections on the interpretation of hypotheses in the astronomicalmathematical tradition in which he was also trained, and from his reading of Ficino’s translation of Plato’s Parmenides. It would be anachronistic to characterize his method as hypothetico-deductive, but the arguments do share some of the features of such reasoning, and they encounter some of the same logical difficulties that modern logicians have raised about inductive reasoning and hypothetico-deductive method. We have pointed out some of these issues above, arguing

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Van Eemeren and Houtlosser, Dialectic and Rhetoric, 3–11.

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that Copernicus adopted the criterion of relevance in evaluating the validity of consequences in a discipline like astronomy. I have taken no position on the validity of such a strategy because these remain very controversial issues in the technical literature that deals with the logic of hypothetico-deductive method and inductive reasoning. We have argued that Copernicus’s strategy was controversial in his own day, yet there is evidence that it was taken for granted in specialized and practical disciplines that had to apply the standard logical criteria to the actual problems and issues of those disciplines. In such circumstances, scholars tended to regard the strictly logical criteria as theoretical, modifying them to make it possible for them to reach conclusions that were more reasonable than other alternatives. They could fall back onto Aristotle’s own statements about truths and derivative truths, a text on which Copernicus himself may have relied for his controversial statement about the true not following from the false. The texts provide abundant evidence that Copernicus was sensitive to logical issues, and that he gave serious thought to principles and criteria that would make it possible for astronomers to advance beyond the impasse that blocked the way to further progress in astronomy. That impasse, as he saw it, resulted from geocentric assumptions, and that fact was revealed to him by the failure of those assumptions to produce results in conformity with the fundamental principles of the discipline. That part of his argument is, I believe, indisputably logical. Whether, however, Copernicus’s hypotheses yielded the results that he claimed to achieve remains both historically and logically controversial to this day. We examine further historical dimensions of his philosophical assumptions and of his relation to the Aristotelian tradition in the remaining two chapters.

CHAPTER NINE

COPERNICUS AS NATURAL PHILOSOPHER 1. Introduction When two of the leading experts on Copernicus characterized him as an Aristotelian, they were without doubt referring to his retention of celestial spheres as the movers of the planets and to his views in natural philosophy.1 Although other experts have pointed to non-Aristotelian sources of Copernicus’s account of motion and natural elemental motion, I have concluded that Copernicus also drew on schools and communities of the Aristotelian tradition. He combined them into an uneasy synthesis with all of the ambiguities and inconsistencies that one would expect. Teachers and students within the Aristotelian tradition modified Aristotelian doctrine, often interpreting it in ways that combined the fundamental principles of other authors and JudaicChristian doctrines, and thereby created a synthesis that is difficult to

1 Rosen, Introduction to Letter, Complete Works, 3: 134, comments: “[F]amiliarity with Aristotle’s treatises does not of course make Copernicus an Aristotelian in the sense that he regarded the Stagirite as infallible. On the contrary, where he detected a flaw in Aristotle, as in the Stagirite’s division of simple motion into three mutually exclusive types, he did not hesitate to correct it. But he did not undertake to overthrow Aristotelianism, as he did the Ptolemaic astronomy. On the other hand, what he believed was sound in both systems, he retained with gratitude and affection, an attitude which some of our contemporaries would do well to consider.” Compare with the assertion of Swerdlow, “Copernicus,” 162–168, esp. 164–165: “For these physical problems raised by the motions of the earth, which should also affect the motion of birds, clouds, and projectiles, Copernicus made what he considered to be a minimal alteration of Aristotelian natural motion of the elements, such that the natural motion of a spherical body, whatever its substance, is to rotate in place by virtue of its form alone. The daily rotation of the spherical earth together with the surrounding water and air is, therefore, entirely natural; projectiles, birds, and clouds are simply carried along with the rotating earth; and heaviness (gravitas), the descent of heavy bodies to their natural place, the surface of the earth, in straight lines, is due to a ‘natural inclination placed in the parts’ to come together to form a globe. In proposing this explanation, Copernicus did not intend to overthrow or displace Aristotelian physics but to adapt it to the motion of the earth, unlike Galileo Galilei (1564–1642), who later used much the same principles as Copernicus for a devastating attack on Aristotle. In fact, the objections to the motion of the earth were not completely answered until Isaac Newton (1642–1727).”

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reconcile with genuine Aristotelianism. Be that as it may, this was the Aristotelianism that Copernicus encountered, and it is far from clear how much he realized or, for that matter, even cared about the authenticity of classical authors’ views. Or, to put it differently, his concern, shared by the authors of the Aristotelian tradition, was to arrive at the truth, and to adopt Aristotelian views where they agreed and adapt his views where they did not.2 2. Copernicus’s Critique of Geocentrism In chapter four, I summarized the principal Aristotelian cosmological assumptions and conclusions relevant to Copernicus’s arguments. From the point of view of natural philosophy and physics in particular, we have been conditioned to view Copernicus as having anticipated the successful mechanical principles enunciated definitively by Newton some one hundred and forty-four years after the appearance of De revolutionibus. Despite the successful historical revision of Copernicus’s astronomical achievements as a conservative continuation and even fulfillment of the goals of Ptolemaic astronomy, the topos of anticipation still dominates the standard representations of his vision of cosmology, natural philosophy, and physics.3 Even when some readers acknowledge the survival of Platonic and Aristotelian principles in Copernicus’s understanding of cosmology, they have still left the impression that he anticipated essentially antiAristotelian solutions to several problems and questions. Because of the success of the Newtonian program, such readings of Copernicus seem plausible.4

2

See chapter four on the Aristotelian tradition and on Aristotelian schools and sects. An excellent example is Pedersen and Pihl, Early Physics, 317. This text provides one of the best accounts of ancient and early modern astronomy but reads Copernicus’s intentions about natural philosophy from the viewpoint of contemporaneous negative reactions by Aristotelians and from the viewpoint of later physical astronomy. In his text, Birth, chs. 1–3, Cohen adopts for pedagogical purposes a portrayal of Aristotelian dynamics that was so incompatible with the Copernican theory that a new theory had to be developed. My own earlier essays, for example, Goddu, “Dialectic,” 95–131, at 125–131, also portray Copernicus as having left the physical questions for a later day, thus suggesting that Copernicus anticipated a non-Aristotelian solution. 4 Exceptions are Moraux, “Copernic et Aristote,” 225–238, and Swerdlow, “Copernicus,” 163. 3

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Several scholars in the Middle Ages criticized Ptolemaic astronomy on a variety of grounds. Still, no one in the Middle Ages through the fifteenth century proposed multiple motions of Earth as a solution to the problems found in Ptolemy’s theory. What, then, led Copernicus to suppose, contrary to common sense, to naked-eye observations of the stars, and to the geocentric principles of Ptolemaic astronomy and Aristotelian natural philosophy that the Earth has not only one, not just two, but three motions? As far as we know, Copernicus never recounted the process that led him to those conclusions. About thirty years after he proposed a heliocentric theory, the reasons that he provided may represent the evolution of his thought, but his statements in 1542 (the dedication to Pope Paul III) were clearly intended to persuade readers to suspend judgment until they saw the results. In other words, we do not know whether the account was rhetorical, autobiographical, or a little of both. In that account he tells us that he took the original aims and principles of astronomy as absolutely correct—to represent all of the known celestial phenomena with geometrical models that do not violate the principles of perfect uniformity and circularity. The models would thereby reveal the true, perfectly uniform and circular motions existing behind the phenomena. That was the challenge that Plato had supposedly presented to astronomers in the Republic. Expressed in his own words written probably in the mid-1520s, Copernicus saw his study as “concerned with the most beautiful objects, most deserving to be known.”5

5 De revolutionibus I, Introduction, 487, 1–3: “Nter multa ac varia literarum artiumque studia, quibus hominum ingenia nego[ci]antur ea praecipue amplectenda existimo: summoque prosequenda studio: quae in rebus pulcerrimis et scitu dignissimis versantur.” Plato’s challenge in the Republic appears at VII, 529a–530d. Plato’s view has been the subject of much controversy. See Bulmer-Thomas, 107–112, for a brief survey. Several scholars have rightly criticized the distinction between mathematical astronomy and physical astronomy, and rejected Duhem’s instrumentalist/ realist dichotomy. See, for example, Lloyd, “Saving,” and Goldstein, “Saving,” for their assessments and references to additional literature. Knorr, “Plato,” has also shown that Plato did not formulate the challenge about saving the phenomena, although later Neoplatonic authors and others did attribute it to him. See also Evans, “Simplicius.” For the interpretation of the text especially by astronomers, see Pedersen and Pihl, Early Physics, 26–30, 65–67. For these reasons, when I refer to it, I place it in quotation marks (“Plato’s axiom”) to indicate the spurious yet customary nature of the attribution. On chronology, see Birkenmajer, Mikołaj Kopernik, 350–389, esp. 352–354 and 362–373; Rosen, “When Did Copernicus,” 144–155. Compare Schmeidler, Kommentar, 1–5.

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He believed that God had created a perfect system and human beings capable of discovering that perfect system. From Plato, Aristotle, and Ptolemy, he accepted the belief that the motions of planets and stars are perfectly uniform and circular and so must be represented by circles and combinations of circles that preserve perfect uniformity and circularity. Sometime between 1496 and 1509—this is where his account of 1542 lacks details—he came to the following conclusion. All homocentric representations and the more complicated, but more adequate, epicycle-deferent models had failed to achieve the principal goal, namely, the representation of a coherent system using only circles that preserved perfect uniformity with respect to their proper centers. In spite of all the hypotheses and models they devised, all of his predecessors had failed. The next step in his account is far from clear. In chapter seven we presented a reconstruction of how Copernicus arrived at his theory, but the account underscores his silence and the differences among the experts. Somehow he began to wonder about the placement of Earth at the center of the system and to ask whether, perhaps, the Earth itself moves. Why he thought a moving Earth would remedy the mistakes of his predecessors is not at all clear. In addition to the questions and problems that led him to his cosmological theory, he presumably adopted the Earth’s motions initially as a working hypothesis. He evidently believed that models constructed according to a heliocentric hypothesis would preserve the principles and achieve the goal of representing celestial motions with circles that preserve perfect uniformity with respect to their proper centers. If we judge the results with the same severity that he judged those of his predecessors, we have to be puzzled why he thought that switching the positions of Sun and Earth and putting Earth in motion would work better.6 The alternatives are not perfectly equivalent, but neither was completely successful. Let me hasten to add, however, that his decision to work out the details is what separates his work from all earlier heliocentrists. Clearly, something else emerged that persuaded Copernicus that his hypotheses were right. In other words, although his initial reasons 6

Actually, the center of Copernicus’s cosmos is the center of Earth’s orbit, which is eccentric to the Sun. In other words, the center is the mean Sun, not the true Sun. Many experts have pointed this fact out, for example, Swerdlow and Neugebauer, Mathematical Astronomy, 1: 159–161, but for a clear exposition see Evans, History, 415.

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for proposing heliocentrism may have been frustrated, the results persuaded him that he had it basically right, regardless of the problems that remained. “The problems that remained” refers to the construction of completely equantless models that preserved uniform and circular motions. Copernicus’s planetary models required him to construct small epicycles to account for their motions in latitude and for the non-uniformity of the planets’ motions. In the models for the superior planets the resulting path of the planet is slightly oblong or, as he himself expressed it, “imperceptibly” not a perfect circle, and the problem of non-uniform motion is solved by what amounts to a hidden equant.7 The models for the inferior planets raise even more difficulties, but again there are hidden equants and other paradoxical results. Copernicus acknowledges that the path of a planet is not perfectly circular, but it is composed of uniformly moving circles.8 “Results” refers to the achievements that Copernicus himself either emphasized or clearly implied. First is the natural explanation of bounded elongation of Mercury and Venus and of retrograde motions of all the planets. Second is the ordering of the planets according to sidereal periods. Third is the estimate of relative distances of the planets from the Sun. Copernicus concluded that ordering the planets according to sidereal periods was the only way in which they could be ordered, otherwise the wonderful commensurability and harmony of the system would be destroyed. The planets had to be ordered in this way, and he knew that he was right about that even if he could not prove it. Alas, everything else was murkier. The experts have explained most of the astronomical difficulties adequately.9 Copernicus himself recognized, of course, that philosophers and theologians would likely reject out of hand his hypothesis of a moving Earth. While he did not compose a text of natural philosophy to accompany his mathematical treatise, he did address himself to the most serious objections. By and large, his approach was dialectical, that is to say, he raised questions

7 De revolutionibus V, 4: 366, 34–35: “Hinc etiam demonstrabitur, quod sidus hoc motu composito, non describit circulum perfectum iuxta priscorum sententiam mathematicorum, differentia tamen insensibili.” An excellent explanation is provided by Evans, History, 420–422. Cf. Swerdlow and Neugebauer, Mathematical Astronomy, 1: 295–297. 8 Swerdlow and Neugebauer, Mathematical Astronomy, 289–299, 372–374, 403– 415, 483–491, and 535–37; Evans, “Division,” 1009–1024. 9 Especially Swerdlow and Neugebauer.

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about some principles or about their application. This is why I will subordinate the analysis to his critique of geocentrism, for Copernicus was inclined to revise principles rather than reject them altogether. He rejected a number of assumptions, but his rejection of an assumption led him to revise, not reject, a principle. The result, then, was an adaptation to the heliocentric system. And the purpose was to delay the anticipated abrupt and unreflecting reactions of philosophers and theologians. If he could get them to take some questions seriously, perhaps he could move them to re-examine the issues from a fresh perspective. In other words, I subordinate the interpretation of his views in natural philosophy to the rhetorical and dialectical strategies adopted in Book I of De revolutionibus. There is a third alternative. After Copernicus concluded that only a heliocentric cosmology could achieve the goals of ancient astronomy, he drew inspiration from sources that he recognized as unconventional. As he produced his sketch of natural philosophy, he likewise drew inspiration from sources that he also recognized were unconventional while presenting its details as much as he could in a way that he thought that his contemporaries could assimilate. Later thinkers went further than what Copernicus had envisioned and in a manner that he tried to avoid, namely, by adopting principles and constructing arguments that would eventually entail the destruction of Aristotelian natural philosophy.10 The alternative, as I have expressed it, may seem to require only a subtle or nuanced modification of my thesis. What the alternative contributes in very clear terms—that the authors whom I have cited in support of a modification of Aristotelian principles fail to make clear—is the extent to which Copernicus relied on especially ancient unconventional and anti-Aristotelian sources to support his unconventional cosmology. We cannot simply argue, as Rosen and Swerdlow implied, that Copernicus altered Aristotelian principles as demanded by his theory without resorting to unconventional sources that were incompatible with genuine Aristotelianism. They all agree that Copernicus did not intend to overthrow, destroy, or displace Aristotelian or scholastic cosmology.11

10 This alternative depends on a private communication from Dilwyn Knox, which I have modified to emphasize the difference between cosmology and natural philosophy. 11 Knox, “Copernicus’s Doctrine,” 157–211.

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In chapter four I enumerated eight themes held by several medieval scholastics that are non-Aristotelian, some of which can be characterized as even anti-Aristotelian, yet such scholastics were perceived as Aristotelian and as carrying on the Aristotelian tradition. As I conceded in that chapter, several of Copernicus’s views in natural philosophy and cosmology are decidedly anti-Aristotelian and anti-scholastic. Heliocentrism and geokineticism are obviously contrary to scholastic Aristotelianism. Because there appears to be consensus that Copernicus did not intend to destroy Aristotelian natural philosophy altogether, we apparently agree that he intended to transform, modify, and adapt Aristotelian and alternative principles to a heliocentric cosmology. What means did he employ to fulfill this intention? He relied on ancient opponents of Aristotelian doctrine, and he exploited scholastic modifications to propose theories about nature, natural motion, elemental motions, spheres, celestial spheres, and the properties of celestial bodies that are compatible with his heliocentric cosmology. We cannot, however, overlook the fact that nearly all of his sources were also geocentrists. His conclusions were equally opposed to their cosmological views. The construction of an entirely new natural philosophy consistent with heliocentrism was beyond even Copernicus’s considerable imagination. He was freed but also limited by ancient and scholastic conceptions. He had seen Aristotelian principles rejected, transformed, and adapted in almost countless ways. He could not have proposed his transformations without ancient and scholastic critics of Aristotelian doctrine, but he had sufficient and even defensible reasons for questioning the dogmatic acceptance of Aristotelian principles that were incompatible with heliocentrism. The prevailing view was that the universe is an open system and behaves like an open system. If the Earth moves, then, we should be able to perceive it. Copernicus’s proposal implied that the universe is an open system, yet it behaves as if it were an enclosed system. Because Copernicus did not grasp this problem adequately, he thought that modifying ancient and scholastic principles would suffice to construct a sketch of a natural philosophy compatible with a heliocentric cosmology. The modifications were non-Aristotelian, some were anti-Aristotelian, yet they seemed to fit with transformations that Copernicus proposed without explicitly rejecting Aristotelian natural philosophy or the Aristotelian tradition. Again, these are further reasons why I am persuaded that his critique of geocentrism motivated his transformation of ancient and scholastic natural philosophy, Aristotelian and non-Aristotelian.

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Three important themes will serve to illustrate how the critique of geocentrism guided Copernicus to his principles of natural philosophy. The motions of celestial bodies, the motions of elemental bodies, and the question of whether the universe is finite or infinite will illustrate Copernicus’s principles and mutual dependence of his answers to these problems. These themes will also help us to solve some thorny problems of interpretation as well.12 In chapter ten, we will deal additionally with the problems of the existence of spheres and the nature of celestial matter. 3. The Motions of Celestial Bodies Aristotle assumed that the eighth sphere (the sphere of the fixed stars) has the daily, circular motion that we observe it to possess. Circular motion is simple; hence there must be an element that performs such a motion by its very nature. The circle is a more perfect figure than a straight line, and it follows that circular motion is more perfect than linear motion. Bodies that move in a circle are more divine than the elements of the sublunar region. The heavenly bodies that move in circles are eternal and uncreated, although the actuality of their movement can be traced back to the unmoved mover. The motion of the eighth sphere causes the motions of the lower planetary spheres. I have here combined accounts from De caelo, Physics, and Metaphysics, as scholastic readers were inclined to do, and as Copernicus himself suggests by his indirect references to Aristotle.13 Copernicus replaced the motion of the eighth sphere with the Earth’s daily rotation on its axis; hence he had to revise the Aristotelian account of the motions of the planetary spheres. In his theory, of course, Earth is a planet. How does he explain the motion of Earth? Everyone agrees that Earth is a sphere. It does not follow necessarily

12 Szczeciniarz, Copernic, has provided an alternative interpretation of motion and infinity in the Copernican theory that relies on supplying answers to questions about which Copernicus preferred to remain silent. 13 We do not know whether Copernicus consulted Aristotle’s texts or relied on references made by others, or was simply referring to Aristotle from memory. We know that in specific places he was referring to certain chapters of De caelo and Metaphysics, and generally to principles contained in the Physics. Here the relevant texts are De caelo I, 2–3, Metaphysics XII.6.1072a18–35, and Physics VIII, 5–10. On Copernicus’s knowledge of Aristotelian texts, see Moraux, “Copernic et Aristote.” See chapter four for late fifteenth-century commentaries at Cracow on natural elemental motions.

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from that fact that it moves, but if it moves, then surely there would be nothing unnatural about its moving in a circle. His explanation of the motion of a sphere is that such motion is natural to a sphere. That motion is not a property of all spheres, however, follows from his belief that the Sun and the sphere of the stars are motionless.14 Form is not the cause of motion, that is, the form of sphericity by itself does not cause a sphere to rotate. An external efficient cause may be necessary to put a sphere in motion or to remove an obstacle to motion, but once moved the sphere would move in a circle according to its nature. For Copernicus, then, “according to nature” indicates a potentiality in conformity with the form or shape of a thing, or to put it differently, the spherical shape of a body disposes it to move naturally in a circle, but its shape does not necessarily entail that the body revolves.15

14 Knox, “Copernicus’s Doctrine,” 172, n. 76, has quite rightly pointed out an ambiguity in the Latin text of De revolutionibus, where Copernicus seems to imply that the Sun may rotate. See De revolutionibus I, 9: 17, 3–8: “Equidem existimo, gravitatem non aliud esse, quam appetentiam quondam naturalem partibus inditam a divina providentia opificis universorum, ut in unitatem integritatemque suam sese conferant in formam globi coeuntes. Quam affectionem credibile est etiam Soli, Lunae, ceterisque errantium fulgoribus inesse, ut eius efficacia in ea qua se repraesentant rotunditate permaneant, quae nihilominus multis modis suos efficient circuitus.” Yet elsewhere, Copernicus decisively commits himself to the proposition that the Sun is stationary. De revolutionibus 1, 10: 19, 25–28: “Proinde non pudet nos fateri hoc totum, quod Luna praecingit, ac centrum terrae per orbem illum magnum inter ceteras errantes stellas annua revolutione circa Solem transire, et circa ipsum esse centrum mundi: quo etiam Sole immobili permanente, quicquid de motu Solis apparet, . . .” The text could be restricted only to the Sun’s annual motion, but surely he could have found an expression more ambiguous than Sole immobili permanente to express himself. In his astronomical models (De revolutionibus III, 15, 20 and 25), Copernicus entertains motions of the Sun, but these are references to the mean Sun, and they indicate his recognition of alternative mathematical models to account for the appearances. See Swerdlow and Neugebauer, Mathematical Astronomy, 1: 159–161, where they discuss these alternatives, and conclude that Copernicus believed the Sun to be immovable even though he could not prove it. 15 I owe the qualification at the end of the paragraph to a comment by Knox, which is intended to remove any ambiguity. See also Knox, “Copernicus’s Doctrine,” 170, n. 66. See also Wolff, “Impetus Mechanics,” 257–279, esp. 219–220. Compare with Kokowski, Copernicus’s Originality, 230–231. In the pages cited Wolff and Kokowski emphasize the distinction between form and cause of circular motion. See also Aristotle, Metaphysics XII, 6, 1071b3–25. Again, Szczeciniarz, 91–105, re-interprets the exceptions, leaving form as the cause of the motion of a sphere. Yet, on 254, n. 198, Szczeciniarz acknowledges a difficulty with Copernicus’s arguments. See chapter four on natural place and form, and on celestial spheres. Copernicus could have derived some features of his interpretation from Johannes Versoris. Cf. Goddu, “Sources,” 85–114, esp. 86–97; and idem, “Teaching,” 69–75. Versor also denies that shape is a cause of motion. Instead, he regards shape as a cause of speed.

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It is hard to keep the issues separate, but Copernicus evidently realized that the source of the problem was Aristotle’s associations of a natural motion with simplicity, and of simplicity with an element that by its nature performs the observed motion. First, the assumption is a simplification and generalization from observations of clearly more complicated motions. As Aristotle knew, actual elemental things are mixtures, yet he asserted the principle in a theoretically foundational way. Everyone acknowledged the principle of the relativity of motion; only Copernicus recognized it as a problem that no naked-eye observation, or commonsense experience, could resolve decisively.16 Second, if a decision about what is natural and what is contrary to nature is based on such a principle, we may commit a fatal error right at the start. Copernicus had no inkling of an account based on extrinsic, mechanical forces. His only recourse was to re-define the meaning of “natural.” The “nature” of a body suggests a capacity or a possibility, so he had to express it conditionally—if a sphere moves or is caused to move, then its motion in a circle would be “natural” to it. He may have believed that at the creation God set some spheres in motion, although he does not say so explicitly. He maintained that the circular motions of spheres continue uniformly and unfailingly because of their perfect constitution and inherent capacity for circular motion. The rotation of spheres causes the celestial bodies embedded in them to move in circles either by contact or by carrying them. There is no resistance, however, for spherical celestial bodies have a natural capacity for circular motion. Copernicus believed that Earth rotates on its axis because, as a sphere, it possesses the capacity to rotate, and to do so uniformly and unfailingly. He may have supposed, although he nowhere says so, that the great orb moving the Moon and Earth may cause Earth to rotate on its axis. Because Earth possesses a natural capacity for rotation, it offers no resistance. Copernicus could have employed the theory of impetus here, as Michał Kokowski believes, but this would have entailed the consequence that the motion of Earth requires an extrinsic force, violence,

16

Perhaps Nicole Oresme recognized the problem, yet he allowed Scripture to tip the balance of probability towards the geostatic view. Cf. Oresme, Le livre, II, 25: 536– 538. See chapter four for fifteenth-century views at Cracow on nature as an intrinsic principle of motion.

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or an unnatural cause.17 Copernicus is insistent on the idea that the rotation of the celestial spheres and of Earth on its axis is natural, a capacity that is actualized in such a way as to preclude any extrinsic cause or force. But if God put them in motion, then was not a force applied? Kokowski appeals to the Aristotelian maxim in its Latin form, “Omne quod movetur ab alio movetur.”18 But Aristotle also affirms this principle even in the case of self-moved bodies, and the principle constitutes a step in his demonstration of an unmoved mover. Furthermore, Helen Lang has interpreted the principle in the case of projectile motions as a matter of “handing over” the body.19 Although “carrying” for Aristotle is a species of violent motion, for Copernicus the “carrying” of bodies in circles by spheres is not a matter of impressing a force, but natural because spherical bodies are suited for circular motion. These considerations reveal complications in Aristotle’s discussions that lead to the more metaphysical parts of his natural treatises. Did Copernicus also accept the idea that the rotation of spheres is generated by an imitation of the unmoved mover? Copernicus does not speculate. He asserts that in those cases where a sphere rotates, its rotational motion is natural, and that God endowed bodies with the properties that they have. How the potentiality is actualized is not explained. His system requires an immobile center and an immobile periphery. One could speculate that God’s “activity” other than creation requires nothing more than the removal of obstacles, not the direct exercise of a force. Copernicus even used an Aristotelian principle here against Aristotle. Forced motions are of limited duration, gradually giving way

17 As Knox pointed out to me in his reaction to this assertion, Buridan and others argued that the impetus imparted into celestial bodies would constitute an intrinsic and natural principle of motion. Yet there is an ambiguity here. The imparted force or impetus is extrinsic, and is absorbed by the body, so that it seems that the cause of its initial motion is extrinsic even if its continued motion is due to the now intrinsic impetus. Buridan’s famous discussion in Quaestiones II, q. 12, is, as Richard Dales points out, full of conditionals and subjunctives. Buridan offers this speculation as an alternative to celestial intelligences. Furthermore, the motion of the heavenly bodies would be perpetual precisely because they encounter no resistance. If there were no resistance, why would they need a force to move them? This seems to be the sort of objection made by Oresme. Elsewhere, Buridan himself appears to accept Aristotle’s doctrines of heavenly motion without qualification. See Dales, “Medieval De-animation,” 547–549. I owe the reference to Dales to Knox. See also Funkenstein, “Some Remarks,” 329–348, esp. 342. 18 Kokowski, 229–231. Compare with Aristotle, De caelo I, 2, 268b14–269 b17. 19 Lang, “Inclination, Impetus,” 224–251. For a fuller summary, see chapter four.

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to natural motion.20 As a celestial sphere or Earth rotates, its rotation is uniform and enduring, again indicating that circular motion is natural to a celestial sphere. Copernicus otherwise retained all of the other attributes and metaphors of “perfection,” “dignity,” “continuity of motion,” and of quasi-eternity and quasi-infinity in the sense that a circle has no beginning and no end. We do not know whether Copernicus maintained a theory of impetus, or, if he did, whether he thought that a celestial sphere moves a body by means of impetus. It is also not clear whether he thought God moves spheres by means of impetus. He does not explain such details or answer the remaining questions because that is not his goal. Such speculation, in fact, misses the point. Copernicus argued dialectically against the Aristotelian conclusion that a motion of Earth would be contrary to nature, and would generate violent consequences. If Earth moves and we observe no such violent consequences, then its motion must be natural (De revolutionibus I, 8). A single sphere moves a celestial body uniformly (De revolutionibus I, 4). Circular motion is the only simple natural motion, for it is the only motion that is uniform and unfailing (De revolutionibus I, 8). A sphere cannot be the cause of observed non-uniformities in the celestial motions, for this would presuppose either that the moving force varies or that the body varies (De revolutionibus I, 4). Copernicus makes this argument to support the conclusion that the observed non-uniformities are a consequence of Earth’s motions (De revolutionibus I, 4 and I, 8–9). I now turn to Copernicus’s account of the motions of elemental bodies, and again take up the questions about impetus as they relate to his remarks on elements and elemental motions. Aside from the geokinetic hypothesis, the most serious obstacle for an Aristotelian interpretation of heliocentrism is Copernicus’s account of elemental motion. 4. Impetus and the Motions of Elemental Bodies My initial approach to this question is motivated by an effort to understand Aristotle’s views on natural elemental motions. I begin with a

20 De revolutionibus I, 8: 14, 19–21: “Quibus enim vis vel impetus infertur, dissolvi necesse est, et diu subsistere nequeunt: quae vero a natura fiunt, recte se habent, et conservantur in optima sua compositione.” For the doctrines at Cracow, see chapter four.

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brief review of Aristotle’s interpretation of mathematics, and turn to a brief discussion of the analysis that led Aristotle to his conclusions about the motions of elemental bodies. Physics II, 2 and Posterior Analytics I, 13 contain the famous discussions about astronomy and mathematics and their relation to natural philosophy. Mathematics ignores strictly physical characteristics, yet astronomy examines geometrical figures that are indeed mathematical, but deals with them not so much in their mathematical as in their physical aspects.21 Aristotle refers here to form and matter, evidently regarding the formal element in astronomy as mathematical, and hence says that natural philosophy must recognize both the formal and material aspects of nature. Yet, we know that Aristotle explains the natural motions of bodies as the result of the qualitative characteristics that bodies possess. Their mathematical characteristics and the mathematical descriptions of their motions follow from their natures as inferred from their motions. This reading is also consistent with the view he expresses in Metaphysics I, 2, 1001b–1002b, where he denies that mathematical entities are primary beings. A body cannot exist without mathematical properties, yet, we can conceive of mathematical properties in the abstract (1002a4–6).22 In rejecting geocentrism and the priority that Aristotle assigned to qualitative characteristics of bodies, Copernicus evidently reversed the priority of mathematics and natural philosophy at least with respect to questions about the order of the cosmos. In Physics III, 1 and IV, 1–9, Aristotle associated motion with place, and settled the question about the order of the cosmos by means of his doctrine of natural place. Aristotle developed Plato’s ideas on place and elements in a way that led to a major departure from Plato on the origin of the cosmos. Where Plato emphasized the collection of elements as a result of separation from one another according to the principle of “like to like,” Aristotle concluded that the motions of the elements are a part of their nature. Hence, Aristotle rejected Plato’s

21 Aristotle, Posterior Analytics I, 13, 79a1–16. I have substituted a reference to astronomy here for Aristotle’s reference to optics. 22 Edward Hussey has argued for the priority of mathematics over physics in Aristotle’s account, but Hussey is careful to exclude a discussion of motion. He adds, “Aristotle shows no sign of wishing to make a complete subordination of physics to mathematics.” See Hussey, “Aristotle and Mathematics,” esp. 218 and 225.

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hypothesis about the creation of the world.23 With the doctrine of creation, Christian Aristotelians reintroduced Platonic considerations in the doctrine of place, thus combining the two and reinforcing once again a Platonic reading of Aristotle. Copernicus, for his part, was compelled to make the immovable sphere of the fixed stars the place of the universe, and he ordered the remaining spheres by sidereal periods as measured from the Sun at the center. In what follows, I examine his use of the concept of impetus, its relation to the motions of celestial spheres and bodies, and its relation to the motions of elemental bodies. The last topic also requires us to consider his remarks on the elements, especially fire. As we have noticed elsewhere, Copernicus’s remarks are often dialectical, meaning that they make clear what he rejects in the view of a predecessor or opponent. His remarks seldom allow us to attribute to him a complete theory, and so the characterization remains tentative and incomplete. As we saw in chapter four, Cracow philosophers of the 1490s reported the theory of impetus but without adopting it, or, if they adopted it, they adapted it to conform to Aristotle’s doctrine. Perhaps this explains Copernicus’s cautious use of impetus. This is again a case where scholars driven by the logic of their own reconstructions have attributed to Copernicus opinions that are stated in too global and complete a form.24 In short, Copernicus does not work out the details. He is content to point out the weaknesses in the views of his opponents, and offer alternatives that are, at best, suggestive of

23 On the comparison of Plato and Aristotle on the place and motion of the elements, see Solmsen, Aristotle’s System, 127–129 and 266–269. 24 Wolff, “Impetus Mechanics,” provides the most thorough argument in support of Copernicus’s adoption of impetus mechanics. I agree with much in Wolff ’s analysis, but his thesis of continuity between impetus mechanics and classical inertial mechanics drives him to interpret Copernicus’s remarks as implicit adoption of impetus dynamics. Wolff ’s summary of Copernicus’s modifications of traditional impetus theory, 230–231, is superb. But the logic of his argument leads him (227–230) to force Copernicus’s clear restriction of impetus to account for forced or violent motions into Copernicus’s explanation of the natural motions of spheres and the motions of the bodies that they carry. Kokowski, 230, also concludes that Copernicus implicitly applied the theory of impetus to natural motions where he discusses an unfailing cause. For a superb review and critique of the now standard misconceptions about socalled impetus mechanics, see Sarnowsky, “Concepts of Impetus.” Although modest and tentative in his remarks, Drake, “Impetus,” 45–46, already in 1975 warned readers clearly and pointedly about converting the possibility of a relation between impetus and the discovery of the law of free fall into an actuality that is not supported by the documents. See also Goddu, “Impetus.”

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a solution. It is an obvious fact that he does not work out all of the details, but his restraint and caution have not deterred some scholars from developing a full-blown theory on his behalf and attributing their views to Copernicus. This is not to say that efforts to construct complete accounts on his behalf are worthless. On the contrary, they are instructive and informative, always providing evidence with possible sources, and thus contributing to a deeper understanding of Copernicus’s achievement. I have considered them carefully, and rejected them reluctantly. In two cases “rejection” is far too strong a word. I have revised and adapted the interpretations of Michael Wolff and Michał Kokowski to my interpretative framework, although they will likely find my reinterpretation unacceptable. In yet a third case, Dilwyn Knox, we will consider the most comprehensively documented analysis of Copernicus's doctrine of gravity.25 I would like to think that most of our differences are a matter of definition and qualification. I agree that Copernicus’s account is not Aristotelian. His theory requires a drastic re-interpretation of Aristotle’s principles, yet I will argue that Copernicus used other ancient authorities to exploit inconsistencies and ambiguities in Aristotle’s texts precisely to adapt them to a heliocentric cosmology. Let us return to Copernicus’s remarks in De revolutionibus. In I, 4, after characterizing the circular motion of the heavenly spheres as an expression of its form as the simplest body,26 he asserts that a simple sphere cannot move a simple heavenly body non-uniformly.27 The only way that a heavenly body could move non-uniformly, he adds, would be by means of an inconstant force (whether extrinsic or intrinsic) or a change in the revolving body.28 He rejects these alternatives because they are unworthy of objects that are constituted in the best order.29 He concludes the chapter by suggesting that the position and motion of Earth may be the cause of the observed non-uniformities. 25

Knox, “Copernicus’s Doctrine of Gravity.” Gesamtausgabe 2: 9, lines 21–23: “Mobilitas enim sphaerae, est in circulum volvi, ipso actu formam suas exprimentis in simplicissimo corpore, . . .” 27 Ibid. 10, ll. 11–12: “Quoniam fieri nequit, ut caeleste corpus simplex uno orbe inaequaliter moveatur.” 28 As Aristotle affirms in De caelo II, 6. Compare De rev. 10, ll. 12–14: “Id enim evenire oporteret, vel propter virtutis moventis inconstantiam, sive asciticia sit, sive intima natura, vel propter revoluti corporis disparitatem.” 29 As Aristotle asserts in De caelo II, 12, 292a15–28. See section 2 above, and compare De rev. 10, ll. 14–15: “Cum vero ab utroque abhorreat intellectus, sitque indignum tale quiddam in illis existimari, quae in optima sunt ordinatione constituta: . . .” 26

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Note that Copernicus assumes that the sphere exerts a constant moving force (virtus movens expressed negatively in context as virtutis moventis inconstantiam) on the celestial body. The application of the constant moving force generates a uniform motion, which suggests that the sphere, rotating uniformly, moves the body by contact with it or by carrying it. Copernicus follows Aristotle’s “natural” view that celestial bodies do not move themselves or have independent movers but are caused to move by the spheres in which they are fixed.30 There is no suggestion here that the sphere imparts a force or a quality to the body that keeps it moving.31 This is not the doctrine of impetus as espoused by Jean Buridan, who speculated that God imparted a noncorruptible impetus to a celestial sphere.32 As Edward Rosen notes, Copernicus’s expressions here are similar to Aristotle’s in De caelo II, 6, 288a28–288b8, and are a consequence of Aristotle’s principle that everything in motion is moved by another. Copernicus does not explain precisely what moves a sphere or how the sphere moves a celestial body. He apparently thinks that the uniformly rotating sphere carries the celestial body around—only that which is simple can move what is simple, and so it is impossible that its motion should be irregular. The conclusion also echoes the passage in De caelo II, 6.33

30 Of course, Aristotle proposed two theories about the motions of the heavenly spheres. 1) On the assumption that they are animate and their motions voluntary, he proposed intelligences or separate movers whose motions are caused by the prime mover as an object of desire. 2) On the assumption that they are natural, he proposed the fifth element whose nature is to move in a circle. 31 Kokowski, 229–230, assumes that “impetus,” “force,” and “moving force” are synonyms, thus justifying the conclusion that where Copernicus refers to an “unfailing cause” (causa indeficiens), he also means “impetus.” Likewise, Wolff, 218–231, interprets causa indeficiens as a permanent impetus transferred to a “natural” motion by the supposed connection between circular and rectilinear motion. But if “natural,” it needs no impetus or extrinsic force to move it. The body merely needs the “force” to actualize its natural potentiality for circular motion. 32 Again, Copernicus’s account is based on Aristotle, De caelo II, 8, 289b30–35. Buridan proposes the theory as an alternative to Aristotle’s moving intelligences. See Johannes Buridanus, Quaestiones II, q. 12, 180–181: “Posset enim dici quod quando deus creavit sphaeras caelestes, ipse incepit movere unamquamque earum sicut voluit; et tunc ab impetu quem dedit eis, moventur adhuc, quia ille impetus non currumpitur nec diminuitur, cum non habeant resistentiam.” Compare with the edition of Patar, Ioannis Buridani Expositio, 443, lines 81–85. 33 Rosen, Commentary, 349 to p. 11:17. See Kokowski, 221–222 and 229–231, where he reads “impetus” and “moving force” as synonyms. Although he cites the Aristotelian principle in the scholastic formulation (“Omne quod movetur ab alio movetur.”), he overlooks De caelo II, 6, and does not analyze the relation between the moving

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In De revolutionibus I, 8, however, Copernicus uses the word impetus four times. In the first (Gesamtausgabe, p. 14, line 19), he associates impetus with vis, and contrasts things to which force or impetus is applied with things that are moved according to nature. Things moved by an impetus, he says, soon disintegrate (dissolvi) and cannot subsist for long. By contrast, things moved by nature are well ordered and in their best state. From this text it is clear that Copernicus uses “impetus” to account for violent motion, but the rotation of Earth on its axis, he argues, is natural and so cannot be the result of force or violence.34 The next occurrence (14, line 28) is in a context that we may consider counterfactual. Copernicus chides Ptolemy for having overlooked

sphere and the moved body. Wolff, 219–220, similarly reinterprets these passages. As I have argued, Copernicus holds the view that celestial bodies are attached to or embedded in spheres—they carry the celestial bodies. Copernicus does not discuss the relation more specifically, and nowhere does he say that the sphere imparts or gives a force to the body, which continues to move the body. Copernicus also does not explain how bodies move on epicycles or eccentreccentrics; nor does he explain the cause of Earth’s rotation on its axis. It may be that Copernicus adhered to some version of the theory of impetus, but the text from I, 4 is consistent with De caelo II, 6. Kokowski juxtaposed the Latin text of De revolutionibus in the critical edition (Warsaw) and German, French, Polish, and English translations. Translations are interpretations, of course, and Kokowski’s juxtaposition shows that the translators usually rendered “impetus” as “force,” “power,” “violence,” or some such word. The translations are not inaccurate, but reflect the views of the translators, all of whom rejected the idea that Copernicus was an adherent of the medieval theory of impetus. Kokowski notes some similarity between Copernicus’s understanding of impetus and the view held by Nicholas of Cusa, but Kokowski does not assert that Cusa was Copernicus’s source. Rosen cites a text by Cusa in his commentary, 348, but also does not assert Copernicus’s familiarity with it. Unfortunately, we do not know whether Copernicus saw or read any of Cusa’s works. In my checking of the lists of books in the libraries at Lidzbark and Frombork, I could find no mention of Nicholas of Cusa. If there was a copy in either of those libraries, it did not end up in Sweden as far as we know. The library at the Jesuit College at Braunsberg lists a copy of the works of Cusa, but its provenance is unknown. See Hipler, ZGAE, 5: 384. 34 Kokowski, 222–231, cites this text but does not consider it separately from the others, overlooking the contrast between natural and violent. Moraux, 232, also notes in relation to this passage that Copernicus does not specifically invoke projectile motion here, and so Moraux distinguishes the use of the term from Buridan’s version of the theory. As I indicated above, Wolff does not address the question why a natural motion or a natural capacity would require an impetus. He does so, I believe, because he overlooks the alternative answer to the question of what the moving cause is. Copernicus does not explain the motion of those spheres that rotate. Perhaps God moved them or removed hindrances. The sphere carries a celestial body; there is no need of an extrinsic force in the form of impetus being transferred to the body. My remarks are repetitive, but that is because the same objection applies to the relevant steps in Wolff’s and Kokowski’s arguments.

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the tremendous centrifugal force that would be generated by a swiftly moving starry vault.35 The higher they would be carried by the impetus of their motion (motus impetu) the faster they would have to move because of the expanding circumference. Again, impetus is associated with a force that would lead to an infinite motion, which, he reminds the reader, contradicts an axiom of physics that the infinite cannot be traversed or moved. Indeed, the axiom is Aristotelian.36 The implication is clear that he associates impetus with violence and disruption, not with what moves according to nature.37 The third use of the word impetus (15, line 29) occurs in a context where Copernicus explains how air, clouds, and other things suspended in air share in Earth’s rotational motion. He speculates that air may mingle with watery or earthy matter and so by its proximity to Earth would share in its constant revolution without resistance. The air and things in it closest to the surface are tranquil unless the wind or some other impetus drives them this way and that.38 Again, Copernicus applies impetus to explain a motion that is contrary to nature. Copernicus uses impetus one last time (16, line 10) in a context where he explains the compound motion of falling and rising bodies, and why their motions have a rectilinear component. Their rectilinear motion is not simple, uniform, and equal (unvarying), for they cannot be regulated by their lightness or by the impetus of their weight.39 A

35 In fact, Copernicus misrepresents Ptolemy’s view here. I owe this observation to Knox. See Knox, “Copernicus’s Doctrine,” 174, n. 81. Perhaps this was another case where Copernicus was commenting from memory or an earlier misapprehension that he did not question, even though he had texts at hand. 36 For example, De caelo III, 2. 37 Kokowski, 222–231, notes that Copernicus “explicitly applied the term impetus in three places, where he considered the issue of violent motion” (emphasis in the original). Yet, he says, 230, “we must conclude that Copernicus implicitly applied the theory of impetus also in the case of natural motion in these contexts where he writes about causa indeficientia (sic) (‘unfailing cause’).” In his footnote 8, 231, he claims that Copernicus applied the concept of impetus to both violent and natural motions. As we see, however, at the beginning of I, 8, Copernicus contrasts natural motions with violent motions, and it is only with reference to the latter that he uses impetus. 38 De rev. 15, 28–29: “Proinde tranquillus apparebit aer, qui terrae proximus, et in ipso suspensa, nisi vento, vel alio quovis impetu ultro citroque, ut contingit, agitentur.” The 1543 edition, f. 6a, reads “agitetur” at the end. Kokowski, 221–231, overlooks this passage. 39 De rev. 16, 8–10: “Praeterea quae sursum et deorsum aguntur, etiam absque circulari, non faciunt motum simplicem uniformem et aequalem. Levitate enim vel sui ponderis impetu nequeunt temperari.” In De caelo III, 2, Aristotle himself speaks of the impulse of weight and lightness. And in III, 2, 301b17–302a9, he introduces some

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falling body moves slowly at first and increases its speed as it falls, and earthly fire we perceive to relax all at once after it has achieved a high altitude.40 This behavior shows that the cause is the violence applied to earthy matter. This passage does suggest that Copernicus may have adopted the notion that the weight of a body generates an accidental impetus that causes a falling body to accelerate. But he immediately adds that the cause is violent because the motion is not simple, uniform, and equal. A little further below, however, he reminds us that bodies moving with rectilinear motion retain a circular component, so their motions are partly natural (the simple and uniform circular component) and partly violent (the accelerated component of their rectilinear motions). Here we need to introduce more careful distinctions. A falling body has a compound, not simple, motion because its motion is both circular and rectilinear. But the rectilinear component itself is compound and not simple, for the motion produced by gravity is the result of a natural appetite instilled in bodies by God. That is to say, the rectilinear motion produced by gravity is natural. The acceleration, however, requires violence, an impetus.41 As soon as such bodies have reached their own place, they cease to be heavy or light, and their rectilinear motion ends. Circular motion belongs to wholes, rectilinear to parts. He adopts the metaphor that circular abides with rectilinear as being alive abides with sickness. Here the contrast seems to be between the more perfect and the less perfect or the natural and the less natural, not the natural and the violent or contrary to nature. In playing with such comparisons, Copernicus evidently intends to strengthen his conclusion that Aristotle’s division of simple motion into three types (towards the middle, away from the middle, and around the middle) is a rational, not a real, distinction.42 Although the passage contrasting

complications in his understanding of natural motion and how some natural motions are mixed with force or a violent impulse. 40 Knox, “Copernicus’s Doctrine,” 170, interprets in sublimis as “upwards,” one of its possible meanings, but the meaning is ambiguous, and it is not clear how high Copernicus thought fire moved, possibly higher than we can actually perceive. 41 I owe the distinction between the composite motions of a falling body and the composite motions of the rectilinear component of a falling body to Knox. 42 Kokowski, leaning on Markowski, also suggests that Copernicus may have been familiar with a work that derives from Jean Buridan or some other fourteenth-century terminist source. Copernicus uses the expression “ponderis impetu” to explain the acceleration of a falling body. Scholars often claim that medieval interpreters adopted the theory of impetus to account for the acceleration of a falling body. The theory

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being alive with sickness can be interpreted as a contrast between the natural and the violent, the comparison in Copernicus seems softer. As we will see in more detail below, there are reasons for thinking that Copernicus relied on the Suda here, but Copernicus’s rendering suggests that he either softened its contrast between natural and contrary to nature or he read it as intending to soften the contrast.43 Copernicus understood impetus to account for motions that require an extrinsic force and that are not simple, uniform, and equal.44 The motion of a part towards its whole, however, is not a completely violent motion. Such motions retain a circular component, and even the rectilinear component of falling bodies is the result of heaviness, which he calls a natural desire that God implanted in parts for the purpose of gathering them together in the form of a globe (I, 9: 17, lines 29–33). It appears that Copernicus’s doctrine of motion was undeveloped. Its ambiguous and apparently inconsistent features suggest that at this juncture in his argument he was less interested in developing a complete and coherent theory than in raising doubts about Aristotle’s theory.45 His statements are intended to reveal the arbitrariness in the application of the principles. He emphasizes the variations in the dissupposedly corrects Aristotle’s idea that the speed of a body is directly proportional to its weight and inversely proportional to the resistance of the medium (V α W/R, in modern form). Aristotle's apparent belief that one can calculate average speed in this way and the implicit claim that he was ignorant of the fact that a body accelerates as it falls are preposterous on the face of it. It is difficult to believe that observers seeing the different impacts caused by the same body falling over a greater distance or time would not conclude that the body has increased in speed, even if they were in doubt about whether or not the speed increased uniformly. In fact, in De caelo III, 2, 301b21–23, Aristotle asserts that a body accelerates as it falls, and explains that a force makes a falling body move more quickly downwards. The point here is that a force accelerates a natural motion. 43 Hooykaas, “Aristotelian Background,” 111–116, interprets Copernicus’s use of the analogy between healing and the rectilinear motion of a falling body in Aristotelian terms as not wholly natural and not unnatural or violent either. This reading seems to me to square with the ambiguity in Copernicus’s account. Hooykaas suggests that Copernicus could have developed this account by relying on scholastic commentaries, but as we shall see below, Knox has suggested an alternative source, and in my view, I believe that he has found the text on which Copernicus relied for this reading. 44 Perhaps this is what he understood by Aristotle’s remark that “force” is a cause in something else or it is in the thing itself regarded as something else. Weight in a heavy body seems to generate such a force. 45 In comments shared with me, Knox argues that the construction of an account of elemental motion was critical for the reception of Copernicus’s cosmology. The outcome, he argues, was a theory that was consistent, if tortuous and undeveloped. According to Knox, Copernicus intended to do more than raise doubts about Aristotle’s doctrine. It seems to me that its undeveloped character rather supports the

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tances of celestial bodies from Earth (I, 8 and I, 9) to refute the Aristotelian division between motion away from and motion towards the center. With exception of the stars, the observations confirm that all celestial bodies do both.46 He rejects the generalization that a simple body has a simple motion. His principal aim was to move readers to accept the greater probability of Earth’s motions. This still leaves us, however, to examine his remarks about elemental motions more closely. First, Copernicus adopts an account of the elements that diverges from Aristotle’s. The ultimate source seems to be Plato, but the analysis is driven by his recognition of the need to assimilate air to water and earth. He needs to explain how air shares in the motion of a globe that is earthly and watery. He may have rejected Aristotle’s views about elemental fire and aether, but his remarks are ambiguous (I, 7–8 and I, 10).47 He makes these remarks almost in passing. In the autograph he also refers to the theory of atoms to make a point about the immensity of the universe (I, 6), but it is not clear from the comment that he adhered to the theory.48 One may assume from his description of the Sun as a lamp and lantern that he believed it to possess fire, but he does not say so explicitly. Aleksander Birkenmajer pointed out that Copernicus’s reference to blazing smoke (“fumum ardentem”) comes from Aristotle, but he added that the reference to its explosive nature resembles a comment by the Stoic Cleanthes cited by Cicero. The Stoics did distinguish between terrestrial fire and the element fire that is proper to the Sun, an opinion refuted by Aristotle.49 Evidently, Copernicus rejected Aristotle’s speculation about aether, for he attributes the circular motion of a sphere to its geometrical form, not aether.50 In I, 8, he says that earthly fire is the only fire we see, but he refers in I, 10 (19, line 15) to “aether” in a place where we would normally see “fire,” and a little above (line 11), in the autograph, he rhetorical strategy of introducing doubts about Aristotle’s doctrine and suggesting alternatives that would reinforce those doubts. 46 But see the explanation by Johannes Versoris, Quaestiones de caelo et mundo I, [q. 11], f. 3vb. See chapter four, and Goddu, “Sources” and “Teaching.” 47 Rosen’s comment, 353 to p. 17:16, that Copernicus rejects the elemental fire of the traditional cosmology requires qualification. See also Kokowski, 55. 48 Someone, probably Copernicus himself, deleted the passage. See Rosen, 350 to p. 14:19, for comment. 49 Birkenmajer, 368 to p. 16, 27–29. He refers to De generatione II, 4, 331b25–26; and Meteorologica IV, 9, 388a2. 50 Rosen, 348 to p. 10:30.

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again uses “aether” as a synonym for what is called the “fiery element” (“. . . et si placet eitam aethera, quod igneum vocant elementum”).51 From all of these considerations and opinions I conclude that Rosen was hasty in claiming that Copernicus rejected fire as an element. Copernicus says that light bodies such as fire move upwards and in a straight line, but he also says that the motion is a compound of circular and straight. As it rises upwards, it suddenly relaxes, which suggests that once it has reached its proper place, its motion is circular. There are at least four possible sources for Copernicus’s account. The first source is Aristotle himself, in a passage that Rosen evidently overlooked. In Meteorology I, 3, 340b20–25, Aristotle says the following:52 So what is heaviest and coldest, that is, earth and water, separates off at the centre or round the centre : immediately round them are air and what we are accustomed to call fire, though it is not really fire : for fire is an excess of heat and a sort of boiling. But we must understand that of what we call air the part immediately surrounds the earth is moist and hot because it is vaporous and contains exhalations from the earth, but that the part above this is hot and dry.

Note Aristotle’s distinction here between “fire” and “what we are accustomed to call fire.” He continues at 340b30–31: “We must suppose therefore that the reason why the clouds do not form in the upper region is that it contains not air only but rather a sort of fire.” And then a little below at 340b37–341a9 adds:53 It moves in a circle because it is carried round by the motion of the heavens. For fire [i.e. what we are accustomed to call fire] is contiguous with the element in the celestial regions, and air contiguous with fire, and their movement prevents any condensation; for any particle [of fire] that becomes heavy sinks down, the heat in it being expelled and rising into the upper region, and other particles in turn are carried up with the fiery exhalation : thus the one layer is always and continually full of air, the other of fire, and each one of them is in constant process of transformation into the other.

Copernicus’s statements seem to echo the ambiguity in Aristotle’s own account.

51 Opera omnia 1: fol. 8v, line 16. Copernicus evidently cancelled the word “aethera.” In Meteorologica I, 3, Aristotle allows for variety in the purity of ether. 52 I have relied here on Aristotle, Meteorologica, tr. Lee. 53 Ibid. The comments in brackets are supplied by Lee in footnotes.

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A second source is Pliny, Natural History II, III, 10–11, where he places fire in the region of the blazing stars, and echoes the Stoic theory of cosmic cohesion. We know that Copernicus relied on Pliny for some of the comments that he makes that reflect Stoic conceptions of force and constraint.54 Earthly fire is the only fire that we perceive, and in I, 10 Copernicus refers to “what is called ‘the element of fire’.” For the third source Dilwyn Knox argues that the usage derives ultimately from Plato (Timaeus 58d), and that Copernicus probably got it directly from pseudo-Plutarch, Placita philosophorum II, 7.55 In these passages we find distinctions between types of fire and also comparisons with explosion and expulsion. One could argue, however, that Copernicus followed standard conflations of Platonic, Aristotelian, and Stoic doctrines with little attention to inconsistencies. Commentators were more concerned with the general configuration of the cosmos than with the details for their own sake. Even if he relied on Pliny, Plato, and the Placita philosophorum, Copernicus may have interpreted them as roughly consistent with Aristotle’s own ambiguous remarks, but Copernicus used them to argue that the other elements share in the motion of the Earth. The Stoic sources served his purposes.56 This now brings us back to Copernicus’s account of elemental motion. There are clearly non-Aristotelian elements in Copernicus’s account. Wolff and Kokowski tend to regard Copernicus’s comments as anti-Aristotelian. Kokowski argues that Copernicus held some

54 Obrist, Cosmologie médiévale, 253–255, comments on Pliny’s reinforcement of Stoic doctrines. See also Knox, “Copernicus’s Doctrine,” 182–193, where he considers Aristotle, scholastic interpreters, Plutarch, Pliny, and Cicero as sources for Copernicus’s account of gravity. Knox’s distinction between a physical and teleological account of gravity is important. He rejects Krafft’s argument that Copernicus relied on Plutarch’s De facie. See Krafft, “Copernicus Retroversus II.” According to Knox, Pliny and Cicero were almost certainly Copernicus’s sources for his teleological doctrine, although he thinks that Cicero provided the closest doctrinal fit. See Pliny, Natural History II, II, 5, and II, LXV, 163–164. For Cicero, he cites De natura deorum II. xlv. 115–xlvi. 117. 55 Knox, “Ficino and Copernicus,” 412–413, note 54. Compare Kokowski, 55. I believe that Wolff, 221, goes too far in maintaining that “Copernicus intends to get rid of the five Arisotelian elements, . . .” 56 I have tried to conform my interpretation as much as possible to Knox’s authoritative acquaintance with the sources, but he emphasizes departures from Aristotle where, it seems to me, Copernicus has already subordinated his interpretation to the geokinetic theory.

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version of impetus theory that ultimately derives from Buridan.57 Birkenmajer and Moraux, on the contrary, have shown that Copernicus’s comments are not compatible with the details of Buridan’s account.58 Wolff maintains that Copernicus modified the traditional theory of impetus.59 Rosen has also emphasized the difference between Nicholas of Cusa’s “initial impulse” that God imparted to the celestial spheres and Copernicus’s explicit comments.60 Also by contrast, Knox has made a meticulous search for the sources of Copernicus’s comments, from which he has tried to reconstruct Copernicus’s theory of elemental motion. First, Knox argues that Copernicus relied on Pliny and/or Cicero, especially for the teleological doctrine of gravity. Second, he argues persuasively that Copernicus used the Suidae lexicon, and relied on it for the physical doctrine of gravity. Third, he contends that Copernicus’s doctrine of gravity has more in common with the idea presented in the Suda under the lemma kínesis than with any other supposed source. The version in the Suda may derive ultimately from Johannes Philoponus. Knox, of course, also emphasizes the differences, especially in details, between Aristotle’s and Copernicus’s conceptions. For example, Aristotle held that a piece of earth displaced from the center of the universe would return in a straight line to the center regardless of whether or not there was any Earth there already. Not that Aristotle admitted such a possibility really, but the point is that his doctrine of natural place established directionality as absolute, not relative. The same holds for the light element, fire, and for the “circular” element, aether. Copernicus, on the other hand, regards natural place as the whole to which a heavy body (water and earth) moves because God has implanted in the parts a natural desire to be reunited with their whole where they move only with circular motion. Air and presumably fire behave similarly.61 The principle of returning to their respective wholes applies, Copernicus conjectures, to the Sun, Moon, and all of the planets. Copernicus’s natural place, then, is relative, not absolute.

57

Kokowski, 56 and 218–231. Birkenmajer, 368–370; compare Moraux, 232. 59 Wolff, 230–231. 60 Rosen, 348. 61 Knox, “Ficino and Copernicus,” 413–414. In fact, Copernicus argues that as elements return to their wholes, their motion is compounded of straight and circular components. Aristotle’s argument is in De caelo IV, 3. 58

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The idea of returning to a sphere rectilinearly where an element resumes its natural circular motion derives from several ancient sources. As Knox shows, it became a standard Neoplatonic doctrine. Philoponus adopted it, and it reappears in Nicole Oresme’s Livre du ciel et du monde, Nicholas of Cusa’s De docta ignorantia, and Giorgio Valla’s De expetendis et fugiendis rebus. As we saw in chapter seven, Copernicus used Valla’s book extensively, but Knox says that while its account of the doctrine does correspond to Copernicus’s version, it is brief and lacks the details found in Copernicus’s version.62 Next, Knox considers carefully but also eliminates Ficino as the source, concluding that a better fit is a quotation of presumably Philoponus’s account in the Suda under the lemma kínesis as we indicated above.63 I cite the Latin version of the Suda provided in the footnotes of the 1853 edition, and translate the relevant part here:64

62 Knox, “Ficino and Copernicus,” 415, n. 59. In “Copernicus’s Doctrine,” 194–208, esp. 199–201, Knox reviews in detail all of the relevant possibilities. 63 On Ficino and Neoplatonic sources in general, see Schmeidler, Kommentar, 184. 64 In “Copernicus’s Doctrine,” 194–208, Knox bases his analysis on editions of the Suda from 1499 and 1514, one or both of which Copernicus likely knew and used. His translation of the relevant passage is reasonably close in its essentials with one significant exception to my translation of the Latin translation that I used. Of course, readers should consult Knox’s more authoritative source and translation. See Suidae lexicon, columns 260–264. For the complete entry, see Appendix VIII. Here I quote only the translated passage: “ Motus etiam existit, cum res alium ex alio locum mutant.—Quae per orbem aguntur interitu vacant.—Aliter de motu. Non est, inquit [Aristoteles,] glebae naturale moveri deorsum, neque igni sursum ferri: neque enim talis motionis principium in se habent, sed extrinsecus ab alio moventur. unumquodque enim elementum in suo toto quiescit: quippe tota vel stare volunt vel in orbem moveri: est autem motio in orbem quies quaedam. Iam secundum naturam suam gleba cum movetur, in suo toto manet immobilis; quemadmodum hic ignis in sua sphaera. cum vero gleba vel aqua vel hic aer extra locum naturalem existit, singula ad totum suum tendunt, et quieti naturali restitui cupiunt. nam ab vi quadam externa ex loco naturali pulsa moventur ea via, quae est secundum naturam. quando quidem sic moventur, ut quae in alieno loco existant, et toto suo contra naturam privata sint. Non igitur motus ille secundum naturam est, quo res ad locum naturalem tendunt (alioquin enim ipsa tota sic moverentur), sed viae ad id quod est secundum naturam. Potest tamen etiam motus ille naturae consentaneus dici: eo nimirum sensu quo dicimus sanitatem esse secundum naturam, morbum vero contra naturam. illa ducit ad id quod est secundum naturam hic vero ad id quod est contra naturam. id enim quod primum movet, si quidem corpus sit, ipsum etiam movetur. movet enim baculum ianuam, et baculum manus, quae non manet immota, sed ipsa movetur. quod si primum movens sit incorporeum, nihil necesse est ipsum quoque moveri, dum alterum movet. nam deus, qui universum movet, ipse est immotus, utpote stabilem habens essentiam et facultatem et actionem.”

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chapter nine Motion also occurs when a thing moves from one place to another place.—Things that are moved in a circle are incorruptible.65—Another account of motion. It is not, says [Aristotle]66 natural for a clod of earth to be moved downwards, nor for fire to be carried upwards: for they do not have the beginning of such motion in themselves, but are moved by something extrinsic. For an element rests when it is together with the whole [of which it is a part]; in fact the whole either tries to remain at rest or to be moved in a circle: but motion in a circle is a kind of rest. When the clod of earth is moved according to its nature, it remains immobile when together with the whole [of which it is a part], just as fire does when it is in its sphere. But when earth, water, or air is outside of its natural place, each tends to its whole, and desires [is inclined] to be restored to its natural quiet. For things moved from their natural place by a certain external impulse are moved in a way that is according to nature. When things are so moved that they are in another place, they are deprived of their whole, contrary to nature. Therefore such a motion by which they tend to their natural place is not natural (otherwise the whole itself would be so moved), but the ways to those places are natural.67 Nevertheless the motion can be said to be consistent with nature: in the same way in which we say that health is natural and disease is contrary to nature. Health leads to that which is natural, but disease to that which is contrary to nature. For that which moves first, if it is a body, is itself moved. When a staff moves a door, and my hand, which does not remain unmoved, moves the staff, it is moved by itself. But if the first mover is incorporeal, it is not necessary for it to be moved itself while the other moves. For God, who moves the entire universe, is himself unmoved, for he has an immutable essence, power, and action.

The context of these assertions is the discussion of Aristotle’s De anima I by Philoponus. The issues concern self-moving beings, the motions of

65 I have interpreted the Latin passage by comparison with the Greek version, which my colleague Nathaniel Desrosiers translated for me. 66 The editors’ addition that the doctrine is from Aristotle is impossible. As Knox suggests in a note to his translation, presumably Philoponus is meant, and I agree. 67 As in Aristotle, De caelo III, 2, the implication here is that the cause, though in the body, is accidental to it, and hence not part of its essence. Knox, however, translates this part thus: “Therefore motion towards natural place is not by nature. For it is the wholes that produce these motions. Hence it is that these motions of parts are not according to nature but are paths to what is natural. It is possible to move ‘according to nature’ otherwise, as when we say that recovering health is according to nature and sickness is, so to speak, contrary to nature. For the former leads to what is according to nature, the latter to what is contrary to nature.” Even in Knox’s translation, however, there still appears to be an ambiguity inasmuch as we are told that “recovering health” is according to nature. It would follow that a body moving to its natural place would be analogous to recovering health, and so according to nature, and it is an ambiguity that Copernicus himself reflects.

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bodies, projectile motions, and the contrast between Plato and Aristotle. In my view, the passage along with other evidence confirms Knox’s speculation that Copernicus used it in his account of natural place and elemental bodies in De revolutionibus I, 8. The similarity between Copernicus’s remarks and the comments in the text are especially clear in the part that has to do with the tendency of bodies to be reunited with their wholes in their proper spheres. The same ambiguity arises about whether such motions are natural or violent. The motion by means of which a thing tends to its natural place is not natural, but the things to which they move are according to nature.68 The motion can be said to consent to nature in the sense in which we say that health is natural and disease contrary to nature. The one leads to that which is natural, the other to that which is contrary to nature, but recovering health is motion back to its natural state. By analogy, even the rectilinear component of a falling body is natural motion to the extent that it is a motion back to its natural state. Even in the case of a moving body, the first mover moves itself, and here the entry uses an example which is reminiscent of the theory of impetus. Yet it can also be read as a confirmation of Aristotle’s principle that everything moved is moved by another, as applied especially in De caelo III, 2.69 That said, we now consider the differences between the entry in the Suda and Copernicus’s comments. First, the body in its proper sphere remains at rest, for there is no suggestion here, except for the equivalence it proposes between motion in a circle and rest, that as a body achieves its natural place it moves in a circle. Motion in a circle is natural for the element fire (and perhaps air) in its sphere, but the natural motion of earth is rest at the center. Indeed, Copernicus requires an explanation for the circular motion of the air nearest to Earth, and here we saw him appeal to conformity of nature or proximity as possible explanations.70 Second, the entry in the Suda tends to regard the

68 This is the significant departure from the Greek to which I alluded earlier. In his comments on my chapter, Knox pointed out that there is no suggestion in the Greek that the path itself is natural. Rather is it the things to which they move that are according to nature. 69 Hooykaas, “Aristotelian Background,” again reads the comparison between recovering health and the rectilinear motion of a falling body in Aristotelian terms as a return to the natural perfection of a body’s Form. 70 Ingram, “Revolution,” 28 and 32, note 18, maintains that impetus helped to explain why falling bodies and airborne phenomena are not left behind by the rotation of Earth. Perhaps, but Copernicus does not appeal to impetus explicitly, rather

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motion of a body back to its whole as violent. Third, they move along a path to those things that are according to nature. Fourth, the entry is less ambiguous than Copernicus’s comparison in asserting that health is natural and sickness is contrary to nature. It may be, however, that Copernicus read the passage as softening the contrast, for Copernicus is insistent on the idea that motion in a circle is more natural than the compound motion of a falling body. And he reflects the same ambiguity in referring to its state as, not unnatural, but less natural. The rectilinear component requires a force, but Copernicus characterizes the tendency in things to return to their whole or sphere as implanted in them by God. This characterization suggests that the inclination is natural and that the motion, while not perfect, is partly natural. Because Copernicus must preserve its motion as compound and hence partly circular, it cannot be completely violent. Hence, he softens the contrast and makes it relative to conform to his theory. I believe that Copernicus combined it with Aristotle’s own account of the force involved in an upward or downward motion as partly natural and partly violent or less natural. Copernicus insists that circular motion is natural, and motion towards a whole is a compound of circular (natural) and rectilinear (partly violent and partly natural, or less natural) motion. Sickness for him is not contrary to nature but nature in a less perfect state. As in scholastic interpretations of Aristotle, Copernicus’s contrast between natural circular motion and rectilinear motion draws on the distinction between the essential and proper as opposed to the accidental and less proper.71 On the whole, then, I am inclined to agree with the view of Aleksander Birkenmajer. While claiming to recognize Copernicus’s reliance on several ancient and Renaissance sources, Birkenmajer nonetheless characterized Copernicus’s natural philosophy as a transformation of Aristotelian doctrine.72 He acknowledged Copernicus’s divergence from Aristotle—most of the differences are obvious, but he rightly distinguished between unavoidable departures from and explicit rejection

he refers to conformity in nature or proximity, indicating that he has not decided on a solution. 71 Compare with chapter four. 72 In fact, however, it is not at all clear to what extent Birkenmajer recognized Copernicus’s reliance on other sources for his doctrines in natural philosophy. In my view, Knox’s studies require us to take these sources far more seriously than any other account has to date.

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of Aristotle’s view.73 Knox has made the differences even clearer and persuaded me to reformulate the role of non-Aristotelian and nonscholastic sources in Copernicus’s accounts of gravity and elemental motion, but the passage in the Suda persuades me that Copernicus adopted the view presented there only in part and tried to reconcile it with his own conception of natural circular motion and the compound motions of rising and falling bodies. From the brief account that Copernicus provides, we are hardly able to construct a coherent physics of elemental motion, or attribute to him the traditional theory of impetus. As Copernicus wrote this chapter in the 1520s, he was probably mindful of disagreements among scholastics about the interpretation of De caelo III, 2 and perhaps Meteorology I, 3. Copernicus tried to move readers to reconsider the arguments in support of geocentrism. His principal aim was to reveal the arbitrariness in the application of his opponents’ own principles by adapting them to the heliocentric theory. Once he established the plausiblity of Earth’s rotation on its axis, he turned immediately in I, 9 to a consideration of other possible motions. All of that said, I beg the reader’s indulgence for the repetitiousness of the above summary and for the following attempt to render Copernicus’s theory as coherent as possible. Copernicus does not think of Earth as floating through space in an orbit; it is being carried with the Moon by a sphere in which it is embedded or to which it is attached.74 He nowhere explains any of this, namely, how the spheres carry or move the planets, probably because he simply took it over as a standard way of combining Ptolemy’s mathematical models with the doctrine of spheres. As he turns to the question of Earth’s rotation on its axis, he appeals to its form. But not all spheres rotate on their axes, or if he thinks so, he does not say so. He does not explicitly say that the Sun rotates on its axis, nor does the Moon, nor do the planets, probably because of the obvious fact that he has no observational evidence that they rotate. Observation shows that the planetary spheres move in circles around Earth in the geocentric system and around the Sun in his system. There is absolutely no explanation of the relation between the circular motions of the spheres and the motions of the bodies in the spheres

73 74

A. Birkenmajer, Études, 372. I will turn in detail to the role of spheres in Copernicus’s cosmology in chapter ten.

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other than the traditional belief and claim that the spheres carry and move the planets. His argument that Earth’s rotation is natural as following its form is dialectical. If it rotates and if there are no violent consequences, then it must be natural. As bodies fall, their motions must be compound, partly circular and partly rectilinear. His purpose in I, 8 was to raise doubts and questions about Aristotelian assumptions and conclusions, and to suggest how the concepts and distinctions could be linked together with other accounts in support of Earth’s axial rotation as more probable. All of that said, however, we still have to try to put this together into something that is at least apparently coherent. Copernicus does not explain how a celestial sphere moves the bodies in it. It appears that he intended his remark about form and spherical shape as a response to two objections. The first, about which he is explicit, is that the circular motion of a sphere is natural, not violent. The form or shape, however, indicates a potentiality, not necessarily actualized. The second objection that is rather implied than stated is more specific. How can a celestial sphere move a bulky object like Earth, a corollary to the objection against placing terrestrial elements in the heavens? By that move Copernicus seemed to shatter the division between celestial and terrestrial elements. He makes two responses to that objection. Ancient authorities, including Aristotle, did not make an absolute division between the celestial and terrestrial. The celestial influences the terrestrial by its circular motion, and there is ambiguity about elements such as aether and fire. Second, the emphasis on Earth’s spherical form means that it has a natural capacity for circular motion and rotation on its axis. The circular motion of the celestial sphere actualizes that potentiality just as the circular motions of the heavens move the bodies and elements below them in Aristotle’s system. Embedded as it is in a celestial sphere, Earth moves in a circle and rotates because its capacity for circular motion has been actualized. As in Aristotle, the higher can act on the lower, that is, the celestial sphere acts on the bodies embedded in it without violence. If correct, the answer is not completely satisfactory, for it does not explain why Earth specifically rotates on its axis.75 The argument from simplicity is

75 Of course, the answer to this question turns out to be very complicated, and was not addressed until cosmologists realized that the solution requires a historical reconstruction of the formation of the solar system.

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also a response to an objection, not a physical explanation. Of course, if Earth did not rotate on its axis, one side would always face the Sun and the other the night sky, so it must rotate, but that is not a physical explanation of its motion. That seems to be as far as Copernicus progressed in dealing with such questions. 5. Infinity and the Finiteness of the Cosmos A similar misunderstanding has arisen with regard to Copernicus’s views about whether the universe is finite or infinite. His system is properly called “heliostatic” for three reasons. (1) The Sun is stationary; (2) the center of Earth’s orbit is the mean Sun, eccentric to the Sun, that is, the center of Earth’s orbit is the geometrical center of his planetary models; and (3) the Sun is the center of the starry vault. He placed all of the stars at an equal distance from the center in the eighth sphere. The confusion about infinity has three sources. First, the failure to observe stellar parallax made the stars much farther than anyone had ever imagined, thus suggesting that the universe might be infinite. In the autograph copy of De revolutionibus, Copernicus said that the universe is infinite-like or similar to the infinite, meaning immense, not infinite pure and simple.76 And if he was referring to the space between the spheres of Saturn and the fixed stars, he suggested that God placed the stars at such a great distance so that we might more easily grasp the difference between planetary phenomena and the fixed stars. The planetary phenomena are effects of the Earth’s annual motion, but these phenomena do not appear in the fixed stars.77 The second source of confusion is a text by Copernicus himself where he raised the question about the infinity of the universe, and did

76 De revolutionibus, Appendix I, 490, 6–7: “Mundum . . . similem infinito.” The comment on the size of the universe appeared at the beginning of Book II, but in his translation Rosen added it with an explanation near the end of I, 11: 26, 39; the Warsaw edition places it at the beginning of I, 12. The same expression is used by Rheticus in Narratio prima. A similar expression appears in Pliny, Naturalis historia, II, 1: “[Mundum est] . . . finitus et infinito similis.” Szczeciniarz, 83–91, evidently believes that an infinite universe corresponds to Copernicus’s true view and his rhetoric. On 248 and elsewhere, Szczeciniarz notes Copernicus’s affirmation of a finite universe, implying that Copernicus contradicts himself. A similar problem arises with Szczeciniarz’s insistence that Copernicus proposed a homogeneous universe, a suggestion that he qualifies on 243 without qualifying his conclusion. 77 De revolutionibus I, 10: 21, 17–18.

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not settle it decisively, leaving it to natural philosophers to answer. We will return to that text momentarily. Third, the illustration accompanying the partial English translation of Book I of De revolutionibus by Thomas Digges in 1576 appeared to commit the theory to an infinite expanse of stars. Digges also retained the position of the Sun at the center, however, suggesting either that the illustration may not have represented his view or that he still did not quite grasp Copernicus’s mathematics or the idea in the radical way that Giordano Bruno proclaimed in 1584.78 The subsequent failure to observe stellar parallax with the telescopes available in the seventeenth century tended to support belief in the infinity of the universe. Copernicus’s intention is clear with exception of one text. His entire system with the stars located in the eighth sphere and the Sun at the geometrical center of the complete system fits a finite conception of the universe. Why, then, did he not answer his own question decisively? The text in question is about the space beyond the eighth sphere. Responding dialectically to objections against the Earth’s diurnal and annual motions, he wondered why geocentrists were not more worried about the centrifugal effects of a rapidly spinning eighth sphere contained by nothing. Would not the effect lead to an infinite expansion of the universe, in which case how could the eighth sphere move at all since, as every Aristotelian knows, an infinite space cannot be traversed in a finite time?79 With this answer he reflected the fact that natural philosophers were of several minds on the existence and nature of extra-cosmic void. If it existed, then did it possess matter of some sort? Was it like very attenuated air? Did space somehow fix the finite system of starry and planetary spheres? Even if there were nothing, it would be infinite in the sense of being without limit and capable of receiving bodies. Nearly everyone agreed that the universe itself did not move. After all, even Aristotle maintained that “heavy” bodies would have no natural motion in a void.80 The existence and nature of extra-cosmic void, then, were very much open questions in

78 Bruno, La cena de la ceneri (1584) and De l’infinito universo e mondi (1584). Nicholas of Cusa, De docta ignorantia II, 8, seems to affirm an infinite universe, but the subtle way in which he expressed it could be interpreted modally. It is possible from the point of view of God’s power that the universe could be greater. This conception of infinity is compatible with an actually finite universe. See Lai, “Nicholas of Cusa,” 161–167. On Digges, see also Granada, “Origins,” 518. 79 De revolutionibus I, 8. 80 Physics IV, 8, 215a5–18.

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the fifteenth and sixteenth centuries, and Copernicus reflected the lack of consensus. Whether the expanse beyond the eighth sphere is finite or infinite, it would make more sense to suppose the immobility of the eighth sphere and of the container of everything than to suppose that what is contained remains immobile.81 Copernicus demonstrated his dialectical ability to take Aristotelian principles and use them in support of his own view.82 Without maintaining that Copernicus would have remembered details of the teaching at Cracow on the subjects of place, void, and motion, I draw your attention to doctrines taught in the second half of the fifteenth century at the university. The discussions relevant to my inquiry begin with the problem of the place of the cosmos. Philosophers, astronomers, and theologians disagreed about the number of spheres, and some of them concluded that the last sphere, whatever its number, is not in place. The Cracow scholars who taught in the last decade of the century, however, maintained that the last sphere is in place not in the usual way but in an accidental sense, not per se.83 Cracow authors who held that view based it on the theological conception of the empyrean, the heaven that surrounded the last sphere proposed by philosophers and astronomers. Copernicus’s critique of the motion of the last sphere suggests that he was familiar with scholastic discussions and that he did not rely exclusively on the texts of Aristotle. It is not far-fetched to suppose that his speculations here may derive from the questions discussed at Cracow. Cracow natural philosophers were divided on the question of void. Some of them conceived of void as a place where bodies do not exist, but which is capable of receiving bodies. This combination of an Aristotelian with Platonic or Stoic conception, and the fact that one teacher devoted comments to other ancient conceptions, especially Plato’s, could very well have made an impression on Copernicus. For him the issue arises only with respect to the space beyond the eighth sphere. We do not know exactly which texts of Plato he may have read, but as late as 1542 he evidently regarded the diverse points of view about the

81

The argument appears near the end of I, 8. Compare with Aristotle, De caelo I, 5. As Knox suggested in his comments on this chapter, however, this is another respect in which Copernicus would have found Stoic sources congenial. 83 The last sphere was said to be accidentally in place in one of three ways, in relation to bodies on either side, to bodies immediately inside, or to the center. See chapter four. 82

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existence of void and the infinity of space as equally probable because they had not yet been settled conclusively by natural philosophers.84 Copernicus decisively affirmed the finite extent of the planetary spheres up through the sphere of the stars as one, whole, spherical body with a definite geometrical center. Perhaps thinking of the discussions at Cracow and other speculations about the place of God and the place of the finite system of Sun, planets, and stars, he left the question about the infinity of the void beyond the eighth sphere to natural philosophers. Assembling the results of my analysis in the final chapter, however, will lead me to modify this provisional conclusion reached in the context of natural philosophy. 6. Summary In trying to solve the problems of Ptolemaic astronomy, Copernicus discovered the reasons why the Ptolemaic planetary models link the planetary motions to the position of the Sun. He discovered the ordering of the planets, and how their ordering uniquely explains the phenomena of bounded elongation and retrograde motions as a natural and necessary consequence of the planets’ order and of the Earth’s annual motion. Convinced that he was right and convinced that Aristotelian principles were generally correct, he used Aristotelian principles and the views of Aristotle’s critics to criticize the theory of geocentrism. He pounced on the assumption that all observed natural motions are simple. That was the fatal flaw in Aristotelian cosmology. To correct that mistake he tried to adapt Aristotelian principles to the heliocentric system. He took advantage of centuries of combinations of Aristotelian principles with other beliefs, with empirical discoveries, with other philosophical schools, and he took advantage of humanists who harmonized Plato with Aristotle to suggest his own quasi-Aristotelian system.

84 Markowski, 173–179. For Stoic sources and the medieval background, see Grant, Much Ado About Nothing. See chapter four for details. On Asclepius and Hermes Trismegistus, referred to by Copernicus in I, 10, see Grant, Much Ado, 114–115. See also Rosen, Commentary to Revolutions, 359. Marsilio Ficino translated Asclepius into Latin in the fifteenth century.

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The place of natural philosophy in Copernicus’s reflections became clear. On the structure of the universe, natural philosophy is subordinate to astronomy and mathematics. The subordination, which he did not make general, depends on the following considerations: the requirements of geometry or geometrical models, ordering of parts according to a mathematical rule or relation (siderial periods), and mathematical results such as the ratios of planetary orbital radii. For all of these reasons he concluded that natural philosophers should yield to astronomers on the problem of the position and motion of Earth. An epistemological feature of his natural philosophy was his reluctance to draw conclusions of an empirical nature without compelling astronomical reasons or empirical evidence as, for example, in his reluctance to speculate about the axial rotation of the Sun, Moon, and planets other than Earth. He was suspicious of speculation based only on dialectical considerations, which he characterized pejoratively as logical exercises or merely acts of reason.85 The role of natural philosophy in his reflections also became clear— he knew he had to persuade the Aristotelians to reconsider their assumptions. As we all know, his efforts to persuade Aristotelians have to be counted in the short term among the most miserable failures in the history of philosophy. Some sixteenth and seventeenth-century Aristotelians displayed flexibility on the question of the Earth’s motion, but most sixteenth-century Aristotelians rejected the theory out of hand, just as Copernicus had feared. Even the Aristotelians who attributed an axial rotation to Earth explained it, however, as the result of an extrinsic force, not a natural motion. Also, some Aristotelians who adopted this view remained geocentrists. None followed the revisions of Aristotle that Copernicus had recommended. Without Copernicus’s aesthetic vision and mathematical intuition that the planets were ordered in one, and only one, way, late scholastic revisions of Aristotle lacked the coherence of Copernicus’s proposals. Aristotelians continued to maintain that the motion of heavy bodies downwards is simple; that was the assumption that Copernicus rejected.86 In the sixteenth century some Renaissance humanists questioned Aristotle’s

85 De revolutionibus I, 8: 16, 17–20: “Nempe et hoc, quod Aristoteles in tria genera distribuit motum simplicem, a medio, ad medium, et circa medium, rationis solummodo actus putabitur, quemadmodum lineam, punctum et superficiem secernimus quidem, cum tamen unum sine alio subsistere nequeat, et nullum eorum sine corpore.” 86 For the exceptions, see Grant, Defense.

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allegedly infallible authority, but it would take another thirty years after 1543 before explicitly anti-Aristotelian arguments in support of heliocentrism appear and yet another ten years or so before some of those attacks become vicious. We cannot fairly count Copernicus among those critics and certainly not among the vicious calumniators of Aristotle. One could say that sixteenth-century Aristotelians themselves provoked those kinds of reactions as their credibility waned. The discovery of cometary parallax in the 1570s destroyed the theory of celestial spheres of ancient cosmology.87 Although it would take another eighty years to become obvious, the discovery of cometary parallax also doomed Copernicus’s effort to revise Aristotelian natural philosophy.88 In this chapter I have tried to provide the likeliest answers to questions that scholars have posed about Copernicus’s natural philosophy. I have based the answers in part on an acquaintance with Copernicus’s intellectual milieu, that is, sources that we either know or reasonably assume were available to him,89 and in part on a systematic approach to his major works. In the next chapter I turn to questions about Copernicus’s beliefs about hypotheses, spheres, celestial matter, and mathematical models.

87 Swerdlow’s analysis, “PSEUDODOXIA,” 147–148, is persuasive. See Jervis, Cometary Theory. 88 It goes almost without saying that the effort to revise Aristotelian natural philosophy continued. Indeed, scholars continue to revise Aristotelian natural philosophy. The mysteries of quantum mechanics inspire some to return to Aristotelian holism as an alternative to mechanistic principles of natural philosophy. 89 Although I have examined many of the better-known works, I have relied on Dilwyn Knox’s extensive acquaintance with and persuasive interpretation of the sources.

CHAPTER TEN

COPERNICUS AS MATHEMATICAL COSMOLOGIST 1. Introduction By the time Copernicus began writing the substantial parts of De revolutionibus in the 1520s, he had his most intensive years as administrator and defender of Varmian canonical rights against the Teutonic Order behind him.1 In 1517 he wrote his work on the reform of the currency, and in 1525 the Treaty of Cracow dissolved the Knights of the Teutonic Order, thus ending the war with Varmia but at the cost of the greater dependence of Varmia on the Kingdom of Poland.2 We have concluded that Copernicus formed his fundamental philosophical views by 1510. It is likely, however, that he sharpened his focus on some issues, especially those regarding hypotheses and mathematical models. In this chapter we undertake a systematic analysis of Copernicus’s ideas about hypotheses and models, especially as revealed in De revolutionibus. In chapter seven I showed how his reading of sources persuaded him to adopt ancient assumptions concerning the perfection of spheres and circles. In this chapter I explicate the consequences of that decision. The chapter explains features of Copernicus’s mathematical cosmology that reflect a less robustly realist portrayal of Copernicus’s philosophy than one often encounters in surveys of his contribution to early modern science.3 Above all, the chapter presents some new insights explaining why Copernicus

1 This is not to say that he no longer had obligations, but they were not as intense as the years of struggle with the Teutonic Knights. See Biskup, Regesta copernicana. Many of the documents for the period 1525–1543 testify to Copernicus’s responsibilities, but many of the documents include personal correspondence relating to medical advice and matters concerning the preparation and publication of De revolutionibus. Cf. Prowe, Coppernicus, I, II, covering the years 1512–1543. On the period 1512–1537, see also Biskup, Nowe materiały. See also Rosen, “Biography,” 348–386. 2 According to Biskup, Regesta, 133, No. 284, Copernicus prepared the final version of the treatise on the reform of the Prussian currency in 1528. 3 One of the classic expressions of that view is found, of course, in Duhem, SOZEIN, esp. 71–109.

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conceived his heliocentric cosmology in a way that was so indissolubly and intimately linked with ancient spherical cosmology. Copernicus was not a philosophically systematic thinker. As a consequence, his reticence about both the physical attributes and mechanical details of his models have left scholars to speculate about his views. Although he provides clues and even makes explicit statements sometimes, they are often puzzling. The contexts of the remarks are often ambiguous. These circumstances have misled many to supply global solutions to problems that are driven by the internal logic of their reconstructions rather than by Copernicus’s texts in their different contexts. 2. Hypotheses My proposal, however basic it may appear, is to begin with a typology of Copernicus’s use of the term “hypotheses” and terms that he often uses in conjunction with hypotheses, namely, “principles,” “assumptions,” and “axioms.” The indexes of the modern editions are incomplete, but the Octavo Edition of the 1543 edition with commentary by Owen Gingerich provides a searchable option.4 I begin with a simple count. In De revolutionibus Copernicus uses the word hypothesis or a variant of it forty-five times. He uses the word principia or a derivative fifteen times, usually in conjunction with hypothesis or axioma or in the sense of axiom. The word assumptio or a derivative such as assumptus or assumere in conjunction with hypothesis, principle, or axiom appears eight times. On one occasion in the holograph in conjunction with principles, hypotheses, and assumptions, he uses the expression “cornerstone,” primarius lapis (Gesamtausgabe 2: 490, line 10). Axioma appears three times, usually in reference to a principle of natural philosophy. What does Copernicus mean by hypothesis? In some cases he clearly means one or more motions of the Earth (along with the implication that the stars and Sun are stationary). I will first discuss the cases

4

Copernicus, De revolutionibus, CD-ROM. To my knowledge, Copernicus never uses the word “theoria” in the sense of “hypothesis.” Compare with Schmeidler, Kommentar, 47, and his claim, 179, that Copernicus uses the word “hypothesis” only in the sense of “axiom.”

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where Copernicus refers to his own hypotheses and, second, to the hypotheses of the ancients. Of the forty-five times he uses hypothesis, twelve of them can be taken as referring to his fundamental cosmological assumption or about one or more of the Earth’s motions (De revolutionibus I, 11; (I, 12 in the Warsaw edition; Gesamtausgabe 2: 490, line 6); II, 1; III, 3; III, 7; V, 10; V, 15; V, 20; V, 22; V, 35; VI, 2, and VI, 8). Eight of these twelve refer explicitly and exclusively to the Earth’s motion as the hypothesis in question (I, 11; II, 1; III, 3; V, 10; V, 15; V, 20; V, 35; and VI, 8). There are three occasions where he refers to geometrical models in conjunction with the motion of Earth (III, 7; V, 22; and VI, 2). On one occasion in the holograph, Copernicus uses hypothesis to refer explicitly to principles of natural philosophy (Gesamtausgabe 2: 490, 3–10). He specifies the following: that the universe is spherical, immense, and similar to the infinite; and that the sphere of the fixed stars as the container of everything is stationary. It is in this same context that he refers to the “assumption” that the Earth moves in certain revolutions as the “cornerstone,” on which he depends to erect the entire science of the stars. Hypothesis here includes the assumption of Earth’s motion as well as propositions of natural philosophy. In VI, 2, Copernicus refers to the approach and withdrawal of a planet as commensurable with the motion in parallax “by hypothesis.” The hypothesis is the Earth’s annual motion, but it appears in the context of “hypotheses of circles.” In VI, 8, Copernicus refers to the Earth’s annual motion as well as to the librations of Mercury and Venus that follow as a result. The expression, “hypotheses of circles” (hypotheses circulorum) in VI, 2, however, brings me to the second way in which Copernicus talks about his own hypotheses, namely, as a reference to geometrical models. There are nineteen examples, of which I select only three as representative (IV, 3; V, 25; and VI, 2).5 In IV, 3, after he has pointed out the defect in the assumptions of the ancient lunar models, he concludes that the lunar epicycle appears bigger and smaller not on account of an eccentric but rather another arrangement or system of circles (alium modum circulorum). After describing his double-epicycle model, he claims that all of the other phenomena related to the Moon’s motion will be as observed.

5 The complete list includes I, 13; I, 14; II, 12; IV, 3; IV, 16; V, 5; V, 9; V, 11; V, 16; V, 19; V, 25 (twice); V, 28; V, 29 (twice); V, 30; VI, 2; VI, 7; and VI, 8.

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He says that he will demonstrate the agreement later by means of his “hypothesis,” although, he adds, he can produce the same phenomena by eccentrics just as he did with regard to the Sun (in III, 15). Now, this is a remarkable passage for three reasons. First, the hypothesis in question is the geometrical model for the motion of the Moon, that is, the double-epicycle model—it has nothing explicitly to do with Earth’s motion. Second, he makes it clear that the same phenomena can be demonstrated by assuming eccentrics. Third, in III, 15, Copernicus referred to the equivalence of epicycle and eccentric solutions for demonstrating the non-uniformity of the Sun’s apparent motion. In that context Copernicus comments:6 From all these analyses it is clear that the same apparent non-uniformity always occurs either through an epicycle on a concentric or through an eccentric equal to the concentric. There is no difference between them provided that the distance between their centers is equal to the epicycle’s radius. Hence it is not easy to decide which of them exists in the heavens.

On the basis of this quotation, it is hard for me to see why we should suppose that Copernicus always believed in the reality of his models. True, Ptolemy preferred the eccentric model here and Copernicus implies that one of them is true, but he does not seem to be completely certain about which is true. He proposes and uses them as mathematical solutions that he regards as superior to the models and solutions of his predecessors, but he is not always confident that he has found the uniquely true solution to the problem. He abandoned most of the double-epicycle models of the Commentariolus because when he realized that the apsidal lines shifted, he found it awkward to continue with the double-epicycle models. He replaced them with eccentricepicycle models for the superior planets, and eccentreccentric models for Venus and Mercury. Furthermore, in III, 20, Copernicus provides three solutions to account for the non-uniformity in the motion of the Earth’s apsidal line and a periodic variation in its eccentricity. He says that one of them must be true, and does eventually settle for the third, but in III, 6 Revolutions III, 15, 156, ll. 41–45, tr. Rosen. Notice here that Copernicus is indirectly referring to Regiomontanus’s Epitome XII, 1–2. On this point, see chapter seven, section eight. When I say that the lunar model has nothing explicitly to do with Earth’s motion, I mean except for the distance between the centers of an equivalent eccentric model, which refers to Earth’s orbital radius.

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25, he proposes yet another alternative and so leaves the matter as something that he could not completely resolve but, as he says, “only to the best of his ability.”7 In V, 25, Copernicus constructs a very complicated model for Mercury. In the context of remarks about the planet’s motion up and down along its diameter, a motion that can be the result of uniform circular motions, Copernicus then goes on to describe his accompanying figure for the purpose of making the “hypothesis” clear. Which hypothesis? He is clearly referring to the devices of his geometrical model by means of which Mercury’s appearances will be demonstrated. To be sure, the purpose of the model is to show how the planet’s motion is linked with the Earth’s motion, but there is little in this passage to suggest that he regarded the geometrical model as anything more than a mathematical solution to a problem. On the assumption of the Earth’s annual motion, geometrical models can be devised by means of which Mercury’s appearances can be demonstrated. Finally among Copernicus’s references to his own hypotheses, I come to VI, 2, the hypothesis of circles by which the motions of the planets in latitude are carried or moved. Some commentators make much of the verb ferre here, concluding that Copernicus is referring to spheres or orbs by which the planets are moved, but in this case Copernicus uses the word circulus, not orbis. The hypotheses refer primarily to the devices of the geometrical model by which he tries to demonstrate the appearances. However, in this case he encounters a problem that cannot be explained by variations in the Earth’s distance, leading him to conclude that the tilt of the planets’ orbits must also oscillate. Near the end of the chapter he indicates that the models proposed are intended to solve one problem at a time. First, (in V, 25) he considered Mercury’s longitude apart from its latitude and, second, (in VI, 2) its latitude apart from its longitude. Therefore, he announces, a single motion and the same oscillation, at once eccentric and oblique, could produce both variations. He adds that there is no other arrangement than the one just described. While the principal connotation here is the geometrical model by which the appearances can be demonstrated, the introduction to

7 Swerdlow and Neugebauer, Mathematical Astronomy, 1: 157–161, and note their comment that one of his statements is “very much in the spirit of poor, abused Osiander.” Cf. Schmeidler, Kommentar, 47.

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Book VI makes it clear that the Earth’s annual motion affects not only the planets’ motions in longitude but also in latitude. Here too, then, he must show how the Earth’s motion controls their deviations in latitude. In this context he does not use the word “hypothesis” but rather “assumption” (assumpta reuolutio terrae and terrae . . . assumptam eius mobilitatem). In VI, 8, he uses the word “hypothesis,” referring to the Earth’s annual motion and the librations of Mercury and Venus that follow as a result. In referring to the demonstrations contained in VI, 7, however, Copernicus makes the following comments. He says that he has recorded the latitudes of Mercury’s and Venus’s declinations at four critical points, adding that what occurs between these points can be derived by the subtlety of the mathematical art from the proposed system or arrangement of circles, but not without effort. Here again, Copernicus is referring to geometrical models by means of which the appearances can be demonstrated on the assumption of Earth’s motion. To sum up the results to this point, the primary sense in which Copernicus uses “hypothesis” refers to the motion of Earth and the stability of the fixed stars and the Sun. But it seems equally clear that Copernicus does use the word to refer to geometrical models, the devices of which are mathematical means by which the appearances can be demonstrated. In other words, in this secondary sense the hypotheses or models are mathematical solutions to a problem, although he does indicate that the combination in some cases is a unique solution. Before we turn to Copernicus’s references to the hypotheses of the ancients, we should address Osiander’s comments about hypotheses.8 In speaking of the “novel hypotheses” of this work, Osiander refers explicitly to the Earth in motion and the Sun at rest. Where Osiander departs from Copernicus, however, is in conflating these hypotheses with mathematical models as all imaginary and fictitious. Although he regards the geometrical hypotheses of the ancients as equally fictitious, Osiander is silent about the geocentric hypothesis, which he seems to take for granted not on philosophical grounds but on scriptural grounds, for only in revelation, he asserts, do we find anything certain.

8 In my count of Copernicus’s use of hypothesis or a variant (45), I did not include the appearance of the word on the title page or in Osiander’s “Letter.”

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Copernicus understood that the ancients distinguished hypotheses that they believed to be true from ones they assumed for the purpose of demonstrating the appearances. The ancient principles and hypotheses that they regarded as fundamental and true include the principles of uniform and circular motion, geocentrism, geostability, and the circular motion of the fixed stars. Copernicus accepts the principles of uniform, circular motion (expressed as the hypothesis of uniform motion in V, 15), but rejects the others as false because from those assumptions they have failed to deduce the structure of the universe. Other hypotheses, however, clearly refer to the devices of the geometrical models. In geometrical contexts, Copernicus refers consistently to the hypotheses of circles by means of which the ancients demonstrated the appearances. In their demonstrations they have omitted something necessary or essential and admitted something extraneous and wholly irrelevant. The necessary or essential that has been omitted refers to one or more of the fundamental propositions of natural philosophy (Praefatio, 4 and V, 35). The extraneous and irrelevant refer most likely to the mathematical models that violate a fundamental hypothesis. The word translated as “extraneous” is alienum, exactly the word he uses to criticize the models that have the epicycle center moving uniformly on an extraneous circle (in circulo alieno). Copernicus says and repeats on several occasions that the defect in the ancients’ assumptions was that their hypothesis of combinations of circles was neither suitable enough nor adequate (IV, 2).9 The principal example that he provides is always of the same sort, namely, while they claim that the motion of the epicycle’s center is uniform around the center of Earth or some other point, it is non-uniform on its own eccentric. Copernicus says:10 Therefore, the epicycle’s motion on the eccentric described by it is nonuniform. But if this is so, what shall we say about the axiom that the heavenly bodies’ motion is uniform and only apparently seems nonuniform, if the epicycle’s apparently uniform motion is really nonuniform and its occurrence absolutely contradicts an established principle and assumption? But suppose you say that is enough to safeguard uniformity. Then what sort of uniformity will that be on an extraneous circle

9

There is another example in IV, 2, and in several other places he refers exclusively to ancient hypotheses, for example, IV, 16; IV, 22; and V, 25 (twice, an ancient mathematical device that Copernicus adopted). 10 Revolutions IV, 2, 176, ll. 1–9.

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So here he refers explicitly to the violation of an axiom, an established principle and assumption.11 His solution is to propose another arrangement or system of circles that he claims does not violate the axiom. I will return to this problem below and a discussion of Copernicus’s “hidden” equant, but here I continue with the recitation of Copernicus’s comments. One of the principal achievements of Book V is to show how the motion of Earth and the motions of the planets account for retrograde motion better than the assumption of motion on an epicycle around a stationary Earth. Here again in recounting the ancients’ theory, he complains that the motion of the epicycle is not uniform around the deferent center but around an extraneous and non-proper center (V, 2: circa centrum alienum et non proprium). He refers explicitly to the case of Mercury, and adds the comment:12 I have already adequately refuted this result in my account of the moon. These and similar consequences furnished the occasion to consider the mobility of the earth and other ways by means of which to preserve uniform motion and the principle of the science and to render the account of apparent non-uniformity more constant.

This is, to be sure, another cryptic comment, but I will return to it later as well. In sum, then, Copernicus uses hypotheses, whether referring to his own or those of the ancients, in two ways. Some hypotheses are fundamental and established propositions, principles, assumptions, or axioms of natural philosophy that are taken to be true (14). Some hypotheses are geometrical models, combinations of circles, or other devices that are assumed for the sake of constructing demonstrations that show how the appearances follow from the models in conformity with the fundamental principles (34).13 From a violation of the fundamental principle about uniform, circular motion, Copernicus

11 It is one thing to conclude that the resultant motion is non-circular and nonuniform but altogether another matter to conclude that the circular motions out of which it is composed are themselves non-uniform! See V, 4. 12 My translation. 13 The total here of 48 includes three cases that fit in both categories, that is, examples where a mathematical hypothesis is used in conjunction with a fundamental hypothesis.

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infers not only that there is something wrong with the models but that some, perhaps all, of the other fundamental principles or assumptions are false. In short, natural-philosophical hypotheses are either true or false. Geometrical hypotheses, by contrast, are sufficient or adequate, and when he criticizes the geometrical hypotheses, it is because they are extraneous or irrelevant. He seems to imply that judging the geometrical hypotheses as true or false would be a category mistake. It is unlikely, however, that Copernicus was that indifferent about his geometrical models. The demonstration of appearances follows from hypotheses of circles. The hypotheses of circles follow from and are subsidiary to the overarching natural-philosophical or cosmological hypotheses. Copernicus believed that the hypotheses of circles must also be true, and so it follows that he regarded the assumption of uniform, circular motion as a fundamental cosmological hypothesis. With respect to strictly geometrical models, however, he is sometimes uncertain about which alternative hypothesis or model is true. In other words, he does not always propose a uniquely true hypothesis but rather suggests alternative ways of demonstrating the same appearances. It would be an exaggeration to say that he regarded these hypotheses as imaginary and as fictions, but his uncertainty about some of them suggests that these hypotheses have a more provisional character than the fundamental propositions do.14 With the results of the typology now in place, I turn to spheres. 14 This is not to say that Copernicus was an instrumentalist. The distinction here has to do with demonstrations in natural philosophy that are propter quid and those in astronomy that are quia. See McMenomy, “Discipline of Astronomy,” 303. See also Barker and Goldstein, “Realism and Instrumentalism,” 232–258. Barker and Goldstein suggest that because astronomers were not fictionalists, then they were realists. Their qualification, 253, that sixteenth-century astronomers were perpetually frustrated realists is a little closer to my meaning. Copernicus believed that true natural-philosophical hypotheses could explain the non-uniformities enumerated in I, 4, but the task of geometrical devices was to deduce adequate demonstrations of the appearances from them in conformity with the natural-philosophical hypotheses. Of course, Copernicus’s justifications for the truth of his natural-philosophical hypotheses appeal to the structure of the universe and the explanations of the non-uniformities. In other words, he has to appeal to the results, the logic of which involves reasoning from whole to part. See Lerner and Verdet, “Copernicus,” 147–173, at 170–171, for the emphasis on the architectonic element in the appraisal of planetary systems. Although the hypotheses are natural-philosophical, their justification rests on properly astronomical reasons. On the logic of this reasoning, see chapter eight. With the benefit of his meticulous analysis of Tycho Brahe’s data and physical assumptions about the motions of the planets, Kepler was able to identify the problem with false hypotheses.

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chapter ten 3. Spheres and the Nature of Celestial Matter

Copernicus was very familiar with the natural-philosophical tradition. Aside from his study of technical astronomy, he knew and had access to the qualitative introductions to astronomy (John of Sacrobosco’s De sphaera and its various commentaries) and the Theorica planetarum literature. He probably received some instruction from Albert of Brudzewo and almost certainly knew of Albert’s commentary on Georg Peurbach’s Theoricae novae planetarum.15 The gaps in Copernicus’s training, whatever they may have been, were likely filled during his years in Bologna where he served as a kind of apprentice to Domenico Maria Novara while presumably attending classes on law. By now there is consensus that Copernicus believed in the existence and reality of the total spheres that move the planets. Aware as he was of the different opinions among natural philosophers, however, he did not take sides on questions that they did not settle. This is not only true of differences about the extent of the universe, whether it is finite or infinite, but on all questions that natural philosophers resolve by means of dialectical argumentation from speculative principles.16 On the reality of spheres and on celestial and earthly matter, Copernicus was less radical than most textbook summaries allege. If Earth is a planet, then it is very likely that the Sun, Moon, and the other planets possess the same impulse implanted by God that causes them to come together in the form of a sphere. With that move he appeared to break with the traditional division between the supralunar and sublunar regions. This similarity among celestial bodies seems to make celestial and earthly matter homogeneous, but the conclusion is hasty. Here we can see that he adapted principles of Aristotelian philosophy, modified and transformed by his reading of other ancient traditions, to the motion of the Earth.17 First, Copernicus attributed a unique position and unique attributes to the Sun. He did not attribute any motion, not even axial rotation, to the Sun. It does not appear that he attributed an axial rotation to the In my view Kepler articulated the distinction that Copernicus left implicit. I return to the issue in the conclusion of this study. 15 Albertus de Brudzewo, Commentariolum. In my opinion, there is no evidence that Copernicus knew this text directly, but he very likely received instruction on astronomy and astrology from Albert’s students. See chapter five for details. 16 See chapter four, sections 3.2 and 3.3; and chapter nine, section five. 17 Grant, “Celestial Matter,” 157–186.

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Moon either.18 Second, the sphere of stars is also unique in position and attributes, so we cannot say without qualification that he made celestial and earthly matter homogeneous or that he simply broke the division between the supralunar and sublunar regions. In fact, he replaced that division with another, which delineates the sphere of the motionless stars from everything from that last sphere down to the sphere of the Sun. Because the Sun’s light penetrates the entire universe, perhaps even to the sphere of the stars, it unites the entire cosmos into one whole. The matter of the stars, however, is either heterogeneous with the matter of the planets or if homogeneous, then of another species, for the properties of stars are clearly different from those of the planets. Copernicus believed moreover that spheres move the planets. He entitled chapter 10 of Book I “The Order of the Celestial Spheres,” and referred several times to motions and revolutions of the celestial spheres in the dedication. The terms “sphere” and “orb” almost always refer to the spheres of ancient cosmology.19 Why did he retain these spheres in his cosmology? First, he believed that the heavenly bodies are moved uniformly in circles. They could not move uniformly unless a single sphere moved them uniformly.20 Some have maintained that his proclaimed rejection of the equant was motivated by mechanical considerations, and others claim that the rejection was motivated by cosmological concerns deriving from real spheres whose axis must rotate uniformly on a diameter.21 I have addressed that issue in chapter seven but take it up again separately in section four below. Second, his models of planetary motions required him to construct epicycles, and for centuries astronomers had combined this scheme with the homocentric spheres of early Greek astronomy. For Copernicus, the spheres could explain the motions of planets on epicycles around the Sun. The planets are either embedded in the spheres, and they rotate with the rotation of the spheres, or planets are attached somehow to the spheres that carry

18

De revolutionibus I, 10; III; and IV. Rosen’s commentary to his translation, 333–334. Cf. Hugonnard-Roche, Rosen, and Verdet, Introductions, 39–42. 20 De revolutionibus I, 4: 10, 11–12: “Quoniam fieri nequit, ut caeleste corpus simplex uno orbe inaequaliter moveatur.” 21 Copernicus never explicitly addressed the anomalies resulting from his own models. On the equant and spheres, see Swerdlow and Neugebauer, Mathematical Astronomy, 1: 289–297. Cf. Barker, “Copernicus, the Orbs, and the Equant,” 317–323. 19

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the planets as they rotate. In other words, the spheres provide the substance by means of which the planets can move on epicycles. Third, he knew that as Earth orbited the Sun, the Earth’s axis is not perpendicular to the plane of the Earth’s orbit around the Sun. The axis is inclined to the plane of its orbit and the axis points towards the polar star. Why did he have to attribute a third motion to the Earth whereby its axis describes a conical motion unless he believed that a sphere moves the Earth around the Sun? In other words, he attributed a third motion to the Earth to compensate for the annual motion of the sphere that moves the Earth around the Sun.22 Fourth, the Moon orbits Earth as Earth orbits the Sun. If the Moon is similar in nature to Earth, what keeps it from falling to Earth? Or, alternatively, what keeps it from flying off, the sort of objection Copernicus made to the circular motion of the starry vault?23 Now this is not a question that he posed directly, but the objection is imminent. How is it possible for the Moon to retain its orbit unless the MoonEarth system is as a whole moved by the sphere in which they are contained with the Earth at the center of this sphere?24 In other words, the fact that he saw no problem here is another indication that he was not thinking in terms of mechanical forces operating across space. All of these considerations leave no doubt that he adopted the celestial spheres of ancient Greek cosmology.25 Once he accepted the existence of spheres, the real problem for Copernicus was in deciding about the nature of these spheres. They cannot be bodies like planetary bodies. On the other hand, if they are not like planetary bodies, then how do they move the planets? He did not have an answer to this question, or one, at least, that was based on a consensus among natural philosophers and astronomers. He knew of the debates about celestial and earthly matter among scholastic Aristotelians at the University of Cracow in the 1490s. None of them

22

Moraux, “Copernic et Aristote,” 229–230. Cf. Smith, “Galileo’s Proof,” 543–551. De revolutionibus I, 8: 14, 24–32. 24 Copernicus’s sketch of the system places Earth and the Moon together in the same sphere. See De revolutionibus I, 10, and Rosen, commentary, 359. 25 De revolutionibus I, 4: 10, 11–12; I, 10: 19, 20–25. Compare Rosen, commentary, 333–334 and 348–349; Copernicus, Commentariolus, tr. Rosen, Complete Works, 3: 122–126; Rosen, “Copernicus’s Spheres,” 82–92; Lerner, Le monde, 1: 131–164, and 315–335; 2: 67–73 and 238–241; Westman, “Astronomer’s Role,” 112–116; Jardine, “Significance,” 174–178; Swerdlow, “Derivation,” 466–478; and Swerdlow, “PSEUDODOXIA,” 108–158, with Rosen’s reply, 301–304. 23

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followed Averroes in denying matter altogether of the heavens. A few followed Thomas Aquinas in regarding celestial and earthly matter as heterogeneous. Some argued that celestial matter and earthly matter were homogeneous, but of a different species. Some affirmed the incorruptibility of the heavens, while others adopting a Christian modification of Aristotelian theory concluded by invoking God’s absolute power that the heavens are generable and corruptible and thus not naturally corruptible. By maintaining the specific difference between celestial and earthly matter they preserved a distinction between the supralunar and sublunar regions. As we saw in chapter four, the teaching of natural philosophy in the 1490s was highly eclectic.26 Cracow natural philosophers accepted the materiality of the celestial spheres, but they disagreed among themselves about whether celestial matter is heterogeneous from earthly matter or homogeneous with, but specifically different from, earthly matter. Their indecision is reflected in Copernicus’s comments—he remained neutral, apparently leaning towards the view that the spheres are material, probably homogeneous with planetary matter, but of a species different from the matter of the planets. Without a consensus among natural philosophers on the issue, however, he left the question open. One idea is clear, though. He did not conclude that the matter of bodies in the entire system of the universe is homogeneous without specific differences, nor did he think that the laws governing all bodies in the universe could be reduced to a single set of laws governing the entire system. He retained a division between the stars and the planets, and he attributed unique properties to the Sun. The word impetus appears four times in one chapter of De revolutionibus, but Copernicus used it as a synonym either for “force” or for “weight.” He did not apply the concept to explain the motions of the planets or spheres, as Buridan suggested.27 In fact, Copernicus used the

26 In addition to chapter four, see Markowski, Filozofia przyrody, 140–172; Włodek, “Note sur le problème,” 730–734; and Grant, “Celestial Matter.” In overreacting to Pierre Duhem, some have adopted a radical discontinuity. See, for example, Ingarden, “Buridan et Copernic,” 120–129. 27 De revolutionibus I, 8. Buridan’s theory is mentioned in Quaestiones Cracovienses, ed. Palacz, q. 141, 251; and in the commentary by Johannes de Glogovia, “Quaestiones in octo libros Physicorum Aristotelis,” f. 240v.

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expression virtus movens only to reject the inconstancy of such a force as unsuited to the constant motion of a sphere.28 The question about how a sphere moves or influences a planet remains. Is the planet affixed or attached to the sphere somehow? Is it just embedded in the sphere and so moves with it as the sphere rotates? How does the sphere transmit its natural circular motion to the planet? Does its motion follow somehow from the principle of like-to-like? To answer these questions we must focus on the nature of the spheres themselves insofar as Copernicus addressed their nature. Created by God and moved initially by God, the spheres that were so moved continue to move in circles by nature. What spherical bodies of heterogeneous matter, or of homogeneous but specifically different matter, share is sphericity, the form of a sphere. The connection is formal. As we saw in chapter nine, even Aristotle maintained that the motions of the celestial sphere influence the motions of terrestrial elements and bodies. The higher can influence the lower, and the relation was often expressed in scholastic sources as a relation between actuality and potentiality, or formal and material, or essential and accidental. Copernicus relied without doubt on Stoic sources such as Pliny and Cicero, but his explanation of the circular and rotational motions of Earth is that as a sphere Earth possesses a capacity for circular motion. The celestial sphere that carries Earth around in a circle actualizes Earth’s capacity to move in a circle. Near the beginning of this section I posed the question, why Copernicus retained spheres at all in his cosmology? His decision is a startling example of how little he anticipated the physical cosmology of seventeenth-century astronomy. His decision also verifies his acceptance of Aristotelian principles, though drastically modified by his reading of other sources, which he also fitted to his own purposes. In other words, his revisions of all ancient and scholastic authorities were motivated by the principles of his own theory. On the material nature

28 De revolutionibus I, 4: 10, 11–15. Let me hasten to explain that my speculative reconstruction here does not require us to suppose that Copernicus would have remembered details about university teaching and debates. It is sufficient to maintain that he left the university with an impression of flexible and diverse interpretations of Aristotle that would have encouraged his own revisions. We can reasonably suppose that he would have remembered differences of opinion on the nature of celestial spheres because we know that his interest in astronomy was awakened during his years of study at Cracow. See Part I for details, and see Swerdlow and Neugebauer, 4.

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of the spheres, his departures from Aristotle had Christian, scholastic, and other ancient precedents. Finally on the spheres, I cannot ignore the problem of “solid” spheres. Copernicus never added the adjective “solid” to his descriptions of spheres.29 He knew that the word “solid” was used of spheres in three senses. First, “sphere” is the same as “hard,” the sense in which Earth is called “solid.” Second, “solid” is the same as “continuous,” the sense in which celestial bodies like the planets are called “solid.” Third, “solid” is the same as three-dimensional, the sense in which any body is said to be “solid.”30 Copernicus sometimes used the words sphaera and orbis interchangeably, but he also used orbis at times to refer to “circle,” and at times to refer to a spherical figure distinct from a sphere in the strict sense. Strictly speaking, some scholars regarded spheres as the most regular of solid bodies bounded by a single surface having only one center.31 Orbs are also solid spherical figures, but they have two surfaces, an interior concave surface and an exterior convex surface. If the surfaces of an orb have the same center, the orb is regular and the part between the exterior and interior surfaces has a uniformly equal thickness throughout. If the surfaces of the orb have different centers, however, then the thickness of the part between the surfaces is non-uniform and irregular. Copernicus maintained that celestial orbs or spheres do not share a common center,32 and because celestial spheres are non-concentric, we conclude that he regarded them as irregular orbs. Are orbs solid throughout or are they hollow in part? Sometimes an orb is described as excavata, meaning “hollow,” but this cannot mean “empty” in the sense of “void,” because natural philosophers rejected the existence of void as a contradiction in terms.33 Spheres and orbs are constituted of aether, or, in alternative theories, of some kind of fire or air, and in these contexts some natural philosophers 29

Rosen, Copernicus and his Successors, 62–63. Thorndike, Sphere,” 76–77; also the commentary by Robertus Anglicus, 145. These distinct uses and hence ambiguity of the term “solid” are rarely reflected in the scholarly literature thus adding to the confusion. Brudzewo, Commentariolum, 5–9, makes similar distinctions. 31 Grant, Planets, chapters 13 and 14, esp. 284–286, where he describes the compromise three-orb system. 32 Commentariolus, Postulate 1; De revolutionibus I, 9. 33 Litt, Corps célestes, 25, 29, and 40. See also Westman’s reference, 113, to Erasmus Reinhold’s commentary on Peurbach’s Theoricae, where he uses the expression sphaera excavata in referring to the sphere of the Sun. 30

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resorted to descriptions that suggest that the area inside a sphere is airlike or fluid.34 Copernicus says nothing about their constitution. Both “sphere” and “orb” are described as solid figures or bodies. The differences between them are their surfaces. An orb has two surfaces that produce another sphere in the interior of the orb, but presumably that sphere is also solid. Earth is a hard solid. No two bodies can occupy the same place at the same time, nor can celestial spheres have terrestrial qualities.35 Hence, Copernicus could not have regarded orbs as solid in the sense of “hard.”36 Celestial bodies are said to be “continuous,” but are celestial orbs solid in this sense? This is harder to decide. Continuous things have nothing of the same kind in between and constitute one thing.37 An orb has an interior surface with another sphere embedded inside the orb, and irregular orbs do not have a common center. Hence, it is unlikely that Copernicus regarded his celestial spheres as solid in the sense of “continuous.” This sense of solid fits the description of the celestial bodies such as the Sun, Moon, and planets. Celestial orbs and

34

Lerner, 1: 115–138; Litt, 56–59 and 340–341; Aiton, “Celestial Spheres,” 75–114; Grant, Planets, chs. 13 and 14; and McMenomy, “Discipline,” 185–303. Copernicus’s conception seems to correspond to the notion of a fluid heaven, but he does not say so. His later sixteenth and seventeenth-century interpreters attributed to him all of the above notions, namely, that the spheres are solid, airlike, or fluid. See Jardine, 174–183. Note Grant’s caution, esp. 345–348, in distinguishing medieval scholastic from late-sixteenth and seventeenth-century scholastic views. 35 Although some authors describe spheres in terms of earth-like elemental qualities, they do not seem to mean that the qualities are homogeneous, suggesting that the attributes are to be understood analogously. I am not referring here to bodies like the Sun, Moon, and planets, which do share properties like gravity with Earth, but that does not tell us explicitly what elements they possess. Copernicus keeps any inclination to speculate about such matters under control. See De revolutionibus I, 9, for one possible exception. 36 Jardine, “Significance,” 174–180. Grant, Planets, ch. 14, esp. 345–348, leans to the view that it was first with Tycho Brahe that “solid orb” became synonomous with “hard orb.” As for Copernicus, Grant, 346, says: “Nothing that Copernicus said or implied in De revolutionibus enables us to decide with any confidence whether he assumed hard or fluid spheres. Copernicus fits the pattern of the Middle Ages, when explicit opinions about the rigidity or fluidity of the orbs were rarely presented.” Aiton, “Peurbach’s Theoricae,” 5–44, esp. 8, suggests that Peurbach settled the issue by his belief in the reality of spheres, but even some commentators on his text (Albert of Brudzewo, for example) rejected the reality of epicycle spheres. The fact is that Aiton nowhere explains how geocentrists could have attributed terrestrial qualities to the celestial realm without rejecting or drastically modifying Aristotelian cosmological principles. The attribution of terrestrial qualities to the heavens seems often to work in contexts where they are best described as analogous. 37 Aristotle, Physics IV, 3.

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spheres were normally regarded as contiguous for there cannot be any gaps or void spaces below the last or eighth sphere, yet there are gaps between Copernicus’s spheres or orbs, so they are also not contiguous.38 That leaves “three-dimensional” as the only appropriate sense in which to describe Copernicus’s orbs. Why, then, did he sometimes use the word “sphaera”? He used the word to refer specifically to the total sphere in which a planet is embedded or to the sphere of the fixed stars or Earth and the other celestial bodies. In sum, Copernicus’s celestial orbs, or what he understood by celestial “spheres,” are “solid” only in the abstract sense of “three-dimensional.” They are not hard, not continuous, nor even contiguous. The Moon-Earth “system” appears to be a regular orb,39 although its center (the mean Sun) is certainly not the common center of the remaining orbs and hence they are all irregular. Distinct spheres or orbs cannot interpenetrate, but they can contain other bodies. Because of the ambiguity of the term “solid,” Copernicus did not call the celestial orbs or spheres “solid” at all. Perhaps he took it for granted that the orbs containing the epicycles that describe the motions of all planets other than Earth are resistant at their surfaces but non-resistant in their interiors. Even Earth is surrounded by an orb that contains the two epicycles that describe the motion of the Moon. It would follow again that orbs are “solid” only in the third sense. The third sense alone would be sufficient to explain his rejection of the equant supposing that he was concerned with cosmological issues such as the interpenetration of real spheres. Yet his concern is strictly with uniform motions on circles around their proper centers, and Copernicus never explained how the spheres move the planets.40

38 Lerner, Monde, 2, 3: 69–70 and 240, n. 16, contrary to Swerdlow and Neugebauer, 58, 160, and 474. There are also some gaps between orbs in medieval models, but they “filled” these gaps with aether. Perhaps Copernicus took the view for granted, or he may have overlooked it. 39 Swerdlow, “PSEUDODOXIA,” 115: “[T]he sphere carrying the earth and moon [has] two concentric surfaces,” a description that fits the definition of a regular orb. 40 Aiton, “Celestial Spheres,” also concludes that if Copernicus followed the view that derived from Sosigenes, “then it was not necessary for him [Copernicus] to commit himself to solid (material) spheres. It was sufficient that the celestial bodies, whatever their precise nature, were moved in accordance with the axiom of Aristotle, as modified by Sosigenes; that is, in accordance with an accepted principle of physics.” See also Goldstein, “Copernicus and the Origin,” 219–235. See my reconstruction in chapter seven. More on the equant below.

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There are several other troubling questions that Copernicus does not answer. Even if we concede that he accepted the existence of orbs, that is, partial orbs, that would presumably commit him to the reality of eccentric or deferent orbs, but not necessarily epicycle orbs. There are a number of reasons for emphasizing agnosticism about their existence. There were several astronomers who explicitly regarded eccentrics and epicycles as imaginary and fictitious. When one considers the devices that Copernicus used in his demonstrations, he seems to have regarded them as primarily mathematical. The traditional accounts of orbs never make it clear how the orbs are consistent with the mathematical models.41 In most illustrations, the epicycle is embedded in the eccentric orb, yet the epicycle center describes the deferent circle, which suggests that the deferent circle is not an orb. And what are we to make of double-epicycle models? Either both are orbs, in which case one orb does interpenetrate another, or they are not orbs at all. These are typical difficulties with the treatises that try to combine physical representations of the spheres with mathematical models. Copernicus was aware of these problems and says nothing to clarify them, although some of his remarks about eccentrics and deferents suggest that these too are spheres. His reticence holds also, in my view, for De revolutionibus I, 4, the text that has been used to justify Copernicus’s supposed belief in real eccentric and epicycle orbs.42 I conclude this section with an exposition of that chapter.43 The motion of the heavenly bodies is uniform, eternal, and circular or composed of circles (or circular motions). The motion of heavenly bodies is circular because the motion appropriate to a sphere is rotation in a circle. A sphere expresses its form as the simplest body by moving in a circle.44 In subsequent sentences, however, Copernicus proceeds to enumerate difficulties with these general principles. The numerous celestial spheres have many motions with the daily motion of the entire universe the most conspicuous. Second are the proper motions of the Sun, Moon, and five planets, which motions differ from the daily motion in many ways. They move west to east 41

Lerner, 1: 136. Jardine, 182–183. There is a summary in chapter seven, but here the focus is on the reality and nature of spheres. 43 The discussion here supplements the analysis in chapter seven, the section on Commentariolus. 44 I resort here and below to a paraphrase of Rosen’s translation and the original by way of summary. 42

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through the zodiac obliquely to the equator; they appear to move non-uniformly in their orbits (first anomaly); the planets retrograde at times (second anomaly) and vary in latitude, sometimes nearer to Earth and at other times farther away. In spite of these difficulties Copernicus says that it is necessary to grant that the motions are circular or composed of circles because their non-uniformities recur regularly according to a certain law, which could not happen if their motions were not circular. By a composite motion of circles the Sun displays a regularity in which several motions are discerned because a single orb cannot move a simple heavenly body non-uniformly. If a single orb were the cause of nonuniformity, then it would have to be caused either by an inconstancy in the moving power (virtus movens) or by some difference or change in the revolving body. In other words, if an object moves in a circle, what could cause it to move non-uniformly? Such defects cannot be attributed to bodies that are constituted in the best order. It follows, then, that their motions are uniform but appear nonuniform to us. There are two possible causes. Either their circles have poles different from Earth’s or the Earth is not at the center of the circles on which they revolve. The planets seem to vary in distance, and their motions appear non-uniform in equal times because of their varying distances. Because of these observations Copernicus advises us to consider diligently the relation of Earth to the heavens so that we may not make the error of attributing to the celestial bodies what belongs to the Earth, and so ends Chapter 4. It is reasonable to infer from these passages that Copernicus believed in real eccentric spheres, but it is difficult to understand how some commentators have extracted from this passage the conclusion that Copernicus believed in epicycle orbs as well. The celestial spheres move in circles and move the bodies in them. A single orb cannot cause the observed non-uniformities. Far from concluding that several distinct orbs must cause these non-uniformities, however, Copernicus is clearly trying to prepare the reader for the conclusions announced in I, 5 and I, 9–11. The motions of Earth cause the regular non-uniformities and variations in distance, thus eliminating or explaining some of the most peculiar non-uniformities. As for his belief that the motions of heavenly bodies are circular or composed of circles, he is anticipating Earth’s motions. Earth’s rotation on its axis eliminates the diurnal rotation of the entire universe. Earth’s annual motion around the Sun explains the regularity of the seasons, and the direct motions of all of

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the planets and their varying distances from Earth. In short, just as in Commentariolus, he is far from mentioning the complications of the geometrical models but is rather content here to insinuate the Earth’s motions as providing an initial approximation of the solutions and explanations of the observed non-uniformities. As for his comment implying that sphericity is the cause of motion in a circle, as in I, 5 where he appeals to the Earth’s sphericity as entailing rotation on its axis, once again some commentators have drawn conclusions that are too global.45 Copernicus’s own theory requires the sphere of the stars and the Sun to be stationary. Aside from the spheres that move the planets, he does not attribute axial rotation to any continuous body other than Earth. No such rotations have been observed and rather than let a general principle settle a question a priori, Copernicus says nothing. As for Earth’s annual revolution with its Moon through the great orb, Copernicus offers no explanation as to how Earth with its bulk is carried by the orb, nor does he speculate about what the stuff or matter of the orbs is.46 Even when he does speculate about the Sun, Moon, and planets forming into spheres by virtue of having parts endowed by their creator with a tendency or desire to gather into a whole, he does not explicitly conclude that they must be constituted of the same elements as Earth is. He leaves that question open as well. In sum, then, we have no reason to assert that Copernicus believed in the existence of real epicycle orbs, only in the large orbs or spheres and the eccentric or deferent orb in which the planets are embedded. Furthermore, his celestial orbs are not hard, continuous, or even contiguous. They are three-dimensional, the only sense in which we may call them “solid.” And we have no idea about their constitution or attributes other than their capacity for uniform, circular motion, their function as containers of the planets, and their ability to cause the planets to move in circles uniformly or in ways that are composed of circular motions. I turn now to equants, Copernicus’s dissatisfaction with them, and the “hidden” equants in his models.

45 46

In this regard I agree with Jardine. Westman, 112–115.

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4. Equants There are some who maintain that Copernicus’s dissatisfaction with equants can be explained only by supposing that the problem is contrary to simple mechanical sense, and others see it as a cosmological objection to spheres rotating about an axis that is not a diameter.47 As Copernicus discusses the problem, his objection is expressed in purely geometrical terms referring to circles, not orbs. In Commentariolus, Copernicus expresses the objection to the equant as involving a uniform motion neither on its deferent sphere nor its own epicycle center, so here he does refer to a deferent sphere. But he characterizes his own solution as an arrangement of circles (modus circulorum) not spheres. What is more, the double-epicycle devices in Commentariolus raise more doubts about epicycle spheres. In his reconstruction of Copernicus’s derivation of the heliocentric theory, Noel Swerdlow found evidence of a Capellan or Tychonic transitional stage to complete heliocentrism. The reconstruction is attractive except for one dull thud, the speculation that Copernicus would have anticipated the intersection of the solar and Martian spheres. On the assumption that this is not permissible, he would have switched the positions of Earth and Sun as a way of avoiding the intersection of the spheres.48 Because Copernicus is not forthcoming about the nature of 47 Swerdlow, “Aristotelian Planetary Theory,” 36–48, at 36; Swerdlow and Neugebauer, 41, 44, and 50; and Barker, “Copernicus, the Orbs,” 319. In my view, Copernicus’s concern reveals a detail about his understanding of mechanics that departs from Ptolemy’s understanding. Because this point requires another line of argument not strictly relevant to this discussion, I have relegated it to Appendix IX. 48 As I argued in chapter seven, Copernicus considered the Capellan arrangement, which orders those two planets around the Sun and the Earth, and hence orders them according to two different principles, already sufficient reason for Copernicus to reject a geo-heliocentric compromise. In other words, any speculation in that direction was already checked. See Swerdlow, “Derivation,” 477–478. See also Swerdlow and Neugebauer, 54–64. See Goldstein, “Origin,” 221–222, who agrees that Copernicus was unconcerned with the intersection of orbs. But that question is, in my view, independent of whether Copernicus considered a Capellan arrangement as an intermediate step. See chapter seven for my analysis of Commentariolus and the origin of the heliocentric theory. On the “Uppsala Notes” and their dating, see Swerdlow, 426–431; Dobrzycki, “Uppsala Notes,” 161–167. See also Copernicus, Commentariolus, tr. Rosen, 107, n. 69, and 111–113, n. 200. See also Grażyna Rosińska, “Kwestia,” 71–94. His use of the numbers does not help us to date the folio. Also the recto side of the folio (f. 284r or 15r) was written no earlier than 1532, and the next folio was probably written about 1505–1506, according to Dobrzycki, 167. Dobrzycki later withdrew his analysis, but it is not clear what effect the revision has on the proposed dating of the folio. See Dobrzycki, “One Copernican Table,” 36–39.

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celestial spheres, we cannot evaluate this objection. It is likely that he regarded the spheres as impenetrable, but Copernicus nowhere says so. He was aware of the Capellan arrangement, so we may suppose that it played a role. But perhaps his reasoning started from the traditional arrangement of Mars, Jupiter, and Saturn according to sidereal periods and the realization that a switch between Sun and Earth would determine the order of Mercury and Venus according to the same principle. The only explanation that Copernicus provides about the path to his discovery is in a context related to the equant, and those comments, three of them (De revolutionibus, Preface and V, 2; and Commentariolus) are cryptic and ambiguous. The comment in the 1542 Preface is a critique of Ptolemaic method. He says in V, 2 that the uniform motion of an epicycle center around an extraneous center and similar situations or consequences gave him occasion to consider the Earth’s motion and other ways of preserving uniform motion. Earlier, in the Commentariolus, he says that the inadequacy of the equalizing circles, that is, equants, led him to look for “a more reasonable arrangement of circles from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion.”49 Copernicus does not specifically mention the motions of Earth here although he immediately follows this comment by saying that at length he hit upon a solution, and proceeds to enumerate his seven postulates, among which are the Earth’s diurnal and annual motions. It is not possible that Copernicus meant that it was the inadequacy of the equant that led him directly to consider Earth’s motion. Although this is what Edward Rosen implied in his comment on V, 2, it was also Rosen who pointed out that Ibn al-Haytham rejected the equant without being led to geokineticism.50 That fact along with Copernicus’s “hidden” equants forces us to look more closely at Copernicus’s statement in V, 2. Copernicus says that similar situations or consequences, that is, situations or consequences similar to the problem of uniform motion around an extraneous center gave him occasion to consider Earth’s

49

Rosen tr., 81. Citing Pines in his commentary on De revolutionibus, 417. See also Swerdlow and Neugebauer, 43–45. 50

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motions and other ways of preserving uniform motion. Among the other ways are Copernicus’s geometrical models that he thought worked better than the equant. But what were the problems of uniform motion solved by the Earth’s motions? Surely he means the problems he associates with the diurnal rotation of the starry vault, the regular but apparently non-uniform motions of the Sun and Moon through the zodiac oblique to the celestial equator, the retrograde motions of the planets, and the varying distances between the planets and Earth. In short, Copernicus did not mean to imply that it was the inadequacy of the equant that led him directly to geokineticism, but rather the other problems of uniform and circular motion that he enumerated in I, 4, and that are also included among the postulates in the Commentariolus. He conceived of Earth’s motions as a superior way of explaining apparent deviations from uniform circularity more generally conceived than the equant problem. In discussing the varying distances between the planets and Earth, Copernicus concludes in I, 8, that motion around the middle must be interpreted in a more general way; it is sufficient that each such motion encircle its own center.51 Then why does he refer to the equant problem at all in this context? The inadequacy of the model led him to focus his attention on other problems of apparent non-uniformity. These problems led him, in turn, to question the other fundamental propositions about geocentricity and geostability. He might have considered the Capellan arrangement at this point as a transitional stage, which finally led him to consider Earth’s motion. By means of Earth’s motion, he could transfer many of the appearances to the relevant motions of Earth, distinguish them from the regular and direct motions of the other celestial bodies, and then construct models that would demonstrate the appearances in conformity with his fundamental assumptions. In a very indirect way, or, as he says, “at length,” the equant problem led him to a solution. Did Copernicus overlook “hidden” equants? The answer is yes.52 James Evans speculates that Copernicus did not fully understand how

51 Aiton, 96–98, cites Fritz Krafft, who concludes that the traditional distinction between hypothetical astronomy and real physics became largely irrelevant because his axioms annulled the distinction. But this interpretation still does not tell us which geometrical solution is the uniquely correct one. One might still conclude that Copernicus could be satisfied with general solutions to the problems without committing himself to the existence of solid, material spheres. 52 To my knowledge, Michael Mästlin was the first to comment on the fact in a discussion of Copernicus’s general model for the motion of a superior planet in V,

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nearly perfectly his model duplicated Ptolemy’s because of a change he had to make in the eccentricity of the Martian model to make the motion most rapid at perihelion, as required.53 In the Martian model he departed from a bisection of the total eccentricity. The solution, Evans says, was the mechanism proposed by Ibn al-Shatir nearly two hundred years earlier. Evans adds that Copernicus probably did not perceive that the angular motion of the planet was uniform with respect to a point that corresponds to Ptolemy’s equant point. But by the uniform angular motion, Evans means the uniform motion of the planet on its effective or resultant oblong path relative to the equant, not the center of the epicycle relative to its center.54 Copernicus maintains that the motions must be circular or composed of circles. He acknowledges that the path is not perfectly circular, but it must be composed of uniformly moving circles. Is it not likely that Copernicus thought that he had solved the problem without the equant because in his model the planet moves uniformly on its epicycle and the center of the epicycle moves uniformly around its proper center? The departure from bisected eccentricity in the Martian model would also have obscured the equivalence with Ptolemy’s equant model.55 5. Summary Copernicus rejected the equant as a mathematical hypothesis. He proposed a number of devices that result in motions that are not circular and uniform but that he believed could be composed from circles 4. He says that Copernicus omitted the equant in his figure, suggesting that it was an error. See Mästlin’s letter to Kepler dated 9 March 1597 in Kepler, Gesammelte Werke, 13, No. 63: 108–112, at 110, lines 98–102: “Vidi mox, cum relegerem tuum scriptum (vtinam te praesente id factum esset) erroris causam ex schemate Copernici lib. 5. cap. 4, pag. 142. oriri, quo Copernicus centrum aequantis omisit, id ego in appendice post Narrationem Rhetici pag. 170. addidi. Etenim tam in copernici hypothesibus (licet non exprimat ipse) quam apud Ptolemaeum, aequantis centrum est D.” He then goes on to explain how point D corresponds to Ptolemy’s equant point (lines 107–109): “Quod si autem assumatur D eiusque circulus IKLM (quem Copernicus loco allegato omittit) manifestum fit, eum esse verum aequantem, aequanti Ptolemaei absolutissimè correspondentem.” 53 Evans, “Division,” 1012–1014 and 1021–1022. See Swerdlow and Neugebauer, 289–299. 54 Evans, 1023, n. 9. See also Swerdlow, “Copernicus,” 166–167. 55 Evans, 1013. The fact that the “major” axis of the Copernican orbit coincides with the “minor” axis of the Keplerian ellipse means as well that Copernicus’s model represents a step backwards from Ptolemy’s.

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provided the circular motion is uniform around its proper center.56 Whether he actually succeeded is another matter, but he evidently believed that he had. Spheres are not irrelevant. They remain among Copernicus’s natural-philosophical hypotheses, but their nature, function, and precise influence are left vague. Not all spheres move. His tacit rejection of Aristotelian intelligences indicates that he conceived of them as a simple mechanism. If they move, then they move in circles, but a spherical form is not the direct cause of every circular motion and not all spheres move in circles. Copernicus apparently overlooked equants in his models because he thought that he had solved the problem. The circular motions that the spheres generate must be perfectly uniform and circular or composed of circles that move uniformly around their proper centers. We further conclude that, perhaps by way of a Capellan intermediary stage, he recognized that the Earth’s motions eliminated or clarified some of the non-uniformities that he describes in I, 4, by which means he tried to preserve the traditional belief that the heavenly bodies are moved by spheres. My final conclusion is about Copernicus’s method. His fundamental assumptions are natural-philosophical hypotheses, but their justification depends on the relation of the whole to the part. This means that his reasoning depends on architectonic principles that subordinate natural-philosophical hypotheses to astronomical considerations. His argument from whole to part retains a dialectical character for it depends on the greater probability of his architectonic principles.57 His reluctance to answer numerous questions about the nature of the spheres reveals a methodological principle that guided him. He was suspicious of speculation based only on dialectical considerations,

56 Schmeidler, 148–149, comments that the discovery of an effective equant in Copernicus’s model is trivial. We may add that if there are equants in fact, then it means that not all spheres in Copernicus’s models turn on an axis that is a diameter through the center. Or Copernicus noticed the equivalence but ignored it because the equant has nothing to do with spheres. In other words, if there are “hidden” or “effective” equants in Copernicus’s models, then there must in fact be an intersection of spheres or orbs. This means that Copernicus either did not assume the existence of all orbs, or they are mutually penetrable. One might conclude, then, that either because of a lack of consensus or a lack of detail about the nature of orbs, Copernicus left this question, like so many others, unresolved. 57 I agree with Lerner’s reluctance to follow Swerdlow’s and Barker’s robust realism about spheres, and with his criticism that they tend to neglect or oversimplify the effect of the traditions in logic, natural philosophy, metaphysics, and theology on Copernicus.

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which he characterized pejoratively as logical exercises or merely acts of reason.58 He was reluctant to draw conclusions of an empirical nature without compelling astronomical reasons or empirical evidence. Anticipating rejection by Aristotelians, he knew that he had to persuade Aristotelians to reconsider some of their assumptions and suggest how to adapt their principles to heliocentrism. He avoided taking sides on questions about which natural philosophers continued to dispute. The most important conclusion from the analysis is related to Copernicus’s criticism of Ptolemaic astronomers for the flaw in their method. The false hypotheses from which they started out cannot refer to mathematical or strictly astronomical hypotheses. Copernicus accepted the hypothesis of uniform, circular motion as well as the geometrical devices used to save uniform, circular motion. He rejected the equant because it violates a fundamental proposition, not because the proposition is false. The false hypotheses, then, must refer to cosmological or natural philosophical propositions. These include the position and motions of the Sun, the stability and position of Earth, the assumption of a unique center for all celestial motions, the motion of the fixed stars, and that the motions of the celestial bodies can explain the observed irregularities or non-uniformities. As supporting evidence he refers to the disagreements over the ordering of the spheres and planets, and the failure of his predecessors to provide a genuine explanation of bounded elongation and retrograde motion. When Copernicus claimed that his meaning would be clear, he was referring to his own fundamental hypotheses about the Sun, Earth, ordering of the planets, and “natural explanations” of bounded elongation and retrograde motion. This is a promise fulfilled qualitatively in Book I, chapters 4, 8, 9, and 10, and quantitatively in Books II through VI.

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CONCLUSION AND EPILOG 1. Summary This study of Copernicus and the Aristotelian tradition has examined astronomy in relation to philosophical cosmology. Throughout the first two parts I tried to place Copernicus’s work on astronomy in context, providing a concrete sense of his socio-political environment, education, and reading. In focusing on Aristotelian schools, I have accepted them as a community of scholars who modified Aristotle’s doctrines and who represented themselves as Aristotelians.1 Copernicus, I have argued, learned from his university education above all to adapt Aristotelian principles to his own interests and conclusions. There was no question of rejecting Aristotelian metaphysics, natural philosophy, or logic, or of replacing Aristotle completely by adopting the views and criticisms of other ancient philosophers. As Copernicus read the works of other authors, they informed his approach to astronomical issues, his understanding of Aristotle, and his revision of Aristotelian and scholastic traditions. The most important influence that Aristotle exercised on Copernicus was on the highly controversial question of the truth of cosmological hypotheses, Copernicus’s belief that astronomical phenomena (the observational facts, data) can follow only from true hypotheses. Aristotle had affirmed such a view in three different texts, all of which indicate, however, that he was referring to causal connections and to demonstrations propter quid. Relying on the well-developed area of philosophical dialectic, Copernicus expanded Aristotle’s doctrine to stipulate relevance as a condition of validity, and irrelevance and omission as criteria of invalidity in evaluating the connection between the antecedent and consequent of a hypothetical proposition. The arguments supporting such an expansion relied on dialectical topics, and they resulted in conclusions that were probable and even more probable, Copernicus maintained, than their alternatives. Such was his

1 H. Kuhn, “Aristotelianism”; Jordan, “Aquinas.” For the many editions of Aristotle’s works in the sixteenth century, see Cranz, Bibliography. Similarly, on the survival and influence of Aristotelian principles, see Leijenhorst et al., eds. Dynamics.

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debt to Aristotle in logic and to those scholastic Aristotelians who had argued in a similar fashion.2 How Copernicus arrived at this way of interpreting Aristotle is also controversial. There were precedents in Cracow and Bologna, but an annotation that is in Copernicus’s hand indicates that Plato’s views on the thorough evaluation of hypotheses or suppositions provide clues on how Copernicus applied Plato’s advice in astronomy.3 This advice led him to formulate the questions that focused attention on the principal weaknesses of geocentric astronomy. These were initially questions having to do with the principles of uniform, circular motion, the puzzles about the ordering of celestial spheres and the multiple centers of heavenly motions, and the variations in the distances of planets from Earth. This is why I had to address astronomical and mathematical details in chapter seven, and reconstruct his path to the first heliostatic, heliocentric theory.4 Other philosophical questions required discussion of other details about his models. The summaries of the books that he used and read helped to answer other relevant questions about the origin of the heliocentric theory. Much of this is admittedly material intended to persuade readers that I have not ignored the most important literature on Copernicus and his sources. In my view, these summaries strengthen the story of how Copernicus arrived at his theory, and why his arguments take the form that they have.

2

For similar arguments that emphasize Copernicus’s rhetorical strategies, see Westman, “La préface,” 365–384, and idem, “Proof,” 167–205. 3 The evidence that the annotation is genuine is summarized in chapter seven. For the complete analysis see Goddu, “Copernicus’s Annotations,” 202–226. 4 The detailed evidence is presented in Goddu, “Reflections,” 37–53. I have modified and strengthened the argument presented there in chapter seven. On variations in distance, the ratios in Ptolemy and Copernicus are in agreement. In De revolutionibus I, 4, 9, and 10, Copernicus suggests that the large spaces or gaps required by the large epicycles of Mars and Venus, though presumably filled with some substance, seemed to trouble him. He rejected the explanation for placing the Sun between the superior and inferior planets with the Moon. The superior planets show every elongation from the Sun, but so does the Moon, hence, to be consistent they should have placed the Moon beyond the Sun. Even in the Commentariolus, where he adopted doubleepicycle models, he made them as small as possible as if their sizes troubled him and because his theory no longer required epicycles to account for retrograde motion. By placing the Earth in motion, of course, Copernicus explained the variations in distance as a result of the motions of both Earth and the planets, not just the planets. But see chapter seven where I acknowledge the difficulty in distinguishing between a clue and an afterthought.

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In as few words as possible, then, the Aristotelian tradition exercised its most important influence on Copernicus in the areas of logic, dialectic, and argumentation. Neoplatonism as represented by Renaissance scholars and Plato influenced his exercise of dialectical inquiry, and his view on the relation between mathematics and natural philosophy. It was by means of Aristotelian texts and scholastic commentaries or handbooks, however, that he learned how to construct and support arguments. I have examined natural philosophy and cosmology to resolve a number of puzzles, but only to the extent that Copernicus’s texts permit us to arrive at solutions. He left many questions unanswered, and where the texts fail to lead us to a resolution, I have left them undecided. In some instances I believe that Copernicus was simply in doubt. In others, I suspect that he had a preferred answer but judiciously avoided discussing questions that he knew divided natural philosophers. What I have yet to do is document completely his acquaintance with Aristotelian texts. Here I bring together all of the references and contexts that suggest acquaintance with Aristotle’s texts and with the tradition. In section three, I turn to a consideration of his reception, but in keeping with the character of this study, my focus is on the reception of his understanding of hypotheses, their truth, and of his adaptation of Aristotelian natural philosophy to the heliocentric theory. 2. Copernicus’s Interpretation of Aristotle Scholars for the most part have focused on Copernicus’s acquaintance with Aristotelian texts on natural philosophy, especially De caelo, Metaphysics, and Meteorology. In fact, only Aleksander Birkenmajer and Edward Rosen, to my knowledge, made even a single reference to a work of Aristotelian logic. From the point of view of Copernicus’s innovative cosmological ideas, the emphasis on natural philosophy and metaphysics is understandable. From the point of view of his arguments and likely university education in the arts and law, I have tried to reconstruct Copernicus’s training in logic. From a methodological point of view and in light of Copernicus’s criticisms of Ptolemaic astronomers for omissions and irrelevant intrusions in their method, I have constructed an account linking his training in logic to his evaluation of hypotheses.

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Copernicus was familiar with Aristotelian views on demonstration and dialectical arguments. His arguments demonstrate that he was trained in these techniques, and I have emphasized the role that dialectical topics played in the presentation of his arguments. The most important texts by far are those that help us to understand his apparently strong assertions about the truth agreeing with the truth along with the implicit corollary relevant to astronomy, the exact sciences, and natural science in general that false hypotheses will generate results that reveal inconsistencies, irregularities, and striking unexplained facts. This, I suggest, is what Copernicus meant by his promise that his obscure remarks would become clearer in the proper place. I have identified these passages in chapters three and eight, but I gather them here together with comments on the role of dialectic in Copernicus’s arguments. Although not a text on logic, the idea expressed in Nicomachean Ethics I, 8, 1098b11–12 (“with a true view all the data harmonize, but with a false one the facts soon clash”) is reasonably close to Copernicus’s belief that false hypotheses will generate results that are unsatisfactory. In Prior Analytics II, 2–4, Aristotle makes it clear that in cases where demonstration is the aim or where we assert a causal connection between premises and a conclusion, then the premises must be true for the conclusion to follow. Some readers think that Copernicus also believed that he had demonstrated the truth of the heliocentric theory, but I have argued that none of his arguments satisfies the conditions for a genuine demonstration in the Aristotelian sense. Similarly, the text from Metaphysics I minor, 993b26–27 (“that which causes derivative truths to be true is most true”), the text that Copernicus very likely knew, suggests that Aristotle had demonstration in mind.5 I have concluded in light of the dialectical and probable nature of his arguments and conclusions that Copernicus expanded Aristotle’s criterion from causal connections entailed in propter quid demonstrations to the somewhat weaker criterion of relevance. Medieval and later scholastic commentators applying Aristotelian principles to astronomy concluded that astronomical hypotheses could not be certified by observational data because the data can be derived from or made to fit several alternative hypotheses. To put it in the 5

The text is cited by Rheticus, Narratio prima, but in Bessarion’s translation. See Rosen tr. 142, n. 133. Compare the edition by Hugonnard-Roche, Verdet, Lerner, and Segonds with French translation, with that in Rc. For the quotation, see Sc, 71, lines 118–123; Rc, 37, lines 16–20.

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technical terms of Aristotelian terminology, the data and the principles assumed to account for them are not convertible. To assert that they are convertible, as Copernicus seems to imply, is to commit the fallacy of affirming the consequent. The commentators adopted or preferred those hypotheses that agreed with the more fundamental principles of cosmology and natural philosophy.6 That move was already implicit in Ptolemy’s Almagest I, 7, where he took the trouble to recite the Aristotelian objections to the motion of Earth, even adding his own objection based on Aristotle’s ratio of weight to resistance. This was the impasse that Copernicus confronted. In Commentariolus, De revolutionibus I, 4 and in the Preface, he outlined a strategy for breaking through the impasse. He emphasized the failures of his predecessors, explained the alternatives, refuted the Aristotelian assumptions and conclusions related to simple, natural elemental motions, and proposed the motions of Earth as the only way to resolve the problems and produce a coherent system. In the next section on reception, I will return to Copernicus’s insistence on discovering or asserting true hypotheses. The only other citation from a logical text known to me is from Posterior Analytics I, 4, 73b4–5.7 Aristotle says that predicates that belong to a thing as an element of its essence or as included in its definition belong to the thing per se. Predicates that belong to a thing in neither of these ways are said to be accidents. Also in Metaphysics VI, 7, 1033a7–13, Aristotle compares a sick and healthy man. Aleksander Birkenmajer speculated that Copernicus conflated these two passages in his comments in De revolutionibus I, 8, where he compares circular motion with “being alive” and rectilinear motion with “being sick.” Copernicus maintains that rectilinear motion occurs only to things that are not in their proper condition and not in complete accord with their nature, suggesting that he regards rectilinear motion as an accident.8

6 As Crombie, Styles, 1: 530–537, so neatly summarizes in citing Averroes, Thomas Aquinas, Agostino Nifo, Alessandro Piccolomini, Peter Ramus, Christopher Clavius, and Michel de Montaigne. 7 Incorrectly cited by A. Birkenmajer as I, 3 in his commentary to the Latin edition, De revolutionibus, Opera omnia, 2: 369. 8 A. Birkenmajer, 369.

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But it also seems plausible that in this context Copernicus had the following passage in mind from De caelo II, 12, 292b1–25, where Aristotle says the following: That which is in the best possible state has no need of action. That which is nearest to its best possible state should achieve it by little and simple action, and that which is farther removed by a complexity of actions. Just as with men’s bodies one is in good condition without exercise at all, another after a short walk, while another requires running and wrestling and hard training, and there are yet others who however hard they worked themselves could never secure this good, but only some substitute for it.

As I indicated, scholars have been more thorough in identifying Copernicus’s acquaintance with Aristotle’s texts in natural philosophy. Copernicus knew or referred to De caelo I, 1, and especially the following passage (268b7–10):9 Now bodies that are classed as parts of a whole are each complete according to our formula, because each possesses every dimension. But each part is limited by contact with that part which is next to it by contact, for which reason each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and thus, in accordance with the meaning of the word, have being, not in some respect only, but in every respect.

In several passages of De revolutionibus but principally in I, 1–2, Copernicus asserts the completeness of the universe, and implies its finiteness and the relation of the parts of the universe to the whole. In De caelo I, 2, I, 8, and II, 14, where Aristotle argues for the finite extent of the universe, he makes the assumption, implicitly regarded by Copernicus as fatal, that simple elements have simple motions.10 In De revolutionibus I, 7, where Copernicus repeats the ancients’ arguments

9

I have combined the translations by Stocks and by Guthrie, On the Heavens. I have modified all of the translations slightly. To avoid misunderstanding, I repeat here my conviction that Knox, though expressing caution about his discoveries, has correctly identified texts from Pliny, Cicero, and the Suidae lexicon as the sources on which Copernicus relied to re-interpret Aristotle. See Knox, “Copernicus’s Doctrine of Gravity,” 189–208. Knox does not reject the idea that Copernicus was familiar with Aristotelian and scholastic interpretations, but emphasizes the extent to which Copernicus’s account relies on other sources. I am in wholehearted agreement with his view, although I am more inclined than he to understand Copernicus’s modifications as re-interpretations of Aristotle’s principles or of the Aristotelian tradition. 10 These texts are also cited by Rheticus, Narratio, Sc, 58; Rc, 22; Encomium Prussiae, Sc, 85; Rc, 54; and De terrae motu et Scriptura Sacra, Rc, 65 and 69–70.

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supporting the conclusion that Earth is the center of the universe, he refers explicitly to Aristotle without specifying a text. Copernicus implies in I, 7 and explicitly argues in I, 8 that if Earth rotates on its axis, then a falling body would have a compound motion, and, therefore, simple elements would not have simple motions. If Earth rotates and does not exhibit all of the dire consequences predicted by Aristotle and Ptolemy, then its rotational motion would be natural, not violent. It is in this context that he asserts the principle of the relativity of motion and the equivalence between the observations that we make whether Earth rotates or is stationary. There is some disagreement among interpreters whether Copernicus considered the motions of falling bodies unnatural or violent, but Copernicus’s language suggests that he relativized the concepts “natural” and “violent.” He says that bodies that move with rectilinear motion are not in their proper condition and not in complete accord with their nature. He does not say that the motions themselves are violent, but rather implies that the removal of bodies from their natural place or condition involves violence. As we saw in chapter nine, rectilinear motion is natural insofar as it is caused by gravity (a natural appetite), but its acceleration requires a cause, the impetus of its weight. Indeed, Aristotle himself, in the very complicated analysis of self-moving bodies in De caelo III, 2, makes a similar point about natural elemental motions. Aware that bodies accelerate as they fall, he apparently concludes that the cause of acceleration must be partly violent. The passage (301b18–30) is obscure. Aristotle distinguishes between nature as a cause of motion in the thing itself, and force as a cause in something else or in the thing itself regarded as something else. Force accelerates natural motion, as in a stone downwards, and is the sole cause of unnatural. Now, as Aristotle explains, he regards air as an instrumental cause because its nature is to be both light and heavy. Why does it aid upward movement in one case, and downward in another? The answer is because it is pushed and receives an impulse from the original force. The original force transmits the motion by impressing it on the air. Now, what is the original force in the case of a falling body? Aristotle does not say, but what other causes are there for its motion downwards other than the weight of the body and the removal of obstacles to its motion? The original force that causes acceleration must be the body’s weight (the thing itself regarded as something else), and its actual rate of acceleration in a given case is partly the result of the instrumentality of air and of the resistance of

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the medium. Little wonder that some scholastics found the notion of the transfer of motion directly to the body (impetus) compatible with Aristotle’s account.11 It would follow that bodies that fall (or generally move, as fire upwards) or move in a rectilinear fashion are, as it were, striving to return to their most natural condition. Furthermore, Copernicus argues that natural motions are uniform and eternal whereas rectilinear motions undergo variation in the form of acceleration and sudden stops.12 As we noted in chapter nine, Copernicus’s account of fire is ambiguous. Copernicus combines Aristotelian conceptions with non-Aristotelian accounts. Aristotle’s account in Meteorology I, 3 is not consistent with the account in De caelo, and he also seems to make a distinction between some sort of celestial fire and what we call fire. On the one hand, Copernicus appears to adapt Aristotle’s account, but in doing so he suggests that fire is not a terrestrial element and that its motion upwards, which he claims decelerates as it approaches the periphery, is violent. His reference to the expansion of fire as in explosions suggests that the force diminishes with distance from its source.13

11 Even the Latin version of Aristotle’s text in the Leonine version of the works of Thomas Aquinas combines nature and force as causes of motion and acceleration respectively. See Aquinas, Opera omnia, Lectio 7, 249 (Text 28): “Quoniam autem natura est in ipso existens motus principium, virtus autem in alio secundum quod aliud; motus autem hic quidem secundum naturam, hic autem violentus, omnis. Eum quidem qui secundum naturam, puta lapidi eum qui deorsum, velociorem faciet quod secundum virtutem: eum autem qui praeter naturam, totaliter ipsa. Ad ambo autem tanquam organo utitur aere. Natus est enim hic et levis esse et gravis. Eam quidem igitur quae sursum faciet lationum secundum quod levis, cum feratur et sumat principium a virtute; quod deorsum iterum secundum quod gravis: velut enim imprimens tradit utrique. Propter quod et non assequente eo quod movit, fertur vi motum. Si enim non tale aliquod corpus existeret, non utique esset qui vi motus. Et eum autem qui secundum naturam uniuscuiusque motum promovet eodem modo. Quod quidem igitur omne aut leve aut grave, et qualiter praeter naturam habent se motus, ex his manifestum.” 12 This appears to be a case where he uses an Aristotelian principle against Aristotle, for in De caelo II, 3, Aristotle asserts that “the circular movement is natural, because otherwise it could not be eternal for nothing unnatural is eternal.” But, as Dilwyn Knox, pointed out to me, it does not follow from Aristotle’s assertion that everything natural is eternal. 13 Rosen, Commentary, Revolutions, 345, 347–348, 350–351, 353–355. Cf. Moraux, 229–233; A. Birkenmajer, “Commentary,” 363, 370–371, and 387. See also Knox, “Ficino and Copernicus,” 413–414, where he points out that the association of natural places with the wholes to which God has consigned them became a standard Neoplatonic doctrine, and some commentators thought it was Platonic. See also Knox, “Copernicus’s Doctrine.” Rheticus, De motu terrae, Rc, 70, in referring to De caelo II, 14, 296b21–25, shows no indication that he rejected fire as an element.

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Also in this context Copernicus makes the controversial reference to impetus, suggesting that weight generates impetus in the falling body and that bodies cease to be heavy or light when in their natural place. Circular motion, by contrast, continues forever in a uniform manner because it has an unfailing cause. He does not specify the cause. Some have suggested that he is referring here to impetus again, or alternatively, to the form of a sphere, but he may rather have meant the original moving cause, namely, God. Copernicus regarded impetus as resulting from a quality that weakens, as in the case of a falling body. As for the suggestion that the form of a sphere is a cause, not all spheres rotate. For example, he does not attribute rotation to the Sun. The argument about an unfailing cause and the resulting uniform and eternal motion appears to be an adaptation of an Aristotelian passage from De caelo II, 6, 288a28–35: Because everything that is moved is moved by something, the cause of the irregularity of movement must lie either in the mover or in the moved or both. For if the mover does not act with a constant force, or if the moved were altered and did not remain the same, or if both were to change, the result might well be an irregular movement in the moved. But none of these possibilities can be applied to the heavens.

If Copernicus intended to apply the theory of impetus here, then we would have to conclude that in the case of heavenly motions, he regarded impetus as indefatigable. But, as we have just seen, the principle is Aristotelian and has nothing transparently to do with the theory of impetus.14 With Earth itself a sphere with a natural capacity for circular motion and embedded in or attached to a celestial sphere, Copernicus seems to imply that the rotation of the celestial sphere actualizes the capacity of Earth for circular motion and rotation. We have already cited the passage from De caelo II, 12, as a possible source for Copernicus’s comparison of circular with “being alive” and rectilinear with “being sick.” Copernicus does not provide a thorough account here, leaving us to construe his comments in a way that seems the most consistent with his theory. In the next chapter he would also have seen Aristotle’s comments about the Pythagoreans and their view about the motion of Earth around a central fire, although he gives Plutarch as his source in the Preface. He cites it there as evidence that

14 Rosen, 348–349; A. Birkenmajer, 369; and Moraux, 230–233. Compare Schmeidler’s virtual silence, Kommentar, 81–82.

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some ancients proposed the motion of Earth. He does suggest that he derived his hypothesis from such comments, yet the context rather indicates that his intention was rhetorical, namely, as support for the legitimacy of his own speculation.15 Consequently, Copernicus dismisses Aristotle’s analysis in De caelo I, 3–4 (on heaviness and lightness, and the motion of a body as due to a simple quality), as a logical exercise.16 But Copernicus also commits himself to the “Platonic axiom” and Aristotle’s application of it to the uniform circular motions of the heavenly bodies, insisting significantly that each motion encircle its own proper center. In De caelo II, 13; III, 2; IV, 3; and in Meteorology IV, 9, Aristotle argued for the center of Earth as the center of gravity, citing the principle that the motion of the whole is the same as the motion of the part. In De revolutionibus I, 7, Copernicus recites the Aristotelian arguments, which he proceeds to refute in I, 8. In I, 9, he also argues that there is no one center of the celestial circles, which he uses to relativize the notion of center of gravity. Copernicus then adapts the Aristotelian principle about the relation between part and whole to argue for the natural circular motion of earth, leaving the rectilinear component of a falling body as the result of the body’s inclination to be joined with the whole.17 In De caelo I, 5–9, Aristotle goes on to argue for the finiteness of the universe based on the principles and conclusions established in the previous chapters. It seems clear from his insistence on heliocentrism and on the stability of the stars that Copernicus too accepted the finiteness of the universe, yet in De revolutionibus I, 8 he leaves the question of whether the universe is finite or infinite to natural philosophers. Earlier I argued that he adopted this tactic because natural philosophers were divided on the question, but I ended section five of chapter nine with the comment that the conclusion was provisional. Copernicus read Aristotle’s arguments in De caelo closely enough to recognize a problem. Aristotle’s conclusion and that of all Aristotelians followed from their analysis of the motion of the stars in a circle, which has to

15 Moraux, 227, also cites the passage from Aristotle here, but also thinks that Copernicus had only a secondary interest in the ancient theories. Rheticus, Narratio, Sc, 61; Rc, 26–27, also refers to Plato, Timaeus 40 B-C, and Aristotle, De caelo II, 13. But see Knox, “Copernicus’s Doctrine,” for a thorough review of ancient sources and their availability to Copernicus. 16 Rheticus echoes the criticism in De terrae motu, Rc, 65. 17 Rosen, Commentary, 348 and 350–351. Compare A. Birkenmajer, 365–366, 368, and 382; and Moraux, 227 and 231.

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be finite because it is completed within a day, and from the rectilinear motions of sublunar bodies. Because he had placed the Sun and stars at rest, there was now no compelling reason that would generate a logical contradiction for asserting apodictically that the universe is finite. Copernicus may have regarded the question as an empirical one or as one that perhaps cannot be settled at all with certainty.18 In I, Introduction and I, 1, however, Copernicus asserts that the universe is spherical and a complete whole, but his reasons have an a priori and aesthetic character about them. Where Aristotle supports his conclusion about the sphericity of the universe and the heavens as a complete whole as a consequence of its circular motion (De caelo II, 4), Copernicus asserts that spheres are the most beautiful, perfect, and complete objects. Hence, it is fitting that the universe be one complete whole. Where he expressed doubt about its finiteness is also illuminated, I believe, by reference to Aristotle’s remarks in De caelo I, 9. There Aristotle distinguishes three different senses in which the word “heaven” is used. All of them support his belief in the finiteness of the universe, but in De revolutionibus I, 8, there are indications that Copernicus also had in mind scholastic discussions about void space beyond the visible heavens and about even more senses in which Christians talk about the heavens, including the empyrean. Here is an excellent example where the reading of Copernicus’s works benefits from comparison with Aristotle’s texts and their scholastic commentaries.19 These are the sorts of puzzles that motivate discussions about the compatibility of concepts such as “whole,” “infinite,” and “center.” Likewise, Copernicus adapts Aristotle’s argument in De caelo II, 8 that the stars are attached to the spheres that move them in circles, rejecting the idea that each of the stars has its own proper circular motion. Of course, in adopting the Earth’s rotation on its axis, Copernicus eliminates the daily rotation of the stars, but he retains the idea that the planets are attached to spheres, explaining why their motions are circular or compounded of circular motions (De revolutionibus I, 4).20

18 Compare the comments of Birkenmajer, 362 and 366; Rosen, 351–353; Moraux, 231–232; and Schmeidler, 82. 19 Moraux, 229. 20 The idea is also supported by De caelo II, 6–7. See Rosen, Commentary, 348–349; and Moraux, 229. Compare Rheticus, De terrae motu, Rc, 65.

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In De caelo II, 10 Aristotle explained the order of the spheres as a consequence of their distance from the periphery or the most rapid daily motion of the starry vault. As we saw, however, some scholastic commentators known at Cracow interpreted this principle as a causal explanation of their varying motions while describing them as ordered according to periods as measured from Earth.21 Contrary to Aristotle in De caelo II, 11, where he argues that the planets, Moon, and Sun are spherical and yet do not move themselves because a sphere has no inherent capacity for motion, Copernicus argues that a sphere is particularly suited to rotation. Yet nowhere, to my knowledge, does Copernicus conclude that the planets, Moon, and Sun have an axial rotation. To that extent, then, he seems to have been following Aristotle’s reasoning here as well, for Aristotle keeps the spherical Earth at rest.22 Copernicus agreed with Aristotle (De caelo II, 14) about the shape of Earth, and that bodies falling towards its surface strike the surface at an angle perpendicular to the tangent of the curved surface, and tend towards the center of Earth. He rejected Aristotle’s objections to the motions of Earth based on astronomical observations. Aristotle could not understand how the observations of the stars would remain the same if Earth moved. Ptolemy, we know, considered Earth’s rotation on its axis, and realized that the observations would be exactly the same. Ptolemy did not object on astronomical or mathematical grounds, but on strictly physical ones, that is, what we would observe of the motions of bodies here on Earth. As for the motion of Earth from one place to another, Ptolemy did not consider orbital motion. Following Aristotle and influenced by Stoic ideas, Ptolemy assumed that if Earth moved from its place at the center, it would have a rectilinear motion. He objected again on physical grounds. Here we might also suppose an astronomical objection, for if Earth moved in a straight line, then it would presumably approach stars in one direction and recede from the stars in the opposite direction, a motion that should produce a visible difference in the distances between the stars. This would be another version of the problem of stellar parallax, but Ptolemy did not in fact raise this objection. Aristotle seemed

21 This, of course, was the opinion advanced by Johannes Versoris. See chapters four, seven, and nine for the details. Compare Birkenmajer, 373; and Rosen, 350 and 355. 22 As Rosen, 347, emphasizes.

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to think that if Earth moved from place to place that it would have a motion along the ecliptic. But he evidently failed to recognize that its axis would be tilted to the plane of the ecliptic, and thus he mistakenly concluded that our observations of the stars would be different. Aside from the fact that Aristotle’s assumption was wrong, Copernicus’s only anticipation of such objections led him to suppose that the stars are farther than imagined, and he argued that God put them at such a great distance so that we might detect the motions of the planets more easily. At the end of De revolutionibus I, 10, he says: From Saturn, the highest of the planets, to the sphere of the fixed stars there is an additional gap of the largest size. This is shown by the twinkling lights of the stars. By this token in particular they are distinguished from the planets, for there had to be a very great difference between what moves and what does not move. So vast, without any question is the divine handiwork of the most excellent Almighty.

Copernicus was no doubt familiar with one of Aristotle’s favorite examples, namely, the relation between the observation of the nontwinkling of the planets and the nearness of the planets in Posterior Analytics I, 13, 78a30–78b3 and in De caelo II, 8.23 Physics II, 2 represents the view about the relation between mathematics and natural philosophy. Copernicus modified Aristotle’s account here at least with respect to determination of the order of the cosmos. He also implicitly rejected the Aristotelian doctrine of natural place and its relation to motion as supported in Physics III, 1 and IV, 1–9. Copernicus tended to attribute motions to bodies on the basis of their formal characteristics and their inclination to be united with other like bodies in their most perfect condition. This inclination was implanted in things by God.24 Copernicus went further than Aristotle in Physics IV, 11, where Aristotle relates time to motion, and measures time by distance. By measuring the order of the spheres according to their periods, Copernicus discovered a principle by means of which he could determine the relative linear distances of the planetary spheres from the Sun.25

23

Rosen, 360; A. Birkenmajer, 385; and Schmeidler, 88. A. Birkenmajer, 366 and 382; and Rosen, 359. See also Rheticus, De terrae motu, Rc, 70. 25 Rosen, 367. 24

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Aristotle’s analysis of motion in terms of actuality and potentiality (Physics VIII, 4), and the argument leading to the existence of an unmoved mover (Physics VIII, 6–10) involved consideration of natural elemental motions and projectiles. Natural things have a capacity or potentiality that generates motion towards their actuality, which Aristotle views as their most perfect state. The ambiguity in his account generates some confusion for elemental bodies achieve actualization when they are perfectly at rest in their natural places.26 The proper motion of the heavenly spheres is uniform, circular motion (Physics VIII, 6). Copernicus upset the relation between the unmoved mover and the prime mover of the starry vault. In Copernicus’s natural theology, if you will, God as creator endowed the stars, planets, Moon, and Sun with properties, and God endowed the planets and Moon with their uniform motions. Perhaps the topsy-turvy consequence of his ordering led him in De revolutionibus I, 10 to cite the references to the Sun as the “lantern of the universe, its mind, and its ruler,” “a visible god, . . . the all-seeing.” “Thus indeed, as though seated on a royal throne, the Sun governs the family of planets revolving around it.”27 Copernicus also finds an opportunity to cite Aristotle here in referring to the relation of Earth and Moon: “The Moon has the closest kinship with the Earth.”28 In addition to Metaphysics I, 1, I minor 1, and II, 4–5, Copernicus was evidently familiar with other passages. Metaphysics III, 2 repeats Aristotle’s view about primary beings and his rejection of mathematical entities as belonging to primary being. VI, 7 contains the text in which he characterizes health as the best state and sickness as its privation. Health as product comes out of the privation (1033a11).29 26

Rosen, 348, 351, and 353; and Moraux, 231. Rosen’s translation, 22. See also Rheticus, De terrae motu, Rc, 60, where he refers to Aristotle, Physics VIII, 1, and to Plato, Timaeus 38 B-C. 28 De generatione animalium, IV, 10, 77b18–19. The reference does not fit perfectly, and so commentators have pointed to Averroes as the source. Compare Rosen, 360; and A. Birkenmajer, 383–384. 29 A. Birkenmajer, 369. On Metaphysics I, minor, 1, 993b11–13, see Copernicus, Letter Against Werner, tr. Rosen, Complete Works, 3: 146 and 151, n. 11. As mentioned before, I checked Tiedemann Giese’s copy of the Metaphysics at Uppsala to see if this was Copernicus’s source, and I repeat it here for the sake of convenience. Catalogued at Uppsala as Inc. 31:164, the text on fol. 13v reads: “Non solum autem his dicere gratiam iustum est quorum aliquis opinionibus communicaverit. Sed his qui adhuc superficialiter enunciaverunt; etenim conservunt aliquid.” Giese’s gloss does not correspond with Copernicus’s comment on the passage, hence this version was not Copernicus’s source. 27

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Copernicus implicitly rejected Aristotle’s dialectical argument (Metaphysics XI, 10) that refutes the actual infinite extent of the universe based on the daily motion of the starry vault and the centrality of Earth. The motionless stars and the motions of Earth remove the basis for Aristotle’s conclusion, leaving Copernicus with no observational basis for affirming the finiteness of the universe. Still, Copernicus seems to have preferred that view, but he evidently realized that his only justification was a metaphysical preference for sphericity, wholeness, and completeness, principles that Aristotle also preferred.30 Aristotle’s description of the universe as perfect, complete, beautiful, and good, and thus worthy of admiration (Metaphysics XII, 7) accords with Copernicus’s praise of astronomy in De revolutionibus I, Introduction. Aristotle’s acceptance of the spherical astronomy of his predecessors followed from his assertion that the numbering and ordering of the spheres and their motions depend on that mathematical science which is most like philosophy, astronomy. This is so because astronomy studies not just sensible being, but the kind of sensible being that is primary and eternal (1073b1–10).31 I have argued that questions about the ordering of the spheres and their varying distances from Earth led Copernicus to the heliostatic, heliocentric theory. Although he rejected the details of Aristotle’s analysis (Metaphysics XII, 8), Copernicus, I contend, revealed his Aristotelianism most conspicuously in his acceptance of the axiom of uniform circularity and in his belief that we can discover the true order of the spheres, the principal task of mathematical astronomy.32 Guided as they were by a vision of an ordered cosmos, both Aristotle and Copernicus sought a principle of order. Focusing as he did on causal principles, Aristotle emphasized the relation between the unmoved mover and the prime mover. As we saw, scholastic

30

A. Birkenmajer, 366; also 370, where he suggests that Copernicus may also have relied on Metaphysics XII, 6 (1071b20–25) about potentiality and actuality to support his view that the natural capacity for a sphere to move does not entail that all spheres move. As Dilwyn Knox pointed out to me, the reference seems forced because Aristotle does not address the problem of spherical motion explicitly here. 31 Rosen, 348; A. Birkenmajer, 370; and Moraux, 229. 32 Rosen, 348; A. Birkenmajer, 370; and Moraux, 229. See also Rheticus, Narratio, Sc, 57 and 71; Rc, 21 and 37. Of course, the origin of concentric spheres is attributable to Eudoxus, and the axiom of uniform circular motion was attributed to Plato, but Aristotle transformed it unambiguously into a physical, not just a mathematical, computational device. Copernicus adopted Aristotle’s physical interpretation of celestial spheres.

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commentators like Johannes Versoris adopted Aristotle’s dynamic analysis, and combined it with astronomical models that ordered the spheres from the center. Copernicus adopted the astronomical ordering from the center. Even Aristotle, however, in Metaphysics XII, 10, emphasized the unity of the universe. Everything in the world is connected for all things are ordered to one end. In some translations, the idea is expressed from the point of view of the relation of all things to a common center. The Greek text reads pròs hén “ad unum” in Latin, but Aristotle uses the analogy of a household, suggesting order around a central reference such as a hearth. Copernicus rejected the idea that all circular motions have a unique center, but he retained the principle of ordering the spheres from the center.33 In Meteorology, Aristotle addressed more specific questions about the elements and comets. How are they ordered? How is Earth heated? Again, Aristotle’s analysis proceeds from consideration of causal relationships and the nature of the celestial spheres. Fire is a sublunar element, hence the heat generated by the Sun is the result of its motion. The fire that surrounds the terrestrial sphere is driven downwards by the motions of the celestial sphere. Celestial rotation also causes the circular motion of air (I, 3 and 7). Copernicus’s comments in De revolutionibus I, 8 (about the air moving with the rotating Earth) represent another example where he adapts an Aristotelian explanation, even referring to the Aristotelian account of comets.34 Copernicus does not explicitly adopt the Pythagorean notion of a central fire (De caelo II, 13), but he does refer to the Sun as a lamp that lights up the entire universe (De revolutionibus I, 10). He thereby suggests that heat is generated by light.35 Aristotle (Meteorology I, 14) emphasized the smallness of Earth in comparison to the whole universe, a view that Copernicus (De revolutionibus I, 6) shared, but to argue to the contrary that Earth’s distance from the center is as a point to the immensity of the universe.36

33 See the translation of Metaphysics XII, 10, 1275a18–25 by Hope, 336, 24a. Compare Schmeidler, 83. Ordering around a hearth presumably did not inspire Copernicus to order the cosmos around the Sun, yet the metaphor is consistent with his vision. 34 Although Pliny, Natural History II, 22, 89, is the likely direct source. See A. Birkenmajer, 367; and Rosen, 352. Compare Schmeidler, 82. See also Knox, “Copernicus’s Doctrine,” 167, n. 48. 35 Rosen, Commentary, 352, and A. Birkenmajer, 367. 36 Moraux, 229.

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Meteorology IV, 9 and De generatione et corruptione II, 3–4 discuss the relation between the elements, especially water and earth. As commentators have pointed out, Copernicus’s citation of the definition of fire as “blazing smoke” is from these passages in Aristotle. Copernicus evidently relied on some Aristotelian source, for he rejected what he calls the Peripatetic view on the proportion of water to earth. Earth and water form that which moves towards the center—on that Aristotle and Copernicus agree.37 As we have noted, Aristotle attributed a centripetal impulse (De caelo II, 14) to the motions of the heavenly spheres, that is, that their circular motions generate an inward pressure towards the center.38 With the exceptions noted, this study tends to confirm Aleksander Birkenmajer’s judgment that Copernicus conserved those features of Aristotelian natural philosophy that he could reconcile with heliocentrism.39 In addition to Birkenmajer and other such interpretations, however, I accept Knox’s exhaustive examination of other sources on which Copernicus relied to accomplish his transformation of Aristotelian doctrine.40 Copernicus achieved a drastic adaptation of Aristotelianism to heliocentrism by reliance on other ancient sources made available by printed editions of texts, summaries, encyclopedias, and dictionaries. 3. Epilog: Reception of Copernicus’s Interpretation Originally, I had intended to end this study with a general summary of the reception of the Copernican theory down to 1600. That overly ambitious idea I put aside as soon as I began to assemble bibliography on reception. Such a summary would be premature, for ever more specialized studies are appearing, all making it clear that the story of the reception of the Copernican theory will require a very long book.41

37 De revolutionibus I, 2–3. See also Pliny, Natural History II, 65, 164–165; Rosen, Commentary, 345. 38 A. Birkenmajer, 368; and Rosen, 353. 39 A. Birkenmajer, “Éléments,” 37–48, and approved by Moraux, 233 and note 53. 40 Knox, “Copernicus’s Doctrine,” above all. See Tatarkiewicz, “Mikołaj Kopernik,” 7–18, for parallels between Copernicus’s texts and ancient/medieval sources on cosmic symmetry. 41 Foundational remains the work of Zinner, Entstehung. Compare Westman, “Essay Review,” 259–270. See also Costabel, “État,” on methodological problems with the whole notion of reception. For more recent sources and studies, see Rc, and also

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My study is about Copernicus’s appropriation and adaptation of Aristotelianism to the heliocentric theory. The epilog constitutes a modest contribution to the evolution of ideas on the nature of astronomical and cosmological hypotheses by tracing the reactions to Copernicus’s interpretation of Aristotelian logic and natural philosophy. Despite my narrowing of its goals, even this survey is not exhaustive. My aim is rather to try to illuminate the reception of Copernicus’s claims about the truth of astronomical hypotheses and the extraordinary transformation that Kepler achieved in how we should understand hypotheses and models in astronomy.42 The parties to these discussions interpreted Aristotle’s comments about truth and consequences in ways that we can distinguish into five types recognizable by the different nuances in their interpretations. The first I call the genuinely Copernican view, according to which we can conclude that some cosmological hypotheses are more probable than other alternatives because the results are consistent with the fundamental assumptions of astronomy and account for otherwise inexplicable facts. Of alternative mathematical models, one must be true on the assumption that we have exhausted the alternatives, but we may not be able to decide which alternative is true because there is no compelling reason or consensus. The second I ascribe to Rheticus, who adopted a more robust view of the truth of cosmological hypotheses, and who was more optimistic about the demonstrability of the conclusions. He may have been equally realist about the truth of astronomical hypotheses, and his recognition that the Sun is somehow the cause of planetary motions surpassed Copernicus’s view, which was compromised by having the

on the reception as treated in several international meetings and collected as proceedings in Reception, Colloquia copernicana, 1, Studia copernicana, 5. See also the papers on the reception in Colloquia copernicana, 2, Studia copernicana, 6; Colloquia copernicana, 4, Studia copernicana, 14; The Copernican Achievement; and Das 500 Jährige Jubiläum. For an excellent brief summary of the 16th-century reception with extensive bibliography, see Pantin, “New Philosophy,” 237–262. As Pantin turns to the seventeenth century, however, her analysis becomes curiously reductionistic. In addition, see Diffusione; Vermij, Calvinist Copernicans; de Bustos Tovar, “Introducción,” 235–252; Dobrzycki and Szczucki, “On the Transmission,” 25–28; Donahue, “Solid Planetary Spheres,” 244–275, followed by Heilbron, “Commentary” 276–284; and Juznic, “Copernicus in Ljubljana,” 231–232. 42 Crombie, Styles, 530–543, provides a selective but illuminating summary of the logical and methodological issues regarding hypotheses. See Jardine, “Significance,” 168–194; idem, “Many Significances,” 133–137.

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center of Earth’s orbit, not the true Sun, as the center of planetary motions. The third is the standard Lutheran interpretation sometimes referred to as the Wittenberg Interpretation.43 Astronomical hypotheses are fictions devised for the purpose of calculation not for the purpose of ascertaining the truth. Cosmological conclusions are true because derived from the more certain principles of natural philosophy and metaphysics. Even false cosmological hypotheses, however, may yield models that predict the positions of celestial bodies accurately. Aristotle’s pronouncements about truth agreeing with truth refer only to those cases where genuine demonstrations are possible and where the true causes of phenomena have been discovered. The fourth view is Michael Mästlin’s. Mästlin accepted the heliostatic theory, and while judging it as true from a cosmological perspective, he otherwise adopted a thoroughly mathematical interpretation of the theory.44 The fifth and final view we will find in Kepler’s assertions, the details of which I leave for later, but suffice it here to say that Kepler seizes on Aristotle’s assertion that a false hypothesis will sooner or later lead to false results and reveal itself as false. As is by now well known, the first known reactions to Copernicus’s theory were highly critical, accusing him of ignorance of logic and the principles of natural philosophy, of threatening to throw the liberal arts into confusion, and of contradicting the plain meaning of some biblical passages interpreted literally. Roman authorities may have intended to condemn the theory on scriptural grounds, but the criticisms suggest that they were developing a broadly based attack that would refute Copernicus’s understanding of logic, method, natural philosophy, and cosmology. As far as I know, there is no document explaining why that project did not go ahead. We know that its instigators, Bartolomeo Spina and Johannes Tolosani, died, but we do not know why no one else took it up after their deaths. A rehearsal of the circumstances may provide an explanation, after which we may turn

43 Westman, “Melanchthon Circle,” 165–193, and idem, “Three Responses,” 285– 345. I agree with Jardine, Birth, 225–257, that the Wittenberg Interpretation did not constitute an endorsement of skepticism. See also Pantin, 241, n. 19. 44 When Mästlin adopted the theory is unclear, but certainly by 1596. See Methuen, “Maestlin’s Teaching.”

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to Luther’s reaction, Rheticus’s portrayal of Copernicus’s achievement, and the arguments that Tolosani constructed. In 1545, Pope Paul III convened the Council of Trent, a council that met on and off for seventeen years. When it completed its task in 1562, the Church had virtually recreated Roman Catholicism, the Roman Catholic Church that anyone above the age of reason in 1958 would have easily recognized. Aside from reforming its entire bureaucratic structure, establishing a seminary system for the training of its priests, solidifying the authority of the papacy, responding to Lutheran challenges (on the doctrines of faith and works, the priesthood of all believers, and the authority of Sacred Scripture), the Council established the Roman Inquisition under the control of the Holy Office, and, under the jurisdiction of the Inquisition, the Congregation of the Index of Forbidden Books. With respect to Sacred Scripture, the Council decreed that there could be no new interpretation of the Bible that was contrary to the common consensus of the Church Fathers and of modern approved interpretations. Although the interpretation of this decree would take a surprising turn in 1616 by being confused with the doctrine of divine inspiration, there is no evidence that the decree was used against the heliocentric theory until 1616. In spite of the claims of some who ought to know better that the principal objections to the Copernican theory were religious or biblical, nearly everyone rejected the theory on physical, observational, or methodological grounds.45 That is to say, no one, not even the Holy Office in 1616, based restrictions of the theory on exclusively biblical grounds without support from philosophical and the then scientific consensus. The rotation of Earth on its axis and its orbit around the Sun raised numerous physical objections. As we now know, without a physical explanation of how Earth’s atmosphere “sticks” to Earth and insulates us from all of the predicted sensible effects, common-sense objections persuaded the majority of astronomers even to the middle of the seventeenth century that geokineticism was physically impossible. The orbit of the Moon around Earth as Earth orbits the Sun was also physically implausible, and became even more so, not less, after

45 Westman, “Copernicans and the Churches,” 76–113, places theological controversies usefully in the context of standards of textual interpretation.

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Tycho Brahe concluded that the spheres of ancient astronomy were non-existent. The major observational problem, of course, was the failure to observe stellar parallax. That problem also took a while to dissipate. People needed time to adjust to a universe that is much larger than most imagined. Galileo’s telescopic observations and those of more powerful telescopes later in the seventeenth century eventually persuaded most intellectuals that the stars are indeed farther than most had imagined. There was still no observation of stellar parallax, but the excuse that the stars are too far to observe it became entirely plausible. Galileo’s observation of the moons of Jupiter also contributed to acceptance of the plausibility of the Moon’s orbit around Earth as Earth orbits the Sun. From a methodological perspective, we may recognize that there were several major problems, and some of them remain the subject of controversy even to this day. Copernicus adopted the axiom of uniform motions in circles as suited to the heavenly bodies. With all of the resulting epicycles and eccentrics, his mathematical models were as complicated as Ptolemy’s models. Even the supposed elimination of the equant was a dubious achievement, and merely confirms the extent to which Copernicus was obsessed with the axiom of uniform circular motion. Ptolemy’s planetary epicycles were necessary not only to fit the data but also to account for the observation of planetary retrograde motions. Of course, as the epicycle models for the Moon demonstrate, an object can be moved on an epicycle without generating a retrograde motion. Still, the fact that Copernicus proposed a natural explanation for the observation of retrograde motion emphasizes the extent to which he needed epicyclets to regulate the motions of the planets and to account for the latitude of the planets. His planetary epicyclets are very small, but the resulting orbits of the models for the superior planets are not perfectly circular. Copernicus tried to minimize the departure from perfect circularity, but the admission is startling nonetheless. Of course, modern readers who have never looked closely at his book or read more than superficial accounts are surprised to discover that he retained epicycles.46 46

Even Cardinal Bellarmine thought that Copernicus dispensed with epicycles and eccentrics. See his “Letter to Foscarini,” in Finochiarro, Galileo Affair, 67–69. In the document evidently preparatory to the “Letter to the Grand Duchess Christina,” Galileo did not resist the opportunity to correct Bellarmine on this point. See Finocchiaro, 83.

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Beyond that, Copernicus’s eccentreccentric models for Mercury and Venus are complicated and cumbersome. The lunar model is observationally superior to Ptolemy’s, but he achieved it by putting the Moon on a double-epicycle model. And, of course, his latitude theory is another remnant of Ptolemaic geocentrism and his retention of spheres as the carriers of celestial bodies is a remnant of Aristotle’s physical interpretation of concentric spheres. As I have argued, Copernicus distinguished cosmological hypotheses from geometrical ones. The former he held as true, but he adopted a more pragmatic and tentative view on the truth of geometrical hypotheses and models. Only after he thought that he had exhausted all of the mathematical alternatives, did he adopt one, and even then he would commit himself to no more than the assertion that one of them must be true. We have also shown that, like almost all of his contemporaries, he admired both Plato and Aristotle, and he evidently believed that he could adapt ancient and scholastic principles of natural philosophy (Aristotelian and non-Aristotelian) to geokinetic heliocentrism. Unless we appeal optimistically to the survival of Aristotelian conceptions and notions in the ideas of major thinkers down to Leibniz, I concluded that his effort to persuade Aristotelians to adapt their principles to heliocentrism has to be counted among the most abject failures in the history of philosophy.47 That judgment holds at least for the short term. Copernicus understood perfectly well that scholastic Aristotelians would attack him mercilessly. In Book I of De revolutionibus he tried his best to ease them from their dogmatic stance. The first stage was to urge the plausibility of Earth’s motions by means of reinterpreting and adapting Aristotle’s principles accompanied by a brief recitation of the results and advantages of heliocentrism. He probably wrote that effort already in the 1520s. Over the course of the next fifteen years or so he tried to work out the details. Aside from fear over the reception of his theory, numerous calculatory and observational problems that he encountered convinced him by the late 1530s that something was terribly wrong.48 When

47 I take no account of modern neo-scholastic Aristotelians who now find the principles of gravitation, special relativity, and general relativity in Aristotle’s works. 48 Moesgaard, “Hunting,” 93–100, provides an intriguing analysis based on his belief that Copernicus aimed at making the true Sun the center, but found Mars and Venus to be recalcitrant. That failure, Moesgaard thinks, persuaded Copernicus that following Ptolemy had reached its limit. Rheticus reminded Copernicus of what he

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Georg Joachim Rheticus came to visit him in 1539, he stirred Copernicus from his slumber and perhaps even depression. This was a period in which Copernicus experienced several personal problems. Bishop Dantiscus pressured him to end his relationship with Anna Schilling. Copernicus’s legal dispute with a fellow canon, and suspicions of heresy for his support of Alexander Scultetus also troubled him. In addition, there were already indications by 1538 that his health was beginning to decline.49 As Rheticus became familiar with the details of Copernicus’s theory, he became enthusiastic and reminded Copernicus of the advantages of his major results. Perhaps Rheticus’s reaction persuaded Copernicus that there was hope after all that his arguments and results could persuade others. We do not know precisely what happened, but my speculation is supported by several striking facts. Suddenly, Copernicus got back to work. Rheticus did not understand everything perfectly, but he was the first to recognize the true dimensions of Copernicus’s achievement. The change in tone between Book I and the Preface to Pope Paul III (1542) is striking. Still indebted to and respectful of Ptolemy, Copernicus returned to the tone adopted at the beginning of Commentariolus and laid out in more detail than he had ever expressed all of the failures of his predecessors. The most striking are the failures of method and the failure to arrive at the unique structure of the universe. Without much further preparation he explained that he thought that he could find better explanations for the revolutions of the celestial spheres by assuming some motion of Earth, already announced within the first fifteen lines of the Preface and cited in the previous letter from Nicholas Schönberg. By then, of course, word of Copernicus’s theory had spread; there was hardly any reason to hold it back. Still, he explained the circumstances behind the delay, his hesitation, and appealed to the authority of ancient predecessors. Even taking all of those comments into account, we must conclude that his tone is nonetheless startling, more abrupt, and more aggressive. His disdain for objections based on Sacred Scripture takes one by surprise even today. Copernicus had regained his confidence. How else can we account for it except as a result of Rheticus’s intervention? Before we turn to Rheticus’s Narratio prima, however, here

had accomplished, and his enthusiasm persuaded Copernicus to finish the work. On Copernicus’s troubles, see Gingerich, Eye of Heaven, 37. 49 Biskup, Regesta, 171–185; Rosen, “Biography,” 366–372, 382–386, and 394–400.

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is the appropriate place to discuss Luther’s reaction and its very likely effect on Andreas Osiander. The historicity of Luther’s remark in 1541 remains an open question, but supposing that he expressed himself negatively about the heliocentric theory, we can interpret his remark in a plausible way.50 Luther makes two criticisms. Copernicus will turn the whole art of astronomy upside down, another example of innovation for its own sake. Surely what Luther meant is that the relation between natural philosophy and astronomy is clear with respect to questions about the order of the universe. If he did refer to the text from Joshua, the citation has rather the character of a clinching argument than the main reason for rejecting the theory. As we all know, Luther set great store in the biblical text as providing the only legitimate source for Christian doctrine. It is doubtful that he regarded geocentrism as a Christian doctrine, but he probably did see the Bible as supporting the common-sense view about Earth. It is striking that Osiander also warns against the subversion of the liberal arts and appeals to revelation as the only source of certain truth. Whatever Osiander’s motives may have been, he echoed Luther’s reaction. Rheticus seems to have been unimpressed. From correspondence, some of which has disappeared, we know that Osiander was in contact with Rheticus and Copernicus.51 He tried to persuade them to adopt his doubts about astronomical hypotheses. In the “Letter to the Reader,” however, Osiander expressed doubt about all astronomical hypotheses, geocentric as well as heliocentric, but his advice left geocentrism in effect as the standard view in cosmology. Did he mean to imply that geocentrism is divinely revealed? The correspondence makes it clear that he advocated caution and doubt as a strategy to avoid disagreements. But that implies that there were some who would defend geocentrism on biblical grounds, committing themselves to a narrow view of literal interpretation. Perhaps Osiander concluded that this would be a debate without any winners, and so recommended evasion. As we know from Robert Westman’s studies in particular, most Lutherans interpreted astronomical hypotheses in the pragmatic way advocated by Osiander while professing geocentrism

50 Norlind, “Copernicus and Luther,” 273–276. Norlind cites two versions, one by Johann Aurifaber (the one that refers to Copernicus as a fool) and one by Anton Lauterbach, which Norlind considers to be more accurate. 51 For the Narratio prima, see Sc and Rc. For the comment about the correspondence, see the French translation, in Sc, Appendix II, 208.

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on philosophical and cosmological grounds.52 Even Michael Mästlin, who accepted heliocentrism as true, rejected Kepler’s physical interpretation of the theory and his search for a physical explanation of the motions of celestial bodies. I turn now to Rheticus, after whom we may trace the known comments of readers of De revolutionibus. Although the Narratio prima appeared in print three years before De revolutionibus, I include Rheticus in the category of reception. That said, I cannot overlook the fact that the Narratio was written before the Preface to Pope Paul III. Although the ideas in the Preface are, I believe, Copernicus’s, we must consider the possibility that Rheticus influenced Copernicus’s choice of words and the specific formulation of his thoughts. In that respect, we cannot completely ignore Rheticus’s priority.53 In the Narratio, Rheticus cites Aristotle explicitly on several occasions, often in the Greek. We do not know how familiar Copernicus was with the Narratio. It is hard to believe that he did not have his own copy, but if so, then it has disappeared. Its publication in 1540 at Gdańsk and second edition in 1541 at Basel settle some issues, but they also provoke further questions. Rheticus confirms Copernicus’s work with Domenico Maria Novara, yet other remarks are the stuff of legends, as, for example, the report that Copernicus lectured on his theory before a large audience in Rome. Where Copernicus says virtually nothing about astrology, Rheticus cannot resist making predictions and relating them to Copernicus’s efforts to determine the mean motion of the solar apogee. Rheticus expresses Copernicus’s relation to his predecessors ambiguously. Time reveals the errors of astronomy. An imperceptible error at the foundation of astronomy is revealed by the passage of time.54 Rheticus here makes the claim that Copernicus could not just restore astronomy but had to build it anew, for Copernicus’s aim was to arrange the order of all of the motions and appearances in a certain and consistent structure or harmony. On the other hand, immediately after that comment, Rheticus portrays Copernicus’s work as a restoration of Ptolemaic astronomy, arguing forcefully that Copernicus’s 52

Westman, “Melanchthon Circle”; idem, “Michael Mästlin’s Adoption,” 53–63; idem, “Comet and the Cosmos,” 7–30; and idem, “Three Responses,” 285–345. 53 Burmeister, I: 44–62. 54 Sc, 52–53.

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achievement can be understood only as a completion and fulfillment of the chief task of astronomy. Ptolemy had failed to establish the perpetual and consistent connection and harmony of celestial phenomena. By proposing new hypotheses, Copernicus solved the problems, says Rheticus, who proceeds to explain a number of the inconsistencies and observed irregularities and how Copernicus’s hypotheses achieve what Ptolemy’s failed to achieve. In the enumeration of the new hypotheses [IX], Rheticus emphasizes the inconsistencies between natural philosophy and the astronomical observations, soliciting Aristotle’s own authority in support of new discoveries.55 As he turns to the section on the arrangement of the universe [X], Rheticus quotes Aristotle in Bessarion’s Latin translation of the Metaphysics I, minor, 1, 993b26–27: “That which causes derivative truths to be true is most true.”56 Rheticus understands this to mean that Copernicus sought hypotheses that would contain causes capable of confirming past true observations and predicting future true ones. Rheticus understands the connection to be a causal one, but he also seems to be aware of the hypothetical character of the assumptions that we are justified in taking as true provided they include causes from which true results follow. Again a little later, near the end of the section on the motions of the five planets [XIII], Rheticus refers to Aristotle’s dictum that humans by nature desire to know.57 Rheticus immediately relates this desire to our search for causes, and repeats Copernicus’s frustration over ignorance of the causes of the heavenly motions. Near the conclusion of the Narratio, Rheticus again comments on the relation between hypotheses and phenomena [XIV]: “When the observations of scholars have been set forth, the hypotheses of my teacher agree so well with the phenomena that they can be mutually interchanged, like a good definition by the thing defined.”58 Such a characterization is not just Aristotelian, but it is consistent with scholastic accounts of real definitions that express the essence of a thing, that is, the convertibility of the definiens with the definiendum. 55 Sc, 57–58 and 109–110; Rc, 21–22, and the references to Aristotle, De caelo II, 5, and Metaphysics XII, 8. 56 Rosen tr. 142; Sc, 58; Rc, 22. See Blake, “Theory of Hypothesis,” 22–49, esp. 27. In addition, Blake provides a useful summary, and I subscribe to his conclusions on the fallible and probable nature of physical and astronomical hypotheses. 57 Rosen tr. 167; Sc, 71, citing Metaphysics I, 1, 980a21; Rc, 37. 58 Rosen tr. 186; Sc., 80; Rc, 47.

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In the Encomium Prussiae, Rheticus repeats Averroes’s complaint against Ptolemaic astronomy that its models are adapted to calculation, not to reality.59 It is clear that Rheticus thought that Aristotle’s assertions were the justification and perhaps even the source for Copernicus’s critique of Ptolemaic method, especially his strong claim that the whole truth can follow only from true assumptions. Rheticus evidently believed that Copernicus meant knowledge of the causes. Any results that are false must be due to assumptions that are false. Conversely, if the causes are true, then only true results can follow from them. Worth noting is Rheticus’s emphasis on variations in the distance of Mars from Earth, an issue that I have argued constituted a motive for Copernicus’s formulation of Earth’s orbital motion.60 Rheticus’s most important contribution to the development of the heliocentric theory is his belief that the Sun is the source of movement, namely, that it is a cause of motion.61 Rheticus does not provide any explanation of how the Sun moves the planets, but he seems to have derived this conclusion from the ordering of the spheres and from Copernicus’s explanation of why Ptolemy’s planetary models linked the planetary motions to the motion of the Sun. Rheticus’s emphasis on “common measure” and the ordering of the spheres indicates that he understood Copernicus’s use of the topic from an integral whole, yet he does not say so explicitly. His assertions are also stronger, that is, more demonstrative and less dialectical in tone than we find in Copernicus. Perhaps convinced by Copernicus’s arguments, Rheticus tended to present them as more apodictic and more in agreement with “true” principles of natural philosophy than they in fact are.62 He was also the first to introduce the word systema to refer to both the explanatory hypothesis of the celestial motions and the real ordering of the parts.63 We know from Giese’s letter to Rheticus (July 1543) thanking him for the copy of De revolutionibus that Giese approved of Rheticus’s argument that the motion of Earth does not contradict the Bible. Giese 59

Sc, 193, note 278 for the source. Sc, 162, n. 85. 61 Sc, section [X], 60: “Adde, quod orbes maioris ambitus tardius, et propiores Soli, a quo quis principium motus et lucis esse dixerit, velocius, ut conveniebat, suos circuitus perficiunt.” Cf. 23, 113, and 169, n. 129. 62 Compare especially the texts in Narratio, Sc, 52–53, 58, 60, and 80. 63 Lerner, “Origins,” 410–413. 60

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also refers to Rheticus’s biography of Copernicus, which unfortunately has been lost. Giese offers no correction of the biography, adding only a few details about Copernicus’s death. Although Giese was an expert on Aristotle and apparently approved of Copernicus’s theory, he offers no explicit comments in its defense or about its relation to Aristotelian natural philosophy.64 In a letter to Dantiscus, perhaps the first known reaction to Rheticus’s Narratio, Gemma Frisius expresses a view similar to Osiander’s in adopting a purely hypothetical interpretation of heliocentric hypotheses. The question of their truth is of no importance; all that matters is whether the observations follow the models.65 The next known reaction is contained in the now famous treatise by Johannes Maria Tolosani, discovered and partly edited by Eugenio Garin.66 Tolosani wrote his critique around 1546 to 1548. Tolosani was a Dominican friar, an astronomer, and the friend of Bartolomeo Spina, Master of the Sacred Palace during the pontificate of Paul III. Spina had intended to write a refutation of Copernicus’s De revolutionibus, perhaps with the intention of condemning it as contrary to Sacred Scripture, but he died in 1546. Tolosani included in one of his treatises a series of appendixes divided into four chapters intended to fulfill the intention of his friend.67 Tolosani died in 1549, which seems to have ended the matter insofar as official Catholic reactions are concerned, but Garin notes as well that the Dominican Thomas Caccini later held public readings of Tolosani’s work in Florence. This is the same Caccini who accused Galileo of heresy at Santa Maria Novella in 1614.

64 Perhaps this particular argument on the motion of Earth and the Bible may have been lost as well, but a treatise by Rheticus, De motu terrae, was published anonymously in 1551. See Sc, 217–218, n. 11; cf. Rc, 37–73. I have referred in the previous section to the relevant pages that support Copernicus’s interpretation of Aristotle. 65 Sc, 248–249. See Danielson, “Achilles Gasser,” 459. 66 Garin, “Alle origini,” pp. 31–42. See Lerner, “Aux origins,” 681–721. See Granada, “Giovanni Maria Tolosani,” 11–35; and Kempfi, “Tolosani Versus Copernicus,” 239–254. 67 Garin, 41–42: “Unde conqueri non debet de ipsis cum quibus Romae disputavit, a quibus plurimum reprehensus fuit, sed magis eis gratias agere convenit, a quibus didicit quae ignoraverat. Sed illa disceptatio tarde contigit, vel post libri sui publicatam impressionem. Et ideo necesse fuit, ut ea quae ipse falsa conscripsit huius opusculi nostri veritate retundantur, ne legentes eius librum praedictis eius erroribus seducantur. Cogitaverat magister sacri et apostoloci palatii eius improbare librum, sed prius infirmitate, deinde morte praeventus, hoc implere non potuit. Quod ego postea in hoc opusculo perficere curavi pro veritate tuenda in communem ecclesiae sanctae utilitatem.”

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Tolosani begins his critique with a chapter that relies almost exclusively on passages of the Bible interpreted according to the standard medieval view of the universe. It is striking that he neglects the text from Joshua. Such interpretations of Scripture tend to confirm the extent to which scholars read the Bible as a text that supported Aristotelian natural philosophy and even corrected it in those cases where the views of ancient pagan authors could be excused for their ignorance of Scripture. Tolosani cites five passages of Aristotle, supported by the commentary of Thomas Aquinas, emphasizing the agreement between Scripture and natural philosophy. He also cites other ancient authors, even the so-called Pythagorean view, which Aristotle refuted.68 As he begins the second chapter on heaven and the elements, Tolosani comments that the assertions in the first chapter would have sufficed if not for Copernicus’s effort to revive the Pythagorean doctrine. No one but Copernicus really holds the doctrine as true, says Tolosani, but advance it to display ingenuity rather than teach the truth.69 After praising Copernicus’s command of Latin and Greek and his expertise in mathematics and astronomy, Tolosani accuses Copernicus of being very deficient in his knowledge of physical science and logic. Furthermore, adds Tolosani, he appears to be incompetent in Sacred Scripture because some of his principles contradict the Bible thus constituting a danger to the faith and to his readers.70 Here Tolosani makes some astronishing claims in comparison with what Thomas Aquinas maintained, namely, that the observational data can be derived from several assumptions, adding that some other theory might explain them.71 Tolosani, instead, relates natural philosophy to astronomy as a

68

Garin, 33–35. Garin, 35: “Et nullus eam [opinionem quorundam pictagoricorum de mobilitate terrae] sequitur, nisi iste Copernicus, qui ut putamus eam opinionem veram esse non censet, sed in hoc libro suo potius voluit aliis ostendere acutiem ingenii sui, quam rei veritatem docere.” Compare Lerner edition, 701. Later in this section, Tolosani will refer to what we now know as Osiander’s “Letter,” indicating that the author is unknown. 70 Garin, 35: “Peritus est etiam in scientiis mathematicis et astronomicis, sed plurimum deficit in scientiis physicis ac dialecticis, nec non [in] sacrarum literarum imperitus apparet, cum nonnullis earum principiis contradicat, non absque infidelitatis periculo et sibi et lectoribus libri sui.” See Lerner, 701–703. Bracketed words indicate places where I have adopted Lerner’s reading. Although he uses the word dialectica, Tolosani means this in the broad sense to include all of logic, not just probable arguments. For a partial English translation, see Goddu, “Logic,” 32. 71 See Thomas Aquinas, Summa theologiae Ia, q. 32, art. 1, reply to objection 2, No. 47, 18. 69

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superior to an inferior science, the conclusions of which follow deductively from the superior science.72 No astronomers can be perfect in their discipline unless they first learn the physical sciences, because astronomy presupposes natural celestial bodies and their natural motions. Perfect astronomers and philosophers learn logic by means of which they can distinguish between the true and false in disputations, and have the knowledge of arguments that are required in medicine, philosophy, theology, and other sciences.73 Because Copernicus does not know physical science and logic, is it any wonder that he is deceived in his opinion, and takes as true what is false as a result of his ignorance of those sciences? Tolosani asserts that Copernicus’s arguments in Book I on behalf of Earth’s motion and the immobility of the starry vault have no strength and can be easily refuted. It is, he says, foolish to contradict long-standing received opinions supported by the strongest reasons without stronger and irrefutable demonstrations, refuting the contrary reasons fully, something that Copernicus never does. The above argument does suggest that Tolosani’s genuine view is less demonstrative than the passage about subalternation indicates. Yet, it seems that Tolosani is trying to have it both ways, a symptom of what I have elsewhere characterized as “creeping demonstrability.” There is no genuine demonstration of geocentrism, yet we must accept it until there is a genuine demonstration of the contradictory opinion. To accommodate this ambiguity (to put it kindly) in Tolosani’s argument, I conclude that we should distinguish between strong and weak versions. Tolosani proceeds in chapter two to repeat all of the relevant Aristotelian, Ptolemaic, and Thomistic arguments against the Copernican hypotheses, rejecting Copernicus’s claims that those arguments prove nothing, and in effect relying on authority to refute Copernicus. He 72 Garin, 35–36: “Contra negantem autem prima scientiarum principia non est disserendum quoniam ex primis principiis conclusiones rationis discursus deducuntur. Scientia quoque inferior a superiore principia comprobata recipit. Itaque omnes scientiae sibi invicem connectuntur, ita ut inferior superior indigeat, et se invicem adiuvant.” Cf. Lerner, 703. 73 Garin, 36: “Non potest enim esse perfectus astronomus, nisi prius didicerit scientias physicas, cum astrologia presupponat naturalia corpora coelestia et naturales eorum motus. Nec homo potest esse perfectus astronomus et philosophus nisi per dialecticam sciat discernere inter verum et falsum in disputationibus, et habeat argumentoram notitiam: quod requiritur in medicinali arte, in philosophia, theologia et ceteris scientiis.” Cf. Lerner, 703.

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concludes this section by quoting the “Letter to the Reader on the Hypotheses of this Work.” He quotes the remark specifically and approvingly about the foolishness of expecting anything certain from astronomy.74 Tolosani seems puzzled that Copernicus would ignore the advice, for “by those words the foolishness of the author of this book is censured.”75 Worse yet, because the Pythagorean opinion is expressly contrary to human reason and opposite to sacred texts, it could have pernicious results. To avoid such scandal, he concludes chapter two, he wrote this little work.76 In its concluding two chapters, Tolosani quotes Thomas Aquinas’s comments on Aristotle and Ptolemy at length in support of Earth’s stability and centrality. Thomas’s first argument against the natural motion of Earth emphasizes the principle of part and whole. Because the natural motion of the whole and part must be the same, if Earth moved in a circle, then its parts would have to move in a circle. But we see that this is false; the parts of earth move in a straight line towards the center of Earth. It follows that if Earth moved in a circle, then its motion would be violent. But if the motion of Earth were circular and violent, it could not be sempiternal, because no violent motion lasts forever. Yet those who hold this opinion maintain that the order of the universe is sempiternal. Because the motion and rest of the principal

74 Garin, 38: “Unde author ille, cuius nomen ibi non annotatur, qui ante libri eius exordium loquitur ‘ad lectorem de hypothesibus eiusdem operis’, licet in priori parte Copernico blandiatur, in calce tamen verborum, recte considerata rei veritate absque assentatione sic inquit: ‘Neque quisquam (quod ad hypotheses attinet) quicquam certi ab astronomia expectet, cum ipsa nihil tale praestare queat, ne si in alium usum confictam pro veris arripiat, stultior ab hac disciplina discedat quam accesserit.’ Haec ille ignotus author.” Cf. Lerner, 708–709. 75 Garin, 38: “Ex quibus verbis authoris eiusdem libri taxatur insipientia, quod stulto labore conatus fuerit Pictagoricam confictam opinionem iam diu merito extinctam denuo suscitare, cum expresse contraria sit rationi humanae atque sacris adversa literis, ex qua facile possent oriri dissensiones inter divinae scripturae catholicos expositores et eos qui huic falsae opinioni pertinaci animo adhaerere vellent.” Tolosani was evidently not the source of the belief that Copernicus himself had written the letter, an unfortunate mistake that would occasion much confusion in the official Catholic response to De revolutionibus. In spite of Tolosani’s caution, Catholic authorities in the early seventeenth century perpetuated the confusion. For the details, consult the relevant documents in Finocchiaro, Galileo Affair. See especially Bellarmine’s letter to Foscarini (67–69), the Inquisition documents of 1616 (146–153), and the assertions and actions of the committee of the Index in 1620 that was charged with the responsibility for censoring Copernicus’s text (200–202). 76 Garin, 38: “Ad cuius vitandum scandalum, hoc nostrum opusculum scripsimus.”

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parts of the universe belong to the order of the universe, it follows that Earth does not move in a circle.77 With the above comment I conclude the summary of Tolosani’s effort to refute the Copernican theory. His approval of what we now know as Osiander’s view suggests that he understood the comments to support his claim about the deductive relation between natural philosophy and astronomy. According to the strong version of Tolosani’s argument, natural philosophy provides the principles and conclusions, from which the hypotheses of astronomy should be derived. Astronomers should construct their mathematical models in conformity with those hypotheses. Among the critics and supporters of the heliocentric theory, those who insisted on the causally explanatory relation between principles of natural philosophy (physics) and the astronomical hypotheses from which mathematical models should be derived advanced the strongest views.78 The next important reaction brings us back to Rheticus. In the preface to Ephemerides novae (Leipzig, 1550), Rheticus points out the discrepancies in the position of the stars between existing tables and observation. Copernicus, we know, devoted a great deal of time to correcting errors or confusions in the texts available to him, but his models reproduce virtually the same predictive results that we find in Ptolemy. Within a few years of the publication of his book, however, Rheticus emphasizes the discrepancies and points out the efforts of predecessors going back to the Middle Ages to correct the Alfonsine Tables. Again, he repeats the story that Copernicus lived

77 Garin, 38: “Quatuor enim ponit rationes physicas et exponit divus Thomas ibidem. ‘In quarum prima, hoc pro suo principio accipit, quod si terra moveretur circulariter, sive existens in medio mundi, sive extra mundi medium, necesse esset quod talis motus sit ei violentus. Manifestum est enim quod motus circularis non est proprius et naturalis motus terrae, quia si esset ei hic motus naturalis, oporteret quod quaelibet particula ipsius hunc motum haberet, cum idem sit motus naturalis totius et partis. Hoc autem videmus esse falsum. Nam omnes terrae partes moventur motu recto usque ad medium mundi. Si vero motus terrae circularis sit violentus, [praeter] naturam, sempiternus esse non potest; quia nullum violentum perpetuum. Sed si terra movetur circulariter, necesse esset quod talis motus sit sempiternus iuxta ipsius opinionem, quia secundum ipsum oportet quod ordo mundi sit sempiternus. Motus autem vel quies partium principalium mundi pertinent ad ordinem ipsius. Sic ergo sequitur terram non moveri circulariter.’ ” Cf. Lerner, 711. 78 Whether Tolosani was familiar with Thomas’s more cautious view of the relation between astronomical hypotheses and observations is not known, but he may have neglected to see a distinction between a cosmological system and an astronomical theory that follows from it.

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with Domenico Maria Novara and aided him in his observations. He reports that he quarreled with Copernicus over the imprecision, and that Copernicus confessed that he rejoiced when his results came to within10 minutes of arc, pointing out several difficulties. The first was that the ancients often accommodated their observations to the models. Second, the ancients did not achieve a precision of the positions of the fixed stars that was superior to 10 minutes of arc. Little wonder, then, that the planetary positions were no more accurate. Finally, he pointed out what in effect was a complaint about a corrupted tradition. Ptolemy had the advantage of the great many observations of his predecessors, but Copernicus had to make do with what was available and what he himself was able to observe often with great difficulty. It was the task now for Rheticus to establish the data as precisely as possible.79 In effect, Rheticus has drawn the conclusion that follows from Copernicus’s belief that astronomers must postulate true hypotheses, for from false hypotheses false results will follow sooner or later. Thus does Rheticus characterize Copernicus’s achievement, not as a complete success but as a spur to the improvement and perfection of astronomy. He repeats Copernicus’s charge to him in his preface to two works by Johannes Werner (Cracow, 1557).80 Six years later (1563) Peter Ramus wrote the famous letter to Rheticus, in which Ramus complains about the complications and obscurities deriving from astronomical hypotheses. He calls on Rheticus to produce an astronomy that is completely free of hypotheses, an astronomy as simple as that produced by nature itself. Whatever his limitations in mathematical astronomy, Ramus provides a short history of those astronomers who proposed fictional hypotheses to meet Plato’s challenge to astronomers in the Republic to save the phenomena. Ramus considers eccentrics and epicycles to be false and absurd, whether proposed as simple fictions or as real. He pointedly argues that demonstrating the truth from false causes is the highest absurdity. If Rheticus will construct an astronomy that suppresses hypotheses, Rheticus will be regarded as the king of astronomy.81

79 80 81

Sc, 221–223. See Kremer, “Use,” 126. Sc, 227–235, esp. 233. Sc, 238–242 and 244, n. 39.

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Rheticus was evidently not in any great hurry to reply, for his letter has been dated 1568. After explaining what he had done in the meantime, basically a report of his efforts in mathematics and in improving observational accuracy, his response is that by improving observations precisely we may free astronomy from hypotheses.82 I turn now to the annotations reported by Owen Gingerich in his census of the first two editions of De revolutionibus.83 Gingerich estimates that he has located a little over half of the copies. Of the seventy astronomers who might have owned the book, thirty copies have been found. Gingerich further estimates that by 1620 thirty to forty scholars read the book carefully and worked on it. I have focused my attention on annotations in the Preface that Gingerich reported. In many copies there are no annotations at all, according to Gingerich, but I cannot independently verify the completeness of his comments; Gingerich took note of all annotations, he was not just focused on the ones of interest to me. Although we have only a selection that has survived to some degree by chance, the annotations to Copernicus’s comment on method fall into patterns that are consistent with the known views up to about 1600. There are generally three types of reactions, two of which can be distinguised into more subtle versions, thus amounting to a total of five, as I enumerated earlier. The vast majority adopted the pragmatic view advocated by Osiander. A few accepted the heliocentric theory as true or probably true, but they too tended to accept the view that the principal task of astronomy was to generate models from which future positions could be accurately predicted, and which the observations would confirm. At least one astronomer expanded that goal to include the physical causes that with the data would lead to both the correct models and as perfect a match between models, predictions, and data as the data permitted. I will discuss the more subtle versions later. One of the early readers of De revolutionibus was Jofrancus Offusius, a Rhenish astronomer in Paris who annotated his copy around 1550. Other scholars worked from his notes; sometimes they copied or paraphrased his notes. One such copy of the 1543 edition clearly shows a preference for Osiander’s reading of hypotheses, and the comment 82

Sc, 245–246. Gingerich, Annotated Census. See also Gingerich, “Supplement,” 232, who announces that Brill will issue a corrected reprint that will update some entries and add a total of twenty-two copies. 83

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shows that the author believed that Copernicus himself did not believe in the truth of his own hypotheses.84 The copy of De revolutionibus annotated by Erasmus Reinhold Salveldensis, one of the members of the Melanchthon Circle of interpretation contains, unfortunately, no comments on the preface.85 Another copy that apparently belongs to this circle has a quotation from Aristotle on the first flyleaf, a passage that Rheticus also quoted in the Narratio prima:86 Aristot. Verissimum est id, quod posterioribus ut vera sint, causa est. “That is most true which is the cause of something true that follows from it.” On the verso of the flyleaf is a lengthy comment, only part of which I quote here: Anyone can rightly wonder how from such absurd hypotheses of Copernicus, which conflict with universal agreement and reason, such an accurate calculation can be produced and why he did not undertake the correcting of the Ptolemaic hypotheses, which agree with Sacred Scripture and experience, rather than producing such a paradox. Nevertheless, if you at the least will recognize some of the causes and reasons for his admirable discovery, by which he was moved to fashion new [hypotheses], you will stop wondering. Even if those of Ptolemy seem at first glance to be more plausible, nevertheless they commit more absurdities in conflict with geometry, with first principles, and the nature of celestial bodies than those of Copernicus do.

If it seems that the author of these comments is about to adopt heliocentrism, he continues by emphasizing the first axiom of astronomy and Ptolemy’s violation of it, concluding thus: For what comes first ought to agree always with what follows, as Galen teaches in his treatise, On the Best Sect, for Thrasyboulos. Therefore, Copernicus did not invent new hypotheses out of a desire to dissent from Ptolemy, whose hypotheses he everywhere followed to the extent allowed by the demonstrations, but rather that he might restore Ptolemy’s astronomy to its rightful place and dignity.

As these authors see it, astronomical hypotheses do not trump the common sense assumptions of natural philosophy.

84

Gingerich, I, 47: 62. See also Gingerich, I, 218: 278–283. Gingerich, I, 217: 268–278. Typical of members of this circle, Reinhold focuses entirely on the technical, mathematical details, and their relation to the observations. In addition to the reference in Gingerich, see Westman, “Melanchthon Circle.” 86 Gingerich, I, 220: 284–288. The translations have been very slightly modified. 85

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Jerome Schreiber received a copy of De revolutionibus in 1543. Schreiber studied mathematics under Johannes Schöner, and then matriculated in the same class with Rheticus (1532) at Wittenberg. This copy is important because Kepler later owned it, and his remarks in it suggest that Schreiber’s questions and comments may have alerted Kepler to problems with the centering of planetary orbits, not on the Sun, but on the center of Earth’s orbit.87 I will comment on the significance of this issue later. In an anonymous comment possibly from a later period, a copy of the 1566 edition in Venice contains a reference to Michael Mästlin in which Kepler’s teacher makes the curious observation that the comet of 1577 made the superiority of Copernicus’s hypotheses evident.88 Mästlin’s most interesting comments by far appear in a copy that he annotated over several years. To my knowledge, here is the first direct comment on the logic of Copernicus’s view about hypotheses:89 The true agrees with the true, and from what is true nothing follows unless it is true. In the process [of demonstration] if something false and impossible follows from a doctrine or the hypotheses, then it is necessary that the defect be hidden in a hypothesis. If, therefore, the hypothesis of the immobility of Earth were true, then what follows from it would also be true. But in [Ptolemaic] astronomy many inelegant and absurd consequents both in the arrangement of the orbs as in the understanding of their motions follow. Therefore the defect is in the hypothesis itself. The minor proposition is evident from the motion of the Sun, from the length of the tropical year, also from the motion of the three superior planets, but most of all from Venus and the stellar orb.

As we have pointed out, the expression “Verum vero consonant” is of Aristotelian origin, which Mästlin probably took from the Latin edition of Averroes with the analytical index prepared by Marcantonio Zimara. The most proper context involves demonstration from causes

87

Gingerich, I, 68: 76–80. Gingerich, II, 131: 134. For analysis of Mästlin’s reaction to the comet of 1577 and its relation to the heliocentric theory, see Westman, “Mästlin’s Adoption,” esp. 63. See also Jarrell, “Contemporaries,” esp. 26, for an explanation of Mästlin’s mistake. 89 Gingerich, I, 178: 219–227, esp. 222 [translations modified]. For analysis of Maestlin’s interpretation and acceptance of Copernicus’s hypotheses, see Westman, “Mästlin’s Adoption.” Mästlin explains his emphasis on Venus as follows. The demonstration of the epicycle for Venus cannot be constructed from the assumption of an immobile Earth at the center without penetration of orbs. Westman discovered the most important texts on which I have relied for my account. See Gingerich, 223–225. 88

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to effects, but Mästlin understands that Copernicus was concerned with astronomical demonstration of the phenomena:90 This is certainly the main argument, how all of the phenomena as well as the order and sizes of the orbs act in concert with the mobility of Earth.

On the same folio, he added: Such an ordering of the machine of the whole universe, which permits surer demonstrations, is altogether more rational. By means of that ordering, the whole universe moves in such a way that nothing can be interchanged without confusing everything, from which all of the phenomena can be demonstrated very exactly, and in which nothing discordant occurs in the process (for, as far as astronomy is concerned, Copernicus wrote this whole book, not as a natural philosopher, but as an astronomer).

As we will see below, Mästlin preserves the distinction between the task of the astronomer and that of the natural philosopher. Even as he accepts the mobility of Earth, he is careful to limit astronomy to the formulation of hypotheses, the construction of models in accordance with the hypotheses, and the demonstration of the phenomena from the models.91 Mästlin’s principal objections to Ptolemaic hypotheses and models include inconvenient consequences, absurdities, demonstrations that entail penetration of spheres, violations of the foundations of astronomy, disagreements with the observations, and other like catastrophes. From his perspective, the motions of Earth are the causes of the phenomena; the astronomer should not propose explanations for the causes of the motions. In a similar vein, an anonymous early annotator on the 1566 edition commented:92 “In what way are we to understand hypotheses? It is necessary to believe them, for our senses cannot reach farther than

90 Gingerich, 223. On Zimara, see Lohr, Latin Aristotle Commentaries, 507, No. 3, Tabula dilucidationum in dictis Aristotelis et Averrois. The earliest edition is from Venice, 1537, which means that Copernicus could have consulted it prior to writing the Preface in 1542. Lohr lists at least ten editions, two colophons, and one reprint, all published between 1537 and 1576. 91 Gingerich, 227. 92 Gingerich, II, 212: 227–228, esp. 228 [translation modified]. On the title page the same annotator comments that astronomers should be allowed to set forth what hypotheses they please as long as they have a true relation to the motion of celestial bodies.

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our eyes can discern or our hands touch.” Kepler, much to Mästlin’s consternation, would change all of that.93 A Cracow copy of the 1543 edition containing also the 1617 edition is important for the comments in it by Jan Brożek on Osiander’s interpretation of hypotheses:94 Actually [Osiander’s] opinion that ‘it is not necessary for astronomical hypotheses to be true, nor indeed probable, so long as they agree with the phenomena’ is completely absurd. Ptolemy’s hypothesis is that Earth is at rest; Copernicus’s that Earth moves. Is therefore neither true? It is necessary for one of two contradictory hypotheses to be true. If Earth rests, then it does not move. If it moves, then it does not rest. In his preface to the reader, Osiander has deceived many about the hypotheses of Copernicus’s work. . . . But someone will ask how one can know which of the two is truer, Ptolemy’s or Copernicus’s? To answer this question I wish for a judge who knows all of astronomy well, Ptolemaic and Copernican. Only those ignorant of astronomy will base a judgment on sense appearances alone.

In a copy of the 1566 edition that was used at Paris in the early 1600s, probably by David Sinclair, we find comments that display support for Copernicus’s hypotheses:95 The wonderfully respected and learned Copernicus paints for us in this first book the admirable construction of the entire machinery of the world, and supported by using his hypothesis as a very certain foundation, attempts to represent and begins to demonstrate most credibly all the observations of all ages and the appearances of the motions of the stars; to which he attaches as much as the doctrine of triangles as is necessary for his work.

93 On Mästlin’s rejection of Kepler’s program for a dynamical astronomy, in Westman’s phrase (“Mästlin’s Adoption,” 59), see Mästlin’s letter to Kepler, 9 March 1597, Johannes Kepler, Gesammelte Werke, 13: 111: “Veruntamen huic capiti istud adjicio. Non aspernor hanc de anima et virtute motrice speculationem. Verum metuo ne nimis subtilis sit, si nimium extendatur. Qualis illa ipsa est, quam de Luna moues. Vereor profectò, si vltra modum nimis specialis fiat, ne iacturam vel certe ruinam totius Astronomiae post se trahat. Existimo omnino parcè et valde moderatè hac speculatione vtendum. Et vt verè dicam quod sentio: Non aspernor, et profectò languidus est meus assensus, plurima enim contraria mihi obstant. Sed de his alias.” The passage contains several puns, but despite his claim not to reject Kepler’s speculation about a moving soul and force, Mästlin was obviously worried that such speculation would drag along with it the overthrow and ruin of astronomy. See Voelkel, Composition, 67–69. 94 Gingerich, I, 133: 153–155, esp. 154 [translation slightly modified]. 95 Gingerich, II, 260: 294–295.

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These remarks give no indication that the author finds any problem with Copernicus’s models, and so would suggest a lack of familiarity with Kepler’s corrections. Owen Gingerich’s census provides a basis for studying the ways in which subsequent authors used De revolutionibus through the early seventeenth century. Because not all copies have survived, there is a possibility that the surviving copies are not representative. That possibility to the contrary notwithstanding, the surviving copies tend to show that annotators focused on the technical, mathematical parts of the treatise. Only relatively few contain comments on the nature of hypotheses, and many of those relate to the identification of Osiander’s letter. This fact leads us to conclude that we have identified all of the types of interpretation of hypotheses. In order, they are the physical and geocentric (Tolosani, strong version), the mathematical and still geocentric (Osiander, Tolosani’s weak version, Ursus, and the Melanchton Circle), the mathematical and heliocentric (Mästlin), the natural philosophical and heliocentric (Rheticus), and the explicitly physical and heliocentric (Kepler). Kepler’s interpretation is more nuanced than Tolosani’s strong version, but they are superficially contrary. Suffice it to say that my hypothesis warrants closer examination of those copies with annotations on the early material that Gingerich has not quoted in his census.96 Before turning exclusively to Kepler, I include here an additional noteworthy reaction. Erasmus Reinhold’s extensive commentary begins with Book III, and completely ignores the issues on which this study focuses.97 We know from other studies that Reinhold was an important member of the Melanchton Circle.98 In a later reaction by Mästlin we find confirmation of both his reservations about Kepler’s physical interpretation and also of the

96

Gingerich, 378–380. Rc, 191 and 570. See Gingerich, “Role of Erasmus Reinhold,” 43–62 and 123–125; idem, “Early Copernican Ephemerides,” 403–417. 98 Westman, “Melanchthon Circle,” 174–177. See Moesgaard, “How Copernicanism Took Root in Denmark and Norway,” 117–151, esp. 124–126, where he summarizes Caspar Bartholin’s critique of Copernicus (1619). Bartholin follows the pragmatic strategy but also criticizes Copernicus for logical and physical absurdities. Moesgaard concludes his summary, 126, with the comment that “apart from easily discernible sophisms it must be admitted that he has with merciless acuteness unveiled the weakness of Copernicus’ embodying his new cosmology in an Aristotelian vocabulary.” 97

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principal logical or dialectical warrant in Copernicus’s arguments.99 Mästlin criticizes in the strongest terms claims made by Aristotelians that the observation of bodies falling to Earth provides evidence that Earth is the center of the universe. Such observations confirm at best that the observed bodies have a tendency to fall towards the center of Earth. What is the justification for inferring the whole from the part? Copernicus was right to argue from the whole to the parts. Mästlin follows that claim immediately with Copernicus’s hypotheses by means of which he enumerates, arranges, connects, and measures the order and magnitude of all orbs and spheres, such that no change can be admitted without throwing the entire universe into confusion.100 As we argued earlier and throughout, Copernicus relied on the dialectical topic from an integral whole, among other topics, as the warrant for his conclusions. Mästlin implicitly recognizes that the topic from [integral] part to whole can be used only destructively, and that it is a fallacy to use it constructively. The topic from [integral] whole to part, 99 For the complete preface written by Mästlin in 1596 in an edition of Rheticus’s Narratio that was included with Kepler’s Mysterium Cosmographicum, see Rc, 447– 452. See 449 in particular. On his rejection of Kepler’s physical hypotheses, see 451. To my knowledge, Westman was the first to comment on this text. See Westman, “Mästlin’s Adoption,” 59–62. For a translation, see Goddu, “Mereological Vision,” 336–337. 100 Rc, 449–450: “An non omnis sedes et totum domicilium omnium eorum, quae nobis gravia sunt aut levia, Terra, et circa terram Aer est? Sed quid Terra, quid eam ambiens Aer, respectu immensae totius Mundi vastitatis? Punctum sunt, sive punctuli, et si quid minus dici posset, rationem habent. Quod cum sit, an non Philosophum dicturum putas, quod infirma argumentatio a particula sive hoc punctulo ad totum Mundum extruatur? Non ergo ex iis, quae ad hoc punctulum appetunt vel ab eo refugiunt, de spaciosissimi huius Mundi centro certi esse possumus. Locum quidem suum proprium, qui Philosopho teste est perfectio rei, haec nostra gravia et levia a Natura sibi tributum appetunt, quam affectionem, ut Copernicus lib. I cap 9 erudite disserit, credibile est etiam Soli, Lunae caeterisque errantium fulgoribus inesse, ut eius efficacia in ea, qua se repraesentant, rotunditate permaneant: Quod si is locus alicubi simul sit Mundi centrum, id non nisi per accidens contingit. Verum Copernici rationes Astronomicae non a particula, eaque minutissima, ad totum: sed contra, a toto ad partes procedunt. “Sed et ex ipso hypothesium usitatarum et Copernici processu facile agnoscitur, utrae plus fidei mereantur. Etenim Copernici hypotheses omnium Orbium et Sphaerarum ordinem et magnitudinem sic numerant, disponunt, connectunt et metiuntur, ut nihil quicquam in eis mutari aut transponi sine totius Universi confusione possit; quin etiam omnis dubitatio de situ et serie procul exclusa manet.” He goes on to emphasize how predecessors disagreed about the number of spheres, their arrangement, connection, and magnitude, and concludes his argument by contrasting the orbital motion of Earth with the ineffable velocity of the sphere of fixed stars. This is support, of course, for Copernicus’s argument from simplicity, an argument that is dubious from the point of view of the Aristotelian hypothesis about celestial matter.

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conversely, can be used constructively. As far as I am aware, Mästlin is the only commentator to make explicit mention of this feature of Copernicus’s argumentation, although it is virtually certain that all scholars educated in dialectic were familiar with the principle. At the very least, Mästlin confirms my analysis of Copernicus’s logic, and that at least one author of the sixteenth century recognized explicitly the most important logical move in Copernicus’s argument.101 On one point, however, Mästlin made a mistake. His comments fail to notice that Copernicus’s inference about gravity depends on a constructive application of the topic from an integral part. Because all of the observable heavenly bodies appear to be spheres, the rectilinear component of falling bodies led Copernicus to speculate that gravity is a tendency or desire that God implanted in all of the observable celestial bodies that have the form of a sphere (Sun, Moon, and planets). Copernicus’s cosmos, however, is finite, and the spheres of the fixed stars and the Sun are stationary, hence Copernicus did not conclude that all spheres rotate on their axes. Valid inferences from part to whole, then, rely on observation and depend on a critique of existing accounts, eliminating those that do not fit in the already established structure. The same kind of argument would lead Kepler to conclude that the physical principles discovered on Earth must be the principles of all motion.102 In Astronomia nova, Kepler devotes an entire chapter to the issue of hypotheses. Even more so than the important Apologia pro Tychone contra Ursum, this chapter from his war with Mars reveals Kepler’s grasp of the issues and his understanding of the limits.103 At the same time, the chapter suggests his self-consciousness about achieving the complete transformation of astronomy, a suggestion that he confirms

101

See chapter eight for the details. Mästlin, like Copernicus, does not elaborate on the logical technicalities, suggesting that he too relied on a simplified version like that of Peter of Spain. This would also suggest that he shared Copernicus’s view about the universe as a heterogeneous integral and essential quantitative whole. 102 Goddu, “Mereological Vision,” 336–337, also explains the relation between the topic from an integral part and Newton’s Rule 3 of reasoning in natural philosophy. 103 Jardine, Birth. On 41–57, Jardine provides a free translation of a part of the treatise by Nicolaus Ursus defending the interpretation of hypotheses as represented in the “Letter to the Reader.” In the Apologia (1600), Kepler’s response is prolix, although in some places he makes his motivation clear. See Jardine’s translation, 134–207. See also Jardine, “Many Significances,” for criticism of anachronistic interpretations of Kepler’s Apologia.

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later in Astronomia nova. It is a signal moment in the history that I have traced in this study. In Part II, chapter 21, Kepler asks “Why, and to what extent, may a false hypothesis yield the truth?”104 Part II is on Mars’s first inequality, “in imitation of the ancients.” At the beginning of Part II, that is, chapter 7, Kepler explained the circumstances under which he “happened upon the theory of Mars.”105 After referring to Mästlin’s encouragement and support in his preface to Rheticus’s Narratio prima that Mästlin had appended to Kepler’s Mysterium cosmographicum, he says that he “began to think seriously of comparing observations.” He wrote to Tycho Brahe in 1597, who mentioned his own observations in reply, which “ignited” in Kepler “an overwhelming desire to see them.” In 1600 Kepler travelled to Bohemia “in hopes of learning the correct eccentricities of the planets.” He continues: But when I found out during the first week that, like Ptolemy and Copernicus, he made use of the sun’s mean motion, while the apparent motion would be more in accord with my little book [Mysterium cosmographicum] (as is clear from the book itself), I begged the master to allow me to make use of the observations in my manner.106

As he goes on to explain, Tycho’s aide was working on the theory of Mars. If he had been working on a different planet, Kepler would have started on it. I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets.

Tycho’s aide had worked out a table of mean oppositions starting with 1580, and he invented a hypothesis, which, he claimed, represented all these oppositions within a distance of two minutes in longitude.

104 I rely primarily on Kepler, New Astronomy, tr. Donahue, 294–300, based on Astronomia nova, ed. Caspar, See Westman, “Kepler’s Theory,” 233–264. Cf. Evans, “Division,” 1009–1024. 105 Donahue tr. 184–187. 106 In some instances I provide the Latin to reinforce the dramatic feature of Kepler’s discovery. See Caspar ed. 3: 109: “Eo igitur veni sum initium anni MDC spe Planetarum correctas eccentricitates addiscendi. Cum autem primo octiduo didicissem ipsum adhibere cum Ptolemaeo et Copernico medium motum Solis, esset vero apparens motus meo libello accommodiator (quod ex ipso libro patet), ab authore impetravi ut mihi liceret observationibus meo modo uti.”

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“The mean motions, apogees, and nodes were extended over a period of forty years.” He got stuck “in the latitude at acronychal positions and also the parallax of the annual orb.”107 There was a hypothesis and table for the latitudes, “but it failed to elicit the observed latitude.” A similar problem would emerge in the lunar theory. Kepler continues: Now since I suspected what proved to be true, that the hypothesis was inadequate, I entered upon the work girded with the preconceived opinions expressed in my Mysterium cosmographicum. At the beginning there was great controversy between us as to whether it were possible to set up another sort of hypothesis which would express to a hair’s breadth so many positions of the planet, and whether it were possible for the former hypothesis to be false despite its having accomplished this so far over the entire circuit of the zodiac. I consequently showed, using the arguments presented already in Part I, that an eccentric can be false, yet answer for the appearances within five minutes or better, provided that the centre of the equant be correctly known. As for the parallax of the annual orb, and the latitudes, that prize is not yet won, and besides, was not attained by their hypothesis. What remains, then, is to find out whether they with their means of computation, might not somewhere differ from the observations by five minutes. I therefore began to investigate the certitude of their operation. What success came of that labour, it would be boring and pointless to recount. I shall describe only so much of that labour of four years as will pertain to our methodical enquiry.

In fact, in a little more than seventy-one pages of Max Caspar’s edition, Kepler describes how he found a hypothesis to account for the first inequality, showing in chapters 19 and 20 how he refuted the hypothesis, thus bringing us to the conclusion of Part II. I particularly abhor that axiom of the logicians, that the true follows from the false, because people have used it to go for Copernicus’s jugular, while I am his disciple in the more general hypothesis concerning the system of the world. I therefore considered it particularly worthwhile

107 The clearest explanation is in Stephenson, Kepler’s Physical Astronomy, 209: “Acronychal observations: observations of a planet made at the moment when its second anomaly has vanished. In heliocentric theories, an acronychal observation is one made when the earth is directly on a line between the sun and the body being observed, so that the observed direction to the body is also the direction from the sun to that body.”

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conclusion and epilog now to show the reader how it does happen here that the true follows from the false.108

First, you have already seen that what has followed is not exactly the truth. Kepler goes on to explain that his false supposition does not give the planet the right latitude. “So it is not exactly the truth that follows from this false hypothesis.” Even with respect to longitude, “the lack of perceptible difference in effects between the as yet unknown true hypothesis and the false one assumed by us does not make the effect identical.” For there can be a small discrepancy which the senses do not perceive. There are, however, occasions upon which a false hypothesis can simulate truth, within the limits of observational precision, with respect to the longitude.

By means of a sequence of false hypotheses, Kepler goes on to show how each succeeding hypothesis corrects the error in the preceding one, reducing the amount of error at the sixteenths of the period to the point where the results are within the limits of observational accuracy.109 He continues: It is at least now clear to what extent and in what manner the truth may follow from false principles: whatever is false in these hypotheses is peculiar to them and can be absent, while whatever endows truth with necessity is in general aspect wholly true and nothing else. Further, as these false principles are fitted only to certain positions throughout the whole circle, it follows that they will not be entirely correct outside those positions, except to the extent (as shown in this example) that the difference can no longer be appraised by the acuteness of the senses. Also, this same dullness of the senses hides the following additional small error which remains at the eighths of the period.

108 Caspar ed. 183: “CAVSA, CVR FALSA HYPOTHESIS VERVM PRODAT ET QUATENUS? Porro quia ego axioma hoc dialecticorum, ex falso verum sequi, vehementer odi, propterea quod eo Copernici (quem sequor magistrum in hypothesibus universalioribus systematis mundani) jugulum petatur: operae precium putavi lectori ostendere, quomodo his ex falso verum sequatur.” 109 This argument supersedes refutation 9 of chapter 1 of the Apologia, 148–150. By 1602 Kepler had become aware of how more difficult the problems were. See the detailed account of Kepler’s approach after Tycho’s death in Voelkel, Composition, 130–141.

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Kepler shows that the result would place the planet three minutes higher than it should be. “The equation therefore will be seen to be too large, and thus the eccentricity [of the equant] is too large.”110 He concludes chapter 21 thus: This mutual tempering of various influences causes one error to compensate for another, brings the calculation within the limits of observational precision, and makes it impossible to perceive the falsity of this particular hypothesis. And so this sly Jezebel cannot gloat over the dragging of truth (a most chaste maiden) into her bordello. Any honest woman following this false predecessor would stay closely in her tracks owing to the narrowness of the streets and the press of the crowd, and the stupid, bleary-eyed professors of the subtleties of logic, who cannot tell a candid appearance from a shameless one, judge her to be the liar’s maidservant. This is without doubt the reason for the remaining discrepancies of one or two minutes in chapter 18, in Cancer, Leo, Scorpio, and several other places. But the error cannot easily be seen, since the observations used do not fall at the apsides and at the quarters and eighths of the period.

We may take this conclusion as Kepler’s response to both Tolosani and Ramus.111 Kepler immediately concludes Part II: Up to the present, the hypothesis accounting for the first inequality (in which Brahe and Copernicus are in agreement, both different somewhat in form from Ptolemy) has been presented using the sun’s mean motion, which all three authors had substituted for the sun’s apparent motion. Thereafter, it was shown that whether we follow the sun’s apparent motion and the hypothesis found in chapter 16, or the sun’s mean motion and the hypothesis proposed in chapter 8 according to Brahe’s rendition, in both instances there result false distances of the planet from the centre, whether of the sun (for Copernicus or Brahe) or of the world (for Ptolemy). Consequently, what we had previously constructed from the Brahean observations we have later in turn destroyed using other observations of his. This was the necessary consequence of our having

110 Caspar ed. 186: “Ita vel jam patet, quatenus et quomodo verum sequatur ex falsis principiis: nempe id, quod in hisce falsum, speciale est et abesse potest, quod vero necessitatem affert veritati, sub generali ratione verum omnino et ipsum est. . . . Atque utrinque Planeta 3 scrupulis fiet altior justo. Aequatio ergo nimis videbitur magna. Quare eccentricitas nimis magna.” 111 In Apologia, 154, Kepler distinguishes geometrical hypotheses from astronomical hypotheses. The latter describe paths that can be derived from geometrical hypotheses. Later, 156, he distinguishes the practical and mechanical part of astronomy from contemplative astronomy.

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conclusion and epilog observed (in imitation of previous theorists) several things that were plausible but really false. And this much of the work is dedicated to this imitation of previous theorists, with which I am concluding this second part of the Commentaries.

It would take us far afield to follow Kepler to his final results, but we must comment on the meaning of his procedure and its significance for our thesis about Copernicus and the Aristotelian tradition. Although he does not cite Aristotle here and, indeed, expresses contempt for academic logicians, Kepler was in fact following Aristotle’s injunction that a false assumption will sooner or later be exposed by the consequences that follow from it. That was why he found it necessary to test every relevant alternative hypothesis. By contrast, from what is true only the true will follow. Indeed, as Westman has found, Kepler evidently quoted Mästlin’s comment:112 If one considers how easily falsehood is inconsistent with itself and, on the contrary, how the truth is always consonant with the truth [verum vero consonet], then one may perhaps begin from the [argument] alone to understand the most important argument for the arrangement of the Copernican orbs.113

We may find it arguable whether or not we can ever be certain about possession of the truth. Copernicus contented himself with greater probability and the somewhat weaker criterion of relevance between hypotheses and results, but Kepler tried to meet the challenge of an astronomy without hypotheses. In Part IV of Astronomia nova, Kepler treats the inequality in the heliocentric longitudes (the first inequality) from physical causes and his own ideas. As William Donahue has commented, Kepler consid-

112

Westman, “Mästlin’s Adoption,” 60, n. 25, citing Kepler, Gesammelte Werke,

1: 17. 113 The full quotation in context is from Kepler, Mysterium cosmographicum, ed. Caspar, 1: 16–17: “Neque tamen temerè, et sine grauissima Praeceptoris mei Maestlini clarissimi Mathematice authoritate, hanc sectam amplexum sum. Nam is, etsi primus mihi dux et praemonstratur fuit, cùm ad alia, tum praecipuè ad haec philosophemata, atque ideo iure primo loco recenseri debuisset: Tamen alia quadam peculiari ratione tertiam mihi causam praebuit ita sentiendi: dum Cometam anni 77 deprehendit, constantissimè ad motum Veneris à Copernico proditum moueri, et capta ex altitudine superlunari coniectura, in ipso orbe Venerio Copernicano curriculum suum absoluere. Quòd si quis secum perpendat, quàm facilè falsum à seipso dissentiat, et econtrà, quàm constanter verum vero consonet: non iniuria maximum argumentum dispositionis orbium Copernicanae vel ex hoc solo coeperit.”

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ered it nonsense to separate the geometry from the physics on which it is based.114 We need not accept Kepler’s strong causal thesis here, but his reasons for seeking a physically causal explanation of planetary motions are compelling. Kepler concluded that Tycho Brahe’s determination of cometary parallax (along with the interpenetration of spheres required by Tycho’s own geo-heliocentric system) required jettisoning this remnant of Aristotelian cosmology. If there were no spheres, then “epicycles no longer made sense, because they were no longer supported by any substance.”115 And he objected to the idea that bodies could move through space around empty points. Without spheres to support, contain, and move them, Kepler had to try to discover what really moves the planets. In short, the geometry had to work, to be sure, but the actual paths described accurately by the geometry had to be explained by physical principles.116 As we now know, however, it was not necessary for Kepler to have the correct physical principles or causes.117 Simply postulating physical causes that required using the true Sun as a focus along with Tycho’s data led to the correct orbit.118 In chapter 19 of Part II, on which I briefly focused above, Kepler makes one of his most startling and most quoted statements about the “hypothesis constructed according to the opinion of the authorities”:119

114

Donahue, 4. Donahue, 7. On Tycho Brahe, the historiography has become very complicated. See Thoren, “Tycho Brahe,” 3–21; Jarrell, “Contemporaries,” 22–32; and Schofield, “Tychonic,” 33–44. Compare Gingerich and Westman, Wittich Connection; and Granada, “Did Tycho Eliminate the Celestial Spheres Before 1586?” 125–145. 116 In Apologia, 146, Kepler alludes to William Gilbert, suggesting that he had already concluded in 1600 that magnetism could account in part for the Sun’s moving power. 117 Later, in Epitome (1618), Kepler appeals to causas probabiles. See Jardine, Birth, 250. As we know, the term “probabilis” is ambiguous, sometimes meaning “provable,” sometimes “plausible.” It seems likely that Kepler means it in the dialectical sense as supported by the evidence and hence as worthy of approval, as Jardine also concludes. 118 I must leave it to the reader to ponder the apparently ironic consequence that Kepler derived true results from an incorrect physical theory. See Stephenson, Kepler’s Physical Astronomy, 136–137 and 202–205, for his insightful distinction between an unsound theory and the right kind of a theory, and his emphasis on the essential purpose that physical investigations served for Kepler in discovering the relations that we know as “Kepler’s laws.” 119 Donahue, 281. Caspar ed. 3: 174: “Fieri quis posse putaret? Haec hypothesis observationibus acronúchioi tam prope consentiens falsa tamen est, sive observationes ad medium Solis locum sive ad apparentem examinentur.” 115

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conclusion and epilog Who would have thought it possible? This hypothesis, so closely in agreement with the acronychal observations, is nonetheless false whether the observations be considered in relation to the sun’s mean position or to its apparent position.120 Ptolemy indicated this to us when he taught that the eccentricity of the equalizing point is to be bisected by the centre of the eccentric bearing the planet. For here neither Tycho Brahe nor I have bisected the eccentricity of the equalizing point. Now for Copernicus it was a matter of religion not to neglect this anywhere.121 For he made very little use of observations, perhaps thinking that Ptolemy used no more than are referred to in his Great Work. Tycho Brahe balked at this. For in imitating Copernicus, he set up this ratio of the eccentricities, which the acronychal observations require. But when this was gainsaid not only by the acronychal latitudes (for these still underwent some increase arising from the second inequality) but also, and much more forcefully, by observations of other positions with respect to the sun which are affected by the second inequality, he stopped here and turned to the lunar theory, and I meanwhile stepped in. Now the method by which the whole theory of Mars could easily be absolved of error, if the premises were correct, and by which it is demonstrated to be incorrect is this.

After several pages of geometrical demonstration Kepler shows that the result is an error of eight minutes, and concludes:122 Since the divine benevolence has vouchsafed us Tycho Brahe, a most diligent observer, from whose observations the 8´ error in this Ptolemaic computation is shown, it is fitting that we with thankful mind both acknowledge and honour this benefit of God. For it is in this that we shall carry on, to find at length the true form of the celestial motions,

120 Or, in Owen Gingerich’s more colorful translation in his Foreword to Donahue, xii: “Who would believe it! The hypothesis . . . goes up in smoke.” 121 In a marginal comment, Kepler himself explains his point: “In Saturn and Jupiter he bisected it simply; that is, the Copernican form attributes the quadrant to the semidiameter of the epicycle. In Mars, however, since he had attributed to the epicycle the quadrant of the Ptolemaic eccentricity, he argued that in our time the whole Ptolemaic eccentricity must be diminished, but left to the epicycle its original quantity. And so he moved the centre of the eccentric (to speak Ptolemaically) 40 units closer to the centre of the annual orb than to the centre of the circle of the equant. Book 5 ch. 16. See also ch. 16 of this book.” 122 Donahue, 286. Caspar ed. 178: “Nobis cum divina benignitas Tychonem Brahe observatorem diligentissimum concesserit, cujus ex observatis error hujus calculi Ptolemaici VIII minutorum in Marte arguitur; aequum est, ut grata mente hoc Dei beneficium et agnoscamus et excolamus. . . . Nam si contemnenda censuissem 8 minuta longitudinis, jam satis correxissem (bisecta scilicet eccentricitate) hypothesin cap. XVI inventam. Nunc quia contemni non potuerunt, sola igitur haec octo minuta viam praeiverunt ad totam Astronomiam reformandam, suntque materia magnae parti huius operis facta.”

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supported as we are by these arguments showing our suppositions to be fallacious. In what follows, I shall myself, to the best of my ability, lead the way for others on this road. For if I had thought I could ignore eight minutes of longitude, in bisecting the eccentricity I would already have made enough of a correction in the hypothesis found in ch. 16. Now, because they could not have been ignored, these eight minutes alone will have led the way to the reformation of all astronomy, and have constituted the material for a great part of the present work.

Nevertheless, Kepler was never able to free himself completely of Aristotelian physical principles.123 Copernicus had thought that Aristotle’s spheres supported, contained, and moved the planets on their epicycles or eccentrics with uniform circular motion. However much he departed from Aristotelian accounts of the elements and gravity, he remained firmly in the Aristotelian tradition of celestial spheres and their uniform, circular motions. * * * I have now brought this study of Copernicus’s relation to the Aristotelian tradition to a conclusion that contains no little irony. Copernicus had concluded that Earth moves and the Sun is the center of the universe by subordinating natural philosophy to astronomy. Kepler certainly did not abandon metaphysical and architectonic principles, but he restored the traditional relation between natural philosophy and astronomy, yet he did so in part by assuming that the laws that govern motions of bodies on Earth must be the same as the laws governing the motions of bodies throughout the universe. In chapter eight, as I shifted the study from the more biographical approach of the first two parts to concentrate on Copernicus’s philosophy, I constructed an account that traces the application of dialectical topics down to Kepler, and showed how Kepler initiated a transformation of the arguments of his era that contributed to the solutions that he achieved. Copernicus, for his part, relied on mostly printed sources of ancient works to support his departures from Aristotelian and scholastic traditions. He made his bold innovation by overturning the traditional relation of the liberal arts in an effort to break the impasse that had blocked the progress of astronomy. Perhaps no one would have been as surprised as Copernicus to see the outcome within a few generations of his death. 123

Cohen, Birth, 142–148 and 210–211; and Martens, Kepler’s Philosophy, 99–111.

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As it turns out, recent investigations by Polish scholars have also shed light on his death (24 May 1543) and burial. As was already well known, he died in Frombork, and was buried in its cathedral. Earlier scholars concluded that he was buried near an epitaph commemorating him. According to custom, however, Copernicus should have been buried near the altar for which he was responsible among his duties as a canon. Based on the statutes of the chapter and other records, Jerzy Sikorski concluded that Copernicus was indeed buried near his altar (dedicated to Saint Vaclav, later dedicated to the Holy Cross).124 Based on Sikorski’s critique of previous scholarship and research on the statutes and documents of burials at the cathedral, scientists from the Baltic Research Center in Frombork undertook investigations of the site around Copernicus’s altar, discovered a corpse whose age is consistent with Copernicus’s at the time of his death,125 and by means of forensic reconstruction have generated an image of Copernicus’s head and face at the time of his death.126 More recently, DNA analysis comparing hair found in one of Copernicus’s books in Uppsala University Library reportedly matches the remains, so it seems that Copernicus’s remains have indeed been found.127 After the study of Copernicus’s philosophical views I turned to subsequent interpretations of Copernicus’s achievement in the epilog to put Copernicus’s effort and its limitations in relief. As supporters and 124

Sikorski, “Grób Mikołaja Kopernika,” 85–177. Gąssowki and Jurkiewicz, “Poszukiwanie,” 1–26; Pacanowski and Musiatewicz, “Zastosowanie metody,” 45–58; and Czajkowski and Morysiński, “Zastosowanie nowoczesnych,” 75–83. The authors of the archeological and forensic research have expressed their results in appropriately cautious terms as highly probable and not certain. The convergence of historical, archaeological, and forensic evidence tends to support their conclusions. Readers may find a summary of the research with photographs of Copernicus’s self-portrait and reconstruction of his head at the following website: http://archeologia.ah.edu.pl/Frombork_eng.html. For a review, see Goddu, “Copernicus in Person.” The comparison was based on what I called a “probable selfportrait.” The surviving portrait in Toruń may be an original but painted by a professional artist. If not a self-portrait or not copied from a self-portrait, then one of the comparisons between the forensic reconstruction and the portrait may be based on a false inference. See Westman, “Proof,” 201, n. 73. See also Metze et al. “Wandel,” for a review of the literature on portraits of Copernicus. 126 Piasecki and Zajdel, “Badania,“ 27–44. 127 The book is Copernicus’s copy of Calendarium Romanum magnum. The most complete accounts known to me are available at the following websites: http://www .tagesspiegel.de/weltspiegel/Kopernikus;art1117,2673205; and http://www.france24. com/en/20081120–dna-finally-gives-exact-localization-copernicus-remains-geneticshistory. I am grateful to Veronika Wündisch for sending me the article “Ein Geniestreich” by Knut Krohn in Berliner Tagesspiegel. 125

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opponents appealed to Aristotle, they extended the tradition. Opponents clung to principles of natural philosophy, such as the simplicity of natural motions. Copernicus and his supporters cited deeper metaphysical and logical principles while relying on dialectical arguments to generate a revision of Aristotle’s natural philosophy. Even with that revision, however, Copernicus inaugurated a revolution in cosmology. In logic, natural philosophy, and astronomy, Copernicus thought that he could adapt details of the Aristotelian and other ancient-medieval traditions to a heliocentric cosmology. He accomplished much of this cosmological revolution in northeastern Poland in Frombork on the lagoon fed by the delta estuary of the Vistula River. Along its banks he spent his entire childhood and received his early education in Toruń. Later and farther upstream in Cracow, where his father was born and raised, he attended the university. While still an undergraduate in 1493, he purchased astronomical and trigonometrical tables, our first concrete evidence of his interest in astronomy. The codex containing those tables remained his almost constant companion for the next fifty years, and through them we gain an entry into the mind that ordered the spheres of Aristotelian cosmology and ancient astronomy uniquely, by imagining the Earth with its Moon in motion around the Sun.

APPENDICES

APPENDIX I A SUMMARY OF PETER OF SPAIN’S DIVISION AND ENUMERATION OF TOPICS Intrinsic From substance From definition, for example, “A mortal rational animal is running; therefore, a man is running.”1 From the thing defined, for example, “A man is running; therefore, a mortal rational animal is running.” From description, for example, “A risible animal is running; therefore, a man is running.” From explanation of a name, for example, “A lover of wisdom is running; therefore, a philosopher is running.” From concomitants of substance From the whole From a universal whole or from a genus, for example, “A stone is not an animal; therefore, a stone is not a man.” From a species or from a subjective part, for example, “A man is running; therefore, an animal is running.” From an integral whole, for example, “A house exists; therefore, a wall exists.” and From an integral part, for example, “A wall does not exist; therefore, a house does not exist.” From a quantitative whole, for example, “Every man is running; therefore, Socrates is running.” and From a quantitative part, for example, “Socrates is running, Plato is running, etc.; therefore, every man is running.” From a modal whole, [no example provided; formed in the same way as genus and species]. From a locational whole, for example, “God is everywhere; therefore, God is here.”

1 After each example, Peter states the maxim. For example, in the case of from definition, the maxim is “Whatever is predicated of the definition is also predicated of the thing defined.” In the case of from authority, the maxim is “Any expert should be believed in his own field of knowledge.” In the case of from division, the maxim is “If something is exhaustively divided by two things, when one is posited, the other is removed; or, when one is removed, the other is posited.”

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appendices and From a locational part, for example, “Caesar is not here; therefore, Caesar is not everywhere.” From a temporal whole, [no example provided; formed in the same way as locational whole]. From a cause From an efficient cause, for example, “The house is good; therefore, the builder is good.” and From an effect [converse of from an efficient cause; no example provided]. From a material cause, for example, “Iron exists; therefore, there can be iron weapons.” From the effect of a material cause, for example, “Iron weapons exists; therefore, iron exists.” From a formal cause, for example, “Whiteness exists; therefore, a white thing exists.” From the effect of a formal cause [converse, no example provided]. From a final cause, for example, “Happiness is good; therefore, virtue is good.” From the effect of a final cause [converse, no example provided]. From generation, for example, “The generation of the house is good; therefore, the house is good.” and From the thing generated [converse, no example provided]. From destruction, for example, “The destruction of the house is bad; therefore, the house is good.” and From the thing destroyed [converse, no example provided]. From uses, for example, “The riding is good; therefore, the horse is good.” From associated accidents, for example, “He is repentant, therefore, he has done something wrong.”

Extrinsic From opposites From relative opposites, for example, “A father is; therefore, a child is.” From contraries, for example, “The animal is healthy; therefore, it is not sick.” From privative opposites, for example, “He has sight; therefore, he is not blind.” From contradictory opposites, for example, “That Socrates is seated is true; therefore, that Socrates is not seated is false.” From a greater, for example, “The king cannot capture the fortress; therefore, neither can a knight.”

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and From a lesser, for example, “A knight can capture the fortress; therefore, the king can also.” From a similar, for example, “As capable of laughing inheres in a man, so capable of neighing inheres in a horse, but capable of laughing is a proprium of man; therefore, capable of neighing is a proprium of horse.” From proportion, for example, “As the governor of a ship is related to the ship, so is the governor of a school related to the school; and as the governor of a ship should be chosen by art and not by lot; therefore, the governor of a school should be chosen by art and not by lot.” From transumption, for example, “A wise man is not envious; therefore, a philosopher is not envious.” From authority, for example, “An astronomer says that the heaven is revolvable; therefore, the heaven is revolvable.” Intermediate From conjugates, for example, “Justice is good; therefore, what is just is good.” From cases, for example, “What is just is good; therefore, what is done justly is done well.” From division, for example, “If Socrates is an animal, he is either rational or irrational; but he is not irrational; therefore, he is rational.”

APPENDIX II Text 1 [To Chapter 4.3.1]: Quaestiones cracovienses, ed. Palacz, Q. 34, pp. 65–67: “Circa secundum Physicorum primo quaeritur, utrum definitio naturae sit bene posita, in qua dicitur: ‘Natura est principium et causa movendi et quiescendi eius, in quo est primum per se et non secundum accidens.’ . . . “Istis notatis ponitur ista conclusio: Definitio naturae posita ab Aristotele est sufficiens. Probatur conclusio, quia illud est natura, quo naturalia differunt ab artificialibus; sed naturalia differunt ab artificialibus penes primum et per se principium movendi et quiescendi etc.: quia entia naturalia habent in seipsis non secundum accidens; ergo natura est principium movendi et quiescendi. Maior et minor patent ex sequenti quaestione. . . . “Sed diceres, quod natura caeli non est principium movendi et quiescendi; propter hoc dicit Avicenna in Summa sua, quod ‘et’ debet poni pro ‘vel.’ “Sed dicendum est, ut tactum est: non oportet naturam esse principium movendi et quiescendi semper, sed in his, quibus convenit motus, est principium movendi; sed in his, quibus convenit, quies, quies est principium quiescendi. Vel posset dici secundum Aegidium, quod caelum quodammodo quiescit et quodammodo movetur. Movetur videlicet secundum partes, quia partes caeli mutant situm, sed totum caelum secundum substantiam stat et non mutat situm.” Q. 35, pp. 67–69: “Utrum entia naturalia different ab artificialibus, quia naturalia habent in seipsis principium motus et status, sed artificialia neque unum habent impetum mutationis innatum. . . . “Secundo arguitur contra quaesitum, quia motus caeli est naturalis et caelum est res naturalis, et tamen non habet in seipso principium motus, quia intelligentia movet caelum, quae non inhaeret ipsi caelo. Et confirmatur, quia corruptio est mutatio naturalis et non fit a principio intrinseco. . . . “Secunda conclusio: Aliqua est res naturalis, quae non habet in se principium motus et status. Patet de corpore caelesti, hoc enim non stat. “Tertia conclusio: Omnis res naturalis in se habet principium motus vel quietis. Unde omnia, quae sub concavo orbis lunae moventur, aliquando quiescunt et aliquando moventur. Sed corpora caelestia, quae moventur, circulariter moventur sine quiete. “Sed diceres: “Quid tunc dicitur ad Aristotelem, qui dicit: ‘sub copulatione motus et status’? “Dicitur, quod Aristoteles, ponit, quod entia naturalia, quae quiescunt, habent in se principium quietis, et entia naturalia, quae moventur, habent in se principium motus. “Pro sequenti conclusione sciendum, quod duplex est principium motus: quoddam est activum, ut anima, quae est principium activum motus animalis, passivum vero est materia.

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“Est ergo quarta conclusio: Omnis res naturalis habent in se principium activum sui motus. Patet de corpore caelesti, ut argutum est ante oppositum, hoc enim moventur ab intelligentia ei assistente. “Ultima conclusio: In omnibus rebus naturalibus eo modo est principium motus, quo modo convenit eis principium motus; quibus enim convenit movere, eis inest principium activum, quibus vero convenit moveri, eis inest principium passivum motus, scilicet materia. Ex quo patet, quod motus caeli est naturalis tantum a principio passivo, licet a principio activo sit intellectualis. “Per hoc ad rationes: . . . “Ad secundam dicitur, quod, licet caelum in se non habeat principium activum, habet tamen in se principium passivum. Unde intelligentia non inhaeret caelo, sed assistit ei sicut nauta navi. Similiter dicitur de corruptione, quae habet principium passivum intrinsecum, et hoc est pro ultima conclusione.” Text 2 [To Chapter 4.3.1]: Quaestiones cracovienses, Q. 74 pp. 127–128: “Circa initium quarti Physicorum quaeritur, utrum ad physicum pertineat considerare de loco. “Arguitur, quod non, quia quantitas consideratur a mathematico et non a physico; sed locus est quantitas; ergo etc. Minor patet, quia locus est superficies, ut patebit; etiam patet in Praedicamentis, quod locus est species quantitatis. . . . “In oppositum est Aristoteles in textu. . . . “Per hoc ad rationes: Ad primam dicitur, quod quantitas etiam consideratur a physico sub esse naturali. In loco autem est virtus naturalis immobilis salvativa sui locati. Unde, quia posteriora non abstrahunt a prioribus, licet econverso, physicus, qui est posterior artifex, etiam considerat entia mathematicalia, minus tamen abstracte. . . .” Q. 75, pp. 128–129: “Utrum locus sit aliquid distinctum a locato. . . . “Arguitur primo, . . . “Ultimo: Si esset, vel esset mobilis, vel immobilis. Non mobilis, ut patebit, nec immobilis, quia quando locatum augeretur, oportet locum augeri, quia locus est aequalis locato. “In oppositum est Aristoteles. “Pro responsione sciendum, quod duplex est motus: quidam motus est ad ubi et alius est motus ad formam. In motu ad formam per transmutationem cognoscitur materia, quae est commune receptaculum utriusque termini motus. “Est ergo prima conclusio: Locus est. Probatur sic: quia aliquid movetur localiter et, ubi unum corpus fugit, aliud intrat; quare locus est commune receptaculum corporum locatorum. Ex quo patet, quod sicut transmutatio naturalis secundum formam facit scire materiam esse, ita transmutatio localis facit scire locum esse. Secundo probatur conclusio: quia partes et differentiae loci sunt, scilicet sursum et deorsum etc., igitur locus est. “Secunda conclusio: Locus est quid distinctum a locato. Patet, quia manet in mutatione locali tamquam commune receptaculum sub utroque termino. “Tertia conclusio: Locus habet quandam naturalem virtutem, quae salvat locatum ex naturali appetitu corporum simplicium, quae naturaliter omnia

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tendunt in locum et appetunt locum sicut eorum esse, quod non esset etc. Probatur conclusio ex naturali appetitu corporum simplicium, quae naturaliter omnia tendunt in locum et appetunt locum sicut eorum esse; quod non esset, nisi esset quaedam mirabilis virtus loci. . . . “Ad ultimam, cum dicitur: ‘vel est mobilis, vel immobilis,’ dicendum quod in loco duo sunt, scilicet materiale et formale. Materiale est ultima superficies, quae se habet ut vas et continens. Sed formale loci est distantia vel ordo ad totum caelum; talis autem distantia sive ordo non est mobilis, sed materiale loci bene movetur, ut patebit postea.” Text 3 [To Chapter 4.3.1]: Johannes de Glogovia, Quaestiones in octo libros Physicorum Aristotelis, BJ, MS 2017, [Q. 43]: ff. 149r-v: “. . . motus ipsius gravis deorsum in fine est intensior non tamen trahitur a loco effective, sed hoc fit ideo, quia quando grave descendit tunc fortatur grave et fit motus fortificatus non tamen est intelligendum, quod aliquid addatur ad gravitatem corporis descendentis et per remotionem a contrario confortatur gravitas quo ad actum secundum ex quo enim grave circa proprium locum existens ut coniungitur sue perfectioni, scilicet loco deorsum et elongatur a contrario, scilicet a loco sursum imperfectius habet suum actum gravitatis quam prius.” [Q. 47]: f. 161v: “Dubitatur primo unde proveniat successio in motu celesti. Dicendum quod tenendo, quod intelligencia moveat celum naturaliter, tunc successio provenit ex resistentia mobilis, quia ut corpus celeste est in uno situ quodam modo resistit moventi, ut est in alio situ. Sed tenendo, quod intelligencia celum movet intellectualiter et libere, ut dicit Albertus. Dicendum quod successio provenit ex parte finis, intelligencia enim movet celum tanta velocitate quanta exigit finis motus celestis, qui est generacio istorum inferiorum, que requirit successionem.” [Q. 81], f. 228r concludes thus: “Dubitatur tamen Aristoteles in septimo sufficienter ostendit quod omne quod movetur ab alio movetur. Dicendum quod aliter probat Aristoteles ibi et aliter hic quia ibi probat in generali hic autem in speciali applicando diversitatem speciei motus et ad diversa mobilia tam ad mobilia que moventur violenter quam esse ad ea que movetur per se ut dictum est in nostro libro secundo et sic non est superfluitas.” Text 4 [To Chapter 4.3.2]: Quaestiones cracovienses, Q. 16, pp. 31–32: “Utrum infinitum secundum quod infinitum sit ignotum. “Arguitur, quod non, quia hoc implicat contradictiionem, quia ly “secundum quod” explicat rationem infiniti, omne autem, quod habet rationem, est notum, implicat igitur infinitum secundum quod infinitum esse ignotum. “Secundo sic: quia Aristoteles dat hic scientiam de infinito, quod est notum. “Tertio: Infinitum, si esset, esset notum primae causae. “Quarto: Primus motor notificatur octavo huius et tamen ipse est infinitum, ut probatur ibidem. “In oppositum est Aristoteles.

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“Pro responsione sciendum, quod genus entis dividitur penes actum et penes potentiam, infinitum ergo aliquando attribuitur actui, aliquando potentiae. Et sic intelligitur quoddam infinitum in actu, quoddam vero in potentia. Unde infinitum in actu habet se ex parte actus, sed infinitum in potentia tenet se ex parte materiae, quia materia quodammodo infinita est ante formam susceptam, sed forma finit materiam sive claudit potentiam materiae et materia claudit communicabilitatem formae. Ex quo sequitur, quod non potest esse aliquod corpus naturale infinitum, quia in eo sunt materia et forma terminata, quia materia finit formam et forma materiam. “Secundo patet: ex quo ratio infiniti primo reperitur in quantitate, aliquando potest attribui magnitudini, aliquando multitudini. “Tertio sciendum, quod duplex est ratio: quaedam quid nominis alia quid rei. “Istis praemisis est prima conclusio: Quid [nominis]* infiniti est nobis notum. Probatur: quia alias non uteremur nomine infiniti. Et hoc arguit prima ratio ante oppositum. “Secunda conclusio: Quid rei ipsius infiniti, etiam si infinitum esset, esset nobis ignotum. Patet, quia noster intellectus inter terminos suae apprehensionis est finitus, ergo non est apprehendere infinitum. “Tertia conclusio: Infinitum, si esset, bene esset nobis notum in ente, sive sub ratione entis. Patet, quia cognoscimus ens et per consequens omnia ea, quae comprehenduntur sub ente. “Quarta conclusio: Infinitum, si esset, esset ignotum, quantum esset. Patet ex secunda conclusione, quia quid rei infiniti est ignotum, sed quid rei infiniti sumitur in genere quanti, quia ratio infiniti quantitati congruit. “Sed diceres: Utrum illud, quod est dictum, intelligitur de infinito in actu tantum, aut etiam in infinito in potentia? “Pro illo sciendum, quod infinitum in potentia bene est finitum in actu, ut bipedale est in actu et tamen est infinitum in potentia. Secundo sciendum, quod nihil cognoscitur, nisi ut in actu est, quia cognoscibile debet movere potentiam cognoscitivam, nihil autem movet, nisi existat in actu. Dicitur igitur, quod intelligitur de utroque infinito ea parte, qua finitum est. Nam infinitum in potentia bene cognoscitur ea parte, qua est finitum in actu, non autem ea parte, qua infinitum est, quia est in potentia. Ergo de se est ignotum, etiam quia intellectus noster est finitae capacitatis et non capit nisi actu finitum. “Sed diceres: Utrum prima causa cognosceret infinitum, si esset? “Respondetur, quod sic. Quia intellectus eius est infinitus, ergo intellectus eius non finiret ipsum infinitum cognoscendo, sicut intellectus noster, immo magis infinitaret. “Ultimo dubitatur, utrum intellectus noster omnia cognoscat. “Respondetur, quod omnia cognoscit quodammodo, sed non omnia apprehendit. Primum patet, quia obiectum intellectus est ens, ergo cognoscit omne cadens sub ente, quia potentia cognoscit omne illud, quod cadit sub eius obiecto, et hoc mediate vel immediate, quia separata a materia cognoscuntur per suos effectus sensibiles, cum nostra cognitio semper incipiat a sensu. Sed secundum patet, quia intellectus noster finitus est.

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“Ad rationes: Ad primam dicitur, quod habemus quid nominis infiniti, sed non quid rei. Et sic habemus rationem infiniti dicentem quid nominis, et tamen ipsum est ignotum quantum est. “Ad secundam dicitur, quod Aristoteles dat scientiam infiniti per abnegationem, sed de ipso nihil affirmat. “Ad tertiam dicitur concedendo, hoc est contra conclusionem.” *Palacz ed. reads “Quid nobis infiniti . . .,” but BJ, MS 2007, f. 11r reads “Conclusio prima: Quid nominis infiniti est nobis notum.” Text 5 [To Chapter 4.3.2 and 4.3.6]: Quaestiones cracovienses, Q. 81, pp. 138–139: “Utrum ultima sphaera sit in loco. “Arguitur, quod non, quia locus est ultimum corporis continentis; sed ultima sphaera continetur; igitur etc. “Secundo: Caelum omnia continet et est circulare, et ergo a nullo continetur, et per consequens sequitur, quod non est in loco. “In oppositum arguitur: quia caelum movetur localiter, ergo est in loco. “Pro responsione sciendum, quod duo hic faciunt difficultatem. Primum est definitio loci, ex qua sequitur, cum extra caelum nihil sit, continens ipsum in loco non esse. Secundum est motus localis caeli, quia de necessitate corpus, quod movetur localiter, est in loco. “Secundo sciendum, quod tripliciter aliquid est in loco: per se, secundum partes et per accidens. “Est ergo prima conclusio: Caelum non est per se in loco, quia non habet aliquod extrinsecum continens ipsum, eo quod extra caelum non est corpus. “Secunda conclusio: Ultima sphaera est in loco per alterum. Probatur conclusio, quia locus est de necessitate corporis, quod movetur localiter; sed cum ultima sphaera non sit per se in loco, ut prima dicit conclusio, oportet ut per alterum; ex quo necesse est ipsam esse in loco. “Tertia conclusio: Ultima sphaera est in loco per partes eius. Patet per Aristotelem in textu dicentem, quod si ultimum caelum esset aqua, partes eius essent in loco, quia ab invicem continerentur. “Quarta conclusio: Partes ultimae sphaerae non sunt in loco actu, sed solum in potentia. Patet, quia locus actualis debet esse separatus a locato; sed pars continens in ultima sphaera non est actu separata a parte contenta, sed tantum potentia. “Sed diceres: Una pars caeli semper manet sub eodem, ergo non mutat locum. “Dicitur concedendo, quod semper manet et ideo non mutat locum secundum actum, sed secundum potentiam, quia si superadderetur caelum et superior pars quiesceret, inferior pars mutaret locum. “Ex conclusionibus sequitur correlarie, quod caelum per accidens est in loco, quia per partes, in quibus est; partes autem per se sunt in loco in potentia. Secundo ponitur, quod motus caeli est actualissimus, quia tantum variat locum in potentia, et hoc est rationale, quia in primo caelo est minima diversitas, unde plurimum habet de entitate et unitate, et minimum de deformitate.

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“Sed diceres: Totum non est aliud quam suae partes; ideo, si totum non est in loco, nec partes. “Dicitur, quod totum non distinguitur a partibus simul collectis, tamen particularia loca partium in potentia differunt ab actuali loco totius. “Ex istis patet, quod non est dicendum cum Alexandro caelum non esse in loco simpliciter, nec cum Avicenna, qui dicit motum caeli non esse secundum locum, sed secundum situm, nec cum Ioanne grammatico, quod per se sit in loco, nec cum Averroe, Alberto, Aegidio, quod per accidens non sit in loco, sed per centrum; sed dicendum est cum Themistio, Thoma, Aristotele, qui ad hoc expresse sunt, quod caelum sit in loco per accidens et per partes, quae non actu in loco sunt, sed potentia. Dicit enim textus: ‘Alia secundum accidens in loco sunt, ut anima et caelum; per partes enim in loco quodammodo sunt omnes, in eo enim, quod circulariter sunt, continent alia aliam.’ “Ad rationes dicitur, quod sunt pro prima conclusione.” Text 6 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 25, pp. 48–50: “Utrum omnium corporalium et incorporalium sit eadem materia secundum speciem. “Arguitur, quod sic, quia distinctio est per formam, ergo materiae ante formas acceptae non sunt distinctae specie et per consequens erunt eadem specie. . . . “Secundo: si materiae essent specie distinctae, tunc haberent quo convenirent, videlicet genere, et haberent quo distinguerentur. Omne autem habens quo conveniat et quo distinguatur est compositum et non simplex, quod est contra dicta. “In oppositum tamen arguitur, quia, quorum materia est eadem, illa agunt et patiuntur ad invicem; sed corpora caelestia et inferiora non agunt et patiuntur ad invicem; ergo non habent unam materiam. “Pro responsione sciendum, quod Plato dixit esse caelum de natura elementorum et corruptibile ex se, sed quod non corrumpitur, hoc est voluntate opificis. Unde dicitur in Timaeo: ‘O dii deorum quorum ego opifex sum, natura quidem vos mutabiles estis, mea autem voluntate sic permanentis.’ Et loquitur hic in persona Dei ad corpora caelestia. Et sic Plato dicit unam omnium corporalium materiam. Sed Aristoteles posuit, quod corpora contraria habent contrarios motus. Secundo, quod motui circulari nullus est contrarius. Dixit ergo Aristoteles: ‘Cum caelum movetur circulariter, non habet contrarium et per consequens est incorruptibile’; et per consequens secundum Aristotelem caelum est alterius naturae ab elementis. “Est ergo prima conclusio: Materia caelestium et materia corporum elementata non differunt specie. Probatur conclusio, supponendo materiam extra in potentia ad formam. Secundo supponitur, quod omne habens privationem materiae admixtam est corruptibile. Arguitur igitur sic: Si sic esset eadem materia, esset in potentia ad omnem formam tam caelestium quam inferiorum; ergo materia caeli stans sub forma caeli est in potentia ad formam inferiorum et non habet eam; quare ibi est primatio et per consequens caelum est corruptibile per illam secundam suppositionem, quod est falsum. Ergo sequitur quod materia caelestium et inferiorum differunt specie.

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“Sed diceres: quia forma caeli continet formam inferiorum, ideo materia caeli non appetit formam inferiorum, sed forma caeli perfecte faciat materiam caeli. “Respondetur, quod potentia respicit actum et habet se per differentiam ad actum perfectum et imperfectum; ideo stans sub actu perfecto adhuc appetit actu imperfectum. Licet enim imperfectum sit in perfecto, hoc tamen non est secundum actum proprium imperfecti. Et ergo adhuc materia habens formam perfectam appetit formam imperfectam. Et si replicatio valeret, tunc materia stans sub forma hominis nihil amplius appeteret nec relinqueret privationem. Ex quo sequitur, quod in materia caeli non est potentia ad aliquid esse, loquendo de potentia distante ab actu, est tamen ibi potentia ad ubi. “Secunda conclusio: Eadem est materia superiorum secundum analogiam. Patet, quia convenit in ratione potentiae. Unde sciendum, quod Averroes dicit naturam caeli esse actum et quod caelum non esset compositum ex materia et forma. Utrum autem ista forma sit anima aut non, videbitur in De caelo et mundo. “Pro ultima conclusione sciendum: Omne, quod est in praedicamento, ut genus et species, componitur ex quo est et quod est. Unde quod est habet se ut materia sive potentia ad ipsum quo est. “Est ergo tertia conclusio: Omnium corporalium et incorporalium habentium materiam est eadem materia in genere. Patet conclusio ex notabili, quia conveniunt in genere. “Sed diceres: ‘Utrum omnium generabilium et corruptibilium sit eadem materia, in numero, loquendo de materia prima?’ “Respondetur, quod aliquid est unum duobus modis: uno modo actuale, alio modo potentionale. Unde unum potentionale dicitur unum per carentiam actus distinguentis. Dicitur ergo, quod omnium generabilium et corruptibilium est eadem materia numero. Secundo modo per indifferentiam, quia una pars illius massae non habet quo distinguatur ab altera; non tamen una est sicut punctus, ut prius dictum est. “Per hoc ad rationes: Ad primam, cum arguitur: ‘distinctio est per formam’, conceditur. Et quando arguitur: ‘ergo materiae ante formas acceptae non distinguuntur specie’, negatur consequentia, quia materia est in potentia ad formam. Ideo ergo, quod potentiae sunt ad diversas formas distinctae, sunt secundum speciem. “Ad secundam dicitur, quod materia non est species, sed principium speciei, et eius convenientia et differentia sumitur pro quanto est ad formam.” Text 7 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 31, pp. 60–62: “Utrum materia appetit formam. “Arguitur, quod non, quia appetitus est inclinatio consequens formam, qua res intendit in illud, quod est sibi bonum, sicut est declinatio terrae ad centrum mundi. Sed materia non habet formam, ergo non convenit ei appetitus. . . . “In oppositum est Aristoteles in littera dicens: ‘Aliud tamen aptum natum est appetere et desiderare formam secundum sui ipsius naturam.’

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“Pro responsione supponitur, . . . “Secundo supponitur, quod appetens necessario cognoscit id, quod appetit, vel dirigens ipsum, quia omne appetens aut ordinat se in illud, quod appetit, vel tendit in illud, quod appetit, ex ordinatione et directione alicuius cognoscentis, ut sagitta appetit signum non ex ordinatione eius in signum, sed et ordinatione sagittantis ducentis eam in signum. Ex quo sequitur, quid appetitus naturalis non est nisi ordinatio et inclinatio rei secundum propriam eius naturam in suum finem. “Est ergo prima conclusio: Materia appetit formam appetitu naturali. Patet ex correlario, quia appetitus naturalis non est nisi ordinatio alicuius in finem eius; sed forma est finis materiae, eo quod materia est in potentia ad formam sive actum; ergo materia appetit formam. . . . “Sed diceres: Utrum materia appetit formam accidentis? “Respondetur, quod secundario appetit eam, quia primo appetit formam substantialem et postea formam accidentalem. . . . “Ad rationes: Ad primam, cum dicitur: ‘appetitus est inclinatio consequens formam,’ dicitur, quod hoc est verum de appetitu consequente formam, quia sicut materia non intelligitur nisi per formam, ita materiae appetitus non intelligitur nisi per appetitum formae, et sic melius dicitur, quod appetitus naturalis est inclinatio rei secundum propriam naturam in suum finem.” Text 8 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 132, pp. 235–236: “Utrum ad hoc, quod motus sit unus, continuus et perpetuus, oporteat esse movens aliquod immobile, unum et perpetuum. . . . Ex conclusione sequitur, quod motor primus est incorporalis. Probatur conclusio, quia est immobilis; modo omne corpus est mobile, ut patet primo Caeli, primus autem motus est immobilis; ergo incorporalis . . . “Secunda conclusio: Primus motor immobilis est perpetuus . . . “Probatur ergo conclusio aliter: quia motus est perpetuus et unus, ut patet ex principio huius, ergo oportet movens esse perpetuum et unum. . . . “Ponitur tamen tertia conclusio: Primus motor immobilis est tantum unus. Probatur conclusio, quia, ut dicitur in littera, frustra fit per plura, quod aeque bene fit per pauciora; sed ponendo primum motorem unum, omnia salvari possunt; ergo non sunt ponendi plures, cum nihil frustra sit in natura. Verum tamen est, quod istud argumentum magis videtur esse rhetoricum quam argumentum iam tactum, quod sumitur ab unitate ipsius motus. . . .” Q. 133, pp. 237–239: “Utrum primus motor omnino sit immobilis, ita quod non movetur nec per se nec per accidens. . . . “Pro responsione dicendum, . . . “Istis praemissis est prima conclusio: Primus motor est immobilis omnino, ita quod nec movetur per se nec per accidens. Probatur: Nam quod movetur ex se, patet ex praecedenti quaestione. Quod autem non moveatur per accidens, patet, quia motus primus est incessibilis et immortalis motus, ergo necesse est primum motorem immobilem esse, ita quod non movetur per accidens. Tenet consequentia: si moveatur per accidens, ipse non posset esse causa continui uniformis et incessibilis motus, ut patet ex dictis. Quia autem motus sit

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perpetuus, etiam patet ex dictis. Et quod etiam aliquis motus in specie sit perpetuus, patebit in sequentibus. Secundo probatur conclusio a priori: quia primus motor, tenendo, quod ipse sit Deus benedictus, est tantum actum, ergo nullo modo est mobilis, cum omne mobile est ens in potentia. Ex conclusione sequitur, quod primus est perpetuus et incessibilis. Patet, quia primus motor semper est immobilis, ergo semper uniformiter se habet ad motum. “Sed diceret aliquis iuxta primam rationem ante oppositum: Quare, cum intelligentia sit in primo corpore, ipsa non moveatur motu corporis per accidens? Secundum dubium: quare intelligentiae inferiorum orbium dicuntur moveri per accidens? “Pro responsione notandum, quod duplices sunt formae substantiales. Quaedam sunt in corporibus et non informant corpus, et istae dicuntur formae non ab informando, sed a formis manendo, et istae non subduntur legibus corporis nec esse earum et per consequens nec proprietates earum dependent a corpore. Aliae sunt formae, quae sunt in corporibus et informant corpora, immo esse capiunt a corpore, et istae subduntur legibus corporis tam secundum esse quam secundum proprietates. Ergo intelligentiae motrices orbium sunt de numero primarum formarum, cum non subduntur legibus corporis. “Sed contra istud est secundum dubium. Pro quo sciendum, quod dupliciter aliquid dicitur moveri per accidens, ut vult Philosophus in textu: uno modo a seipso, ut anima movendo corpus movetur ad motum illius etiam localiter et successive; alio modo ab altero. Quemadmodum aliquid est in loco per accidens dupliciter: uno modo per alterum, ut caelum, alio modo secundum se, ut partes per accidens sunt in loco totius. Dicitur igitur, quod intelligentiae motrices orbium moventur per accidens non a se, sed ab altero. Nam sicut centrum est aliquid caeli et ob hoc secundum Averroem caelum est in loco, ita orbis quodammodo est aliquid intelligentiae. Ideo motu orbis intelligentia dicitur moveri per accidens, non omnis intelligentia, sed illa, cuius orbis movetur per accidens, qualis est intelligentia inferioris orbis. . . .” Text 9 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 136, pp. 241–243: “Utrum in omni motu necesse sit mobile in puncto reflexionis quiescere. “Arguitur, quod non; . . . “In oppositum est Aristoteles in illo capitulo, in quo probat, quod motus rectus non potest esse perpetuus. . . . “Est ergo prima conclusio responsiva, quod per se omne mobile puncto reflexionis quiescit. Probatur: nam motus accessus et motus recessus, qui sunt inter contrarios terminos, ipsi sunt contrarii, ex quinto huius, ubi patuit, quod motus contrarii non possunt esse continui; ergo oportet, quod illi motus dividantur per quietem mediam. Verbi gratia: motus factus ab a in b et ab b in a contrariantur; quare non continuatur. Eodem modo dicitur de reflexione facta in circulo. “Sed contra hoc obiceret aliquis, quia motui circulari non est motus contrarius, primo Caeli.

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“Respondetur, quod motus dupliciter dicuntur contrarii: uno modo a terminis suis, et sic in circulo non est contrarietas motuum; alio modo, quia unus impedit alium, et sic in circulo est contrarietas motuum. “Sed diceres, quod in circulo motus ab oriente non impedit eum, qui est ab occidente, ut patet in sphaeris planetarum, quae duplici motu moventur. Dicendum, quod illi motus non sunt super eosdem polos facti, sed super diversos; omnes enim planetae moventur ab oriente in occidens super polos mundi et omnes moventur ab occidente in oriens super polos zodiaci. “Pro responsione quaestionis sciendum, quod, si motus contrarii continuarentur, tunc idem moveretur contrariis motibus; dum enim esset in termino a quo, ascenderet; ideo, si non sit media quies, etiam descenderet. Secunda ratio Philosophi est ista et supponit, quod esse in instanti est in potentia, ut patuit alias in quinto. Ex isto patet ratio: cum accedere et recedere dicant actus distinctos, qui actus non possunt esse in eodem instanti et in eodem mobili, sequitur, quod impossibile est, quod in puncto reflexionis non est quies media, quia ex quo illi actus conveniunt mobilibus in diversis instantibus et inter quaelibet instantia est tempus medium, ergo in illo tempore medio necessario fit quies; format autem Aristoteles quattuor rationes logicales, quae patent in littera. . . .” Q. 137, pp. 244–245: “Utrum motus circularis possit esse continuus et perpetuus . . . “Pro responsione ponitur ista conclusio: Motus circularis potest esse continuus et perpetuus per reiterationem. Probatur, quia illud est possibile, ad quod non sequitur impossibile. . . . “Secunda conclusio Aristotelis est, quod motus circularis est continuus et perpetuus. Patet, quia motus localis est perpetuus et non rectus, ut iam probatum est in praecedenti quaestione, ergo circularis. Tenet consequentia ex sufficienti divisione. Verum tamen est, quod ista conclusio non est catholica, immo falsa. Dicimus enim et firmiter credimus, quod motus caeli incepit determinato principio temporis; sed hoc non habemus per philosophiam, sed per prophetiam. Prima vero conclusio simpliciter conceditur . . .” Text 10 [To Chapter 4.3.5]: Quaestiones cracovienses, Q. 120, pp. 210–212: “Circa initium septimi Physicorum quaeritur, utrum omne, quod movetur, moveatur ab alio, id est utrum omne mobile, quod movetur, habeat motorem ab eo distinctum. “Et arguitur primo, quod non, quia animalia moventur a seipsis, quia in hoc different a non animalibus; ergo non omne, quod movetur, habet motorem ab ipso distinctum. “Secundo: grave existens sursum movetur deorsum a removente prohibens; sed grave descendens est removens prohibens; ergo movetur a seipso. “Tertio: aliqua sunt indivisibilia, qualis est anima humana, et moventur a seipsis, sicut anima intelligendo movetur a seipsa; quare non omne motum movetur ab alio. “In oppositum est Aristoteles. “Pro responsione supponitur, quod eorum, quae moventur, quaedam moventur a principio intrinseco, ut animal, quaedam vero ab extrinseco, ut proiectum

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a proiciente. Et de illis non est difficultas dubitationis, sed de primis: quia non cognoscimus principium activum intrinsecum distingui a passivo, credimus mota ab principio intrinseco non habere motorem ab ipsis distinctum. “Secundo sciendum, quod aliquod movetur a seipso vel ab alio dupliciter, scilicet per se primo et per accidens. Et accipitur hic ‘per accidens,’ ut extenditur ad moveri per partem, quia pars non est eadem toti; alias enim una pars esset alia, quia quaecumque uni in eodem sunt eadem, inter se sunt eadem; ergo pars est altera a toto. Unde moveri ab aliquo per accidens est moveri ex esse in eo, quod est per accidens. Unde sciendum, quod illud contingit alicui per se, quod non contingit ei per aliud, sed aliis per seipsum. Ex quo sequitur correlarie: Illud, quod movetur a se ipso per se primo, nullo modo quiesceret quiescente altero. Patet, quia motus eius non dependet ab altero, sed a seipso. “Est ergo prima conclusio: Aliquid movetur a seipso per accidens. Probatur: ut anima movet corpus et, quia est in corpore, movetur per accidens motu corporis, et nauta movet navem et movetur per accidens ex esse in navi mota. “Secunda conclusio: Nihil movetur a seipso et primo. Probatur conclusio demonstratione Aristotelis: nihil, quod quiesceret, si aliud ab eo quiesceret, movetur a seipso per se primo; sed omne, quod movetur, quiesceret, si aliud ab eo quiesceret; igitur nullum mobile, quod movetur, movetur a seipso et primo. Tenet consequentia in ‘Celarent.’ Maior patet ex uno correlario sive ex definitione eius, quod est primo a seipso moveri. Minor probatur, quia omne mobile, quod movetur, quiesceret quiescente una parte. Cum igitur omne sit divisibile, ut patet ex dictis, sequitur conclusio. . . . “Ex omnibus igitur istis habetur, quod omne, quod movetur a seipso, dividitur in partem per se moventem et per se motam, ut animal dividitur in animam et corpus. “Per hoc ad rationes: Ad primam dicendam quod hoc est per partem et non primo; primo enim movetur corpus ab anima et per illud totum animal. “Ad secundam dicitur, quod hoc etiam est per accidens; per se enim dividit aerem et movet, et tunc ipsum grave movetur motu aeris. “Ad tertiam dicitur, quod quaestio intelligitur de motu physico; modo talis non est motus physicus.” Q. 129, pp. 229–231: “Utrum gravia et levia per se moveantur a generante et per accidens a removente prohibens. “Et arguitur, quod non, . . . “Secundo: nam dicitur secundo huius, quod natura est principium movendi et quiescendi, ergo gravia et levia moventur a suis naturis et per consequens non a generante. “Tertio arguitur contra secundam particulam. Nam ponatur lapis supra traben et tandem corrumpat trabem: tunc grave per movetur a seipso; cum igitur ipsum est removens prohibens, ideo per se movetur a removente prohibens. “In oppositum est Aristoteles. “Pro responsione sciendum, quod tria sunt in motu, scilicet movens, mobile et potentia mobilis, qua suscipit motum. Unde movens est duplex, scilicet naturale et violentum. Unde movens est duplex, scilicet naturale et violentum. Naturale est, quod confert formam naturalem mobili, ut actu calidum movet

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naturaliter illud, quod est potentia calidum. Sed per oppositum definitur movens violentum. Similiter distinguetur de mobili, quia quoddam movetur naturaliter, aliud violente. Potentia etiam est duplex: una est essentialis, alia est accidentalis . . . Similiter aqua est in potentia essentiali ad fieri sursum, leve detentum a motu sursum est in potentia accidentali. “Secundo sciendum, ut patet ex praecedenti quaestione: ‘per se’ dicit circumstantiam causae; potest ergo dicere vel circumstantiam materiae, vel formae, vel finis, vel efficientis. “Est ergo prima conclusio: Gravia et levia moventur per se ad loca sua naturalia, ut ‘per se’ dicit circumstantiam materiae. Patet, quia habent in seipsis principium patiendi et sustinendi motum. “Secunda conclusio: Gravia et levia moventur per se ad sua loca naturalia, ut ‘per se’ dicit circumstantiam formae. Patet ex secunda ratione ante oppositum, quia forma gravis et materia eius principiant formaliter motum, quo movetur in loco eius. “Tertia conclusio: Illud, quod est grave in potentia essentiali, vel illud, quod est leve in potentia essentiali, per se movetur a generante, ut ‘per se’ dicit circumstantiam causae efficientis. Probatur conclusio, quia ab illo movetur efficienter grave, a quo suscipit formam, qua movetur; sed grave in potentia essentiali suscipit formam suam a generante; ergo per se movetur a generante. Secundo probatur conclusio, quia gravia et levia moventur ab aliquo et non moventur a seipsis, ut patet ex praecedenti quaestione; ergo a generante. Tenet consequentia, quia nihil vicinius est gravi quam generans ipsum. Unde ad istud est exemplum: aliquis enim diceret parietem esse album ab albedine formaliter; sed est albus a pictore efficienter; sic etiam albescit non ab albedine, sed a pictore efficienter; sic grave non movetur a sua gravitate efficienter, sed a dante gravitatem, sicut est generans. “Quarta conclusio: Grave, quod est in potentia accidentali, movetur a removente prohibens per accidens et a generante per se. Patet conclusio ex notabili primo, quia movens per accidens non confert formam, sed movens per se, et ita generans confert formam, non autem removens prohibens; sed removens prohibens tollit impedimentum. Exemplum est de hoc, ut sol de se elevat vaporem, quem generat; sed si vapor ab aliquo detineatur, removens illud prohibens movet vaporem per accidens. “Ex conclusionibus sequitur correlarie, quod grave, quod est potentia essentiali, movetur successive, secundum quod successive sibi datur forma gravitatis a generante. Unde, si simul daretur sibi forma gravis, simul et subito moveretur. Ex quo sequitur ulterius, quod grave aliquando movetur per accidens a seipso. Patet, quia aliquando ipsummet grave est removens prohibens. “Per hoc ad rationes: Ad primum dicitur concendendo [sic]. Et cum dicitur ‘ergo non movetur a generante,’ negatur consequentia. Et cum dicitur: ‘ab illo, quod nihil est, non movetur,’ dicendum, quod aliquid habet esse dupliciter: primo, quia sua substantia est; secundo, quia virtus sua est. Dicitur ergo, quod ab illo, quod non est secundum suam substantiam, sed tamen est secundum suam virtutem, bene aliquid movetur, ut sagitta posset moveri sagittante interfecto. Et ita est in proposito. Nam manente gravi genito maneret virtus generantis ipsum in eo.

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“Ad secundam dicitur, quod illa procedit secundum intentionem secundae conclusionis. “Ad tertiam dicitur, quod ipsa est pro ultimo correlario.” Text 11 [To Chapter 4.3.5]: Johannes de Glogovia, [Q. 88], ff. 239r–240v. The text has been published by Markowski, Burydanizm, 177–181, and I have corrected it against the manuscript. “Utrum proiecta cessante proiciente moveatur a medio, per quod ferunter, ab ipso proiciente? “Pro intellectione questionis mote notandum primo, quod postquam Aristoteles ostendit primum motorem esse infinite virtutis, de quo tamen adhuc latius dicetur in questione ultima. Ideo consequenter ostendit unitatem primi motoris. Et circa hoc Aristoteles presupponit unum, scilicet quod unitas motus dependet ex unitate moventis et occasione illius querit, quo modo proiecta moveantur. Et primo ostendit, quod non movent se ipsa, quia non sunt animata, modo animal movetur a se non animatum, ut probatum est ante. Nec etiam videatur moveri a proiciente, quia movens effective debet esse simul cum moto, sicut probatum est septimo huius. Constat autem, quod proiectum non est simul cum proiciente, immo constat proiciens esse corruptum et proiectum moveri. Non videtur ergo, a quo /f. 239v/ moveantur talia proiecta. “Notandum secundo, Aristoteles in textu ponit solutionem questionis huius. Et primo excludit opinionem Platonis, que fuit, quod proiciens proiciendo movet aerem proximum et ille aer ulterius moveret proiectum usque ad finem absque motu aeris consequenter se habentis. Sed hanc opinionem Aristoteles excludit et vult, quod si ille aer proximus motus a proiciente esset causa proiecti, tunc proiectum moveretur in aere propinquiori tantum et nunc consequenter hoc apparet manifeste falsum. Et ideo Philosophus ponit unam aliam solutionem et est: Proiciens movet aerem proximum circa se et ille aer movet alium aerem proximum circa se et ille aer movet alium aerem et sic ulterius donec cessat virtus proicientis in aere et illa virtute deficiente deficit motus. Et est simile de inclinationibus, quia parte mota ista movet aliam partem et ulterius ista pars movet aliam, donec cessat virtus primi moventis, sic etiam est in aere, quamvis non ita manifeste apparet ad sensum. Sequitur corrolarie, quod positio Platonis, que dixit proiecta moveri per antiparistasim et per partium positionem, scilicet quod cum proiectum dividit aerem quo aere terminato proiectum se veniret impetuose et impelleret sic impetuose proiectum. Sic etiam sequeretur, quod moto lapide celum moveretur. Lapis enim motus movet aerem et aer iterum alium, cui alter cedit et sic uno motu omnia moverentur. Unde et ipse dixit, quod sicut navis mota cum decursu procellarum deferuntur per impetum, qui est in procellis, ita etiam moveretur proiectum ab aere, in quo est virtus proicientis et tertio Celi loquens de hac opinione dixit, quod aer est organum et instrumentum in motu gravium et levium.” [Cf. Aristotle, De caelo III, 2, 301b16–25.] “Notandum tertio, quod Aristoteles in textu ostendit, quod motus proiectorum non est unus. Fit enim a diversis moventibus consequenter se haben-

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tibus et ex hoc concluditur, quod si non esset unus motus primus et ergo a sensu contrario. Si motus primus est unus, quod verum est etiam, quod motor primus est unus, quod Aristoteles hic intendit. Movet autem Aristoteles istam questionem de motu proiectorum, secundum intentionem Johannis de Janduno, non intentione principali sed potius incidentaliter. Intendit enim Aristoteles hic probare, quod unitas motus deficit propter diversitatem moventium et hoc probat ex motu proiectorum, qui non est unus. Si ergo est unus motus primi motoris, tunc concludit, quod necesse est tantum unum esse primum motorem alias non esset unus motus. “Notandum quarto, quod proiecta moventur a pluribus consequenter se habentibus, cuius rationem assignat Aristoteles in textu istam, quia quanto aliqua virtus est fortior, tanto distantius se diffundit in operationem, sic tamen, quod semper proximum movens simul sit cum proximo motu. Cum ergo virtus proiectiva sit, que virtus ergo diffundit se primo in proximo mobili, quod est aer et ille aer movet alium aerem proximum et etiam proiectum. Ille autem aer proximus ultimus movet remotiorem aerem et hoc fit donec cessat virtus proicientis et tunc etiam cessat motus et sic semper proximum movens est simul cum moto, quia ille aer, qui est immediate circa proiectum est proximum movens, ut declaratum est in declarationibus ipsius aque, in quibus una pars aque movet aliam. Sequitur corrolarie, quod in motu proiectorum est tria assignare: Primum quod est motum tantum et hoc est proiectum. Secundum quod est movens et motum simul et hoc est aer medium, quia talis aer movetur a virtute /f. 240r/ proicientis et movet ulterius ipsum proiectum. Tertium est movens tantum et proiciens. Sequitur corrolarie secundo, quod proiecta moventur a pluribus moventibus consequenter se habentibus, quia a partibus aeris consequenter se habentis. Una enim pars aeris movet aliam, donec cessat virtus proicientis. “Istis sic stantibus est hec conclusio responsalis: Motus proiectorum non est unus motus continuus et proiecta post recessum a primo proiciente moventur ab aere. Modo dato et expresso virtus huius conclusionis patet pro ambabus partibus ex dictis. Sequitur corrolarie primo, quod licet motus proiectorum videtur esse unus et continuus propter unitatem mobilis et temporis, tamen, quia ibi non est unitas moventis, talis motus non est unus. Alii tamen ponunt impetum esse in proiecto. Aristoteles autem dixit in aere. Sequitur corrolarie secundo, quod non oportet omnia moveri tenendo positionem Aristotelis, licet enim aer cedat lapidi, hoc tamen est per condensationem. Sequitur corrolarie tertio, quod impetus concurrit in motu proiectorum et est in aere. “Arguitur primo, ex declaratione sequitur, quod motus celi etiam non esset unus. Probatur, quia motus celi fit a diversis motibus. Videtur ergo, quod motus proiectorum est unus. Dico, quod aliquis motus dupliciter potest dependere ex diversis motoribus: uno modo secundum subordinationem moventium, sic quod moventia sunt subordinata et sic unus motus potest esse ex diversis motoribus. Et ratio, quia tunc secundum movens movet in virtute primi. Secundo modo potest motus dependere ex diversis moventibus non subordinatis et sic ex diversitate moventium impeditur unitas motus et sic est de motu proiectorum qui omnino accidentalis est, quod una pars aeris plus movet quam alia. Sic autem non est in causis subordinatis, quia semper

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causa movet universalior, movet essentialiter particularem et non contra, sic quod particulares cause moverent universalem. “Arguitur secundo. Illud, quod impedit motum, non iuvat motum, sed medium impedit motum, igitur proiectum non movetur ab aere. Maior est nota, quia resistentia fit ex parte medii, ut dictum est in quarto huius. Dico, quod medium, ut aer, acciditur dupliciter: uno modo secundum se et sic non iuvat motum, sed potius impedit motum; secundo acciditur secundum quod in se recipit aliquam virtutem movendi et sic iuvat motum et simile est de alteratione, quia aqua secundum se impedit calefactionem, cum sit secundum se frigida, tamen aqua calefacta iuvat ad calefactionem, quia calefacit carnes in illa. “Arguitur tertio: Proiecta moventur ab impetu in tribus horis, igitur non moventur a pluribus motoribus consequenter se habentibus vel moventibus. Probatur, quia si non, tunc non posset salvari, quoniam tam vehementer moveretur navis contra et sagitta a balista. Dico, quod propter ista argumenta aliqui dicunt, quod necesse est proiecta moveri ab aliqua forma sibi impressa a proiciente ex ignorancia, quod lapis proiectus in manu reciperet in se unam formam sibi impressam a proieciente, per quam moveretur alicuius ad ipsum locum et sic non fieret ab aere moto, quod est contra Aristotelem et etiam hec positio est inconveniens, quod proiecta moveantur a forma de impressa. Patet, quia si sic moverentur, tunc non esset assignare causam cessationis a tali motu occurrente aliquo obstaculo, ex quo enim illa forma est in proiecta, sic ea ratione semper moveretur in tali forma. Non enim apparet, unde posset talis forma corrumpi. Dicendum est ergo, quod ista mobilia, de quibus dictum est, moverentur per formam impressam a movente non proiectum sed in aerem medium et illa impressio faciliter potest fieri in aere, quid est faciliter mobilis et ideo, quando navis velociter movetur contra fluvium, tunc est fortis impressio facta in aqua circa navem et aerem, /f. 240v/ ideo illa aqua et aer moveret navem absque attractione in ea signum. Aqua habet tumorem ante navim et ideo apparet, quod aqua mota fuit et quod aer motus fuit, quia si quis poneret unam plumam etiam navim deberet moveri, quod est signum et ille aer motus est circa navim. Et similiter dicendum est de arcu et balista, quia talis impressio citius recipitur in arcum quam in navim vel in lapidem. “Arguitur quarto, veritas conclusionis videtur esse contra rationem. Igitur probatur, quia mirum videtur, quo modo aer posset ita pellere lapides magnos machinarum, non esset tempus impressus in machinam. Dico, quod non est verum agnoscente naturas rerum. Declaretur enim in libris Metheororum, quod subtilis aer grandia edificia subvertit immo movens elevant terram, facit tremorem. Sequitur corrolarie, quod impetus in motu proiectorum est in aere et non in proiecto. Patet veritas ex duobus signis. Primum, quia sagitta in certa distantia ab arcu velocius movetur et hoc non fieret, si impetus esset in arcu, sed hoc fit ab aere. In principio enim, cum sagitta emittitur ab arcu medius aer motus est et ergo non valde vehementer movetur sagitta, sed postea movetur maior quantitas aeris, unde et maior apparet motus insagitta et vehementer secundum signum, quia videmus tempore tonitrui aerem depulsum grandia edificia subvertere aut arbores dividere. Non ergo mirum,

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si aer motus sufficit lapidem proiectum moveri. Aer enim, quia aliquid levis, aliquid gravis est faciliter, suscipit impetum et postea movet proiectum. “Dubitatur, cuius nature sit virtus proiecta. Dicendum, quod in movente est naturalis potentia, que oritur ex principiis subiecti, sed in aere moto ista virtus non est in aliquo predicamento, quia non potest esse in aere moto actualiter, quia tunc in aere moto esset actualis potentia motiva et sic aer semper moveret proiectum absque extrinseco movente sic nunc facit proieciens. Oportet ergo dicere, quod ista virtus est in aere moto potentialiter et virtualiter et illa virtus solvatur in motu talis aeris, qui motus est de predicamento ubi. Unde potest dici, quod virtus proiectiva in aere acciditur dupliciter: uno modo quo ad eius fundamentum et sic est de predicamento ubi, quia est motus localis aeris; alio modo quo ad actum et sic non est in aliquo predicamento, quia non est ens reale actuale, sed solum virtuale.” Text 12 [To Chapter 4.3.6]: Quaestiones cracovienses, Q. 97, pp. 165–166: “Circa initium huius quinti utrum ab eo, quod inest parti, totum habeat denominari. “Et videtur, quod non, quia si sic, Socrates diceretur eius manus, quia pars eius dicitur manus, et sic Socrates diceretur minor Socrate. Patet, quia pars eius dicitur minor Socrate. “Secundo: quia a parte ad totum non valet argumentum, quia multa praedicantur de parte, quae non praedicantur de toto. “Tertio: Illud, quod inest alicui secundum partem, inest ei secundum quid, igitur etc. “In oppositum est Aristoteles in littera, qui dicit: ‘ex hoc, quod pars mutatur, dicitur totum simpliciter mutari.’ “Pro quo sciendum, quod ad ostendendum species motus Aristoteles declarat mobile tribus modis posse moveri. Primo per accidens, scilicet ex esse in eo, quod per se movetur. Secundo aliquid movetur secundum partem, quia aliquid eius movetur. Tertio aliquid movetur primo, quia movetur, et non secundum accidens neque secundum partem. “Secundo sciendum, quod denominationes convenientes parti sunt in multiplici differentia. Quaedam enim est partis, et est extranea toti, sicut esse simplex convenit animae et tamen non convenit toti homini, immo est extraneum toti homini. Alia sunt accidentia non extranea toti, et illa subdividuntur. Quaedam parti conveniunt ab accidentibus partium, quae per partem afficiunt totum, ut dolor capitis afficit totum hominem. Alia denominatio sumitur ab accidente, quod non afficit totum per partem, et illa subdividuntur. Quaedam determinant sibi certas partes in toto, ut simitas determinat sibi nasum et crispitudo crines. Alia vero non determinant sibi certas partes, sicut albedo. “Est ergo prima conclusio: Accidentia partium, quorum denominatio est extranea toti, non denominant totum per partem. Patet per primam rationem ante oppositum. “Secunda conclusio: Accidentia partium, quae non sunt extranea toti et per partem efficiunt totum, denominant totum, ut quia caput dolet, totus homo dicitur dolere.

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“Tertia conclusio: Accidentia, quae insunt parti et non afficiunt totum, sed determinant sibi certam partem in toto, denominant totum. Patet, quia a naso totus homo dicitur simus et a crinibus totus homo dicitur crispus. “Ultima conclusio: Accidentia, quae insunt parti et non determinant sibi certam partem in toto, illa non denominant totum simpliciter, ut albedo in digito non denominat totum, quia denominatio sumitur ab esse perfecto; quando ergo accidens est in parte et potest esse in toto, tunc exspectat esse perfectius et per consequens non denominat in eo, quod non habet esse perfectum. “Ad rationes: Ad primam dicitur, quod est pro prima conclusione. “Ad secundam et tertiam dicitur, quod sunt pro ultima conclusione.”

APPENDIX III [To Chapter 4.5]: BJ, Inc. 597 is bound with Inc. 596: Lambertus de Monte, Questio de salvatione Aristotelis (Köln, Henricus Quentell, ca. 1498), 2–0. BJ: Inc. 596; Nr. inw. 16528 fol. sig. Aiir: “De salvatione Arestotelis. Questio incidentaliter mota diffuse tamen ac amplissime per venerabilem magistrem nostrum Lambertus de Monte . . .” fol. sig. Bivv: “Idcirco venerandus eximius magister noster Lambertus de Monte sacrarum litterarum interpres et scrutator profundissimus in praehabita questione ostendit et concludit probabiliter per auctoritates scripture divine et iuxta saniorem doctorum sententiam Arestotelem summum et philosophorum principem esse de numero salvandorum.” Inc. 596 is not annotated. Versor Ioannes, Quaestiones De coelo et mundo, De generatione et corruptione, Metheororum, Parva naturalia, Aristotelis (Köln, Conradus Welker, 1488), 2–0. Inc. 597; Nr. inw. 16529 See Inkunabuły Biblioteki Jagiellońskiej, ed. A. Lewicka-Kamińska (Kraków: Jagiellonian University, 1962), p. 23, 364*: 5 III 1488 Versor Joannes. Quaestiones super libros De coelo, Meteora, Parva naturalia, De generatione Aristotelis. 20. HC* 16046; VK 1227 and 1234; Birk. 129; W 544.—Inc. 597. HC = Hain Copinger. VK = Voullième E.: Der Buchdruck Kölns bis zum Ende des fünfzehnten Jahrhunderts. Bonn 1903. Publikationen der Gesellschaft für rheinische Geschichtskunde 24. Birk. = Birkenmajer A.: Die Wiegendrucke der physischen Werke Johannes Versors. Uppsala 1925. Odb.: Bok-och bibliotekshistoriska Studier tillägnade Isak Collijn. W = Wisłocki W.: Incunabula typographica Bibliothecae Universitatis Jagellonicae Cracoviensis inde ab inventa arte imprimendi usque ad a. 1500. Cracovia 1900. Munera saecularia Universitatis Cracoviensis vol. 3. Inc. 597 is annotated is more than one hand, and some annotations appear to date from the late fifteenth or early sixteenth century. fol. sig Aii: “Primus de celo et mundo. Folio i.” fol. sig. Dviv (= f. 27v): “Et hec de questionibus magistri Johannis Versoris super libros de celo et mundo Arestotilis dicta sufficiant.” fol. sig. Eir: “Primus metheororum Folio i.” fol. sig. Gviv (= f. 18v): “Questiones magistri Johannis Versoris supra libros metheororum Arestotilis hic feliciter finem habent.” fol. sig. dir: “Tabula. Incipit remissorium librorum de generatione et corruptione in quo questionum dubitationumque effectus assignantur cum foliorum numero.”

462

appendices

fol. sig. diiir: “De generatione et corruptione. fo. i. Circa initium librorum de generatione et corruptione. Nota textum . . .” fol. sig. fviv (= f. 21v): “Et sic est finis questionum Versoris super duos libros Arestotilis de generatione scilicet et corruptione secundum processum burse montis Anno incarnationis domini nostri M. cccc. lxxx. viii. tertio nonas Martii.” fol. sig. gir: “Recapitulatio secundi libri de generatione.” fol. sig. giv: “Auctoritates primi libri de generatione et corruptione.” The text is lightly annotated in what appears to be a single hand from perhaps the early sixteenth century. In fact, the only annotations appear on fol. sig. civv (= f. 11v)–cvv (= f. 12v), qq. 17–18 on “mixtio.” Here I list the tables of questions from Johannes Versoris, Questiones de celo et mundo and Questiones metheororum. Questiones primi de celo et mundo Tabula [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12] [13] [14] [15] [16] [17] [18] [19]

Utrum scientia naturalis versetur circa corpora et magnitudines? Quid est subiectum attributionis libri de celo et mundo? Quare dicitur in textu fere ubi habetur de natura autem (artem?) scientia fere? Quid Aristoteles intelligit per passiones et motus? Utrum mundus sit perfectus? Que sunt principales partes universi corporei? Utrum probatio ista ternarius est numerus omnis et sufficiens? Utrum sint tantum tres motus simplices? Utrum unius corporis simplicis sit tantum unus motus simplex secundum naturam? Utrum propter motum circularem praeter quattuor elementa sit ponendum unum corpus quintum circulariter motum scilicet caelum? Utrum celum sit grave et leve? Vide ibidem diffinitiones gravis, levis, sursum, et deorsum in tertio notabili. In tertio notabili vide diffinitiones gravissimi et levissimi. Utrum celum sit ingenerabile et incorruptibile, inaugmentabile et inalterabili? Qualiter differunt philosophi a theologiis de productione celi? Utrum in celo sit materia? Utrum omne alterabile sit augmentabili? Utrum motui circulari sit aliquis motus contrarius? Utrum motus planetarum ab occidente in orientem contrarietur motui diurno primi mobilis quae sit ab oriente in occidentem? Utrum corpus circulariter motum possit esse actu infinitum? Utrum in corpore infinito possit dari centrum?

fo. i fo. i fo. i fo. i fo. i fo. ii fo. ii fo. ii fo. iii fo. iii fo. iii fo. iiii fo. iiii fo. iiii fo. iiii fo. v fo. v fo. v fo. v fo. v fo. vi

appendix iii [20] Utrum in tali corpore possit dari medium quaerere ibidem? [21] Utrum in aliquod corpus simplex recte motum possit esse infinitum? Ibidem vide pulcras rationes et propositiones in mathematica. [22] Utrum possibile sit aliquod corpus sensibile esse actu infinitum? Ibidem vide tres conclusiones de tali corpore infinito. [23] Utrum possibile sit finitum pati ab infinito? [24] Utrum si essent plures mundi terra unius mundi moveretur ad terram alterius mundi? [25] Utrum possibile sit esse plures mundos? In prima conclusione eiusdem questiones vide quod extra celum non est corpus et quod celum est ex materia sua tota. Ibidem in secunda conclusione vide pulchram autoritatem gentilis philosophi de substantiis separatis et quod extra celum non est locus neque vacuum nec tempus. [26] Utrum totalis mundus sit genitus corruptibilis? De illa materia vide ibidem quattuor conclusiones. [27] Utrum omnis potentia terminetur ad maximum? [28] Utrum ex parte sempiterni possit demonstrari de ingenitum esse incorruptibile et omne incorruptibile esse ingenitum? [29] Utrum genitum et corruptibile convertantur, et econtra dicitur de ingenito et incorruptibili? [30] Utrum omne corruptibile de necessitate corrumpatur? Questiones secundi de celo et mundo.

463 fo. vi fo. vi fo. vii fo. vii fo. vii fo. vii fo. viii fo. viii fo. ix fo. ix fo. ix fo. x fo. x fo. xi fo. xi.

Tabula [1] [2] [3] [4] [5] [6] [7] [8] [9]

Utrum celum sit sempiternum immortale sempiterne motum et sine fatigatione pena seu labore? Utrum in omni corpore reperiantur sex directione positionum ex natura rei distincte? Utrum in corpore celesti sex directione positionum sint ex natura rei distincte? Utrum in celo polus arcticus semper nobis apparens sit deorsum et polus antarticus sursum, oriens dextrum et occidens? Utrum ad salvandum generationem et corruptionem in istis inferioribus sit necesse celum pluribus motibus moveri? Ibidem vide pulcram conclusionem. Utrum necesse sit celum esse spericum. Ibidem vide pulcra conclusione que est tertia. Utrum celum debeat moveri ad unam partem determinatam, scilicet ad ante, et ab una parte determinata scilicet a dextro? Utrum motus celi sit uniformis et regularis. Ibidem vide pulchram conclusionem. Utrum ad salvandum ea que apparent in motibus planetarum sint in celo ponendi circuli eccentrici et epicicli?

fo. xii fo. xii fo. xiii fo. xiiii fo. xiiii fo. xiiii fo. xv fo. xvi fo. xvi fo. xvii

464

appendices

[10] Utrum astra sint de natura ignis? fo. xviii [11] Utrum de astrum aliud a sole lumen suum a sole recipi? fo. xviii Ibidem vide pulcram questionem et conclusionem. [12] Utrum astra moveantur motu proprio distincto [a motu suorum orbium]? fo. xix Ibidem vide pulcrum et prolixam conclusionem de motu astrorum. [13] Utrum astra et orbes quibus infiguntur causat sonos armonios? fo. xx [14] Utrum orbes superiores et propinquiores supremo celo moveantur velocius motu diurno distantioribus etc.? fo. xx [15] Utrum astra sint sperice figure? fo. xxi [16] Utrum motus orbium celestium debeant multiplicari secundum proportionem uniuscuiusque orbis ad supremum celum? fo. xxii Quare in octavo orbe est tanta multitudo astrorum et non in inferioribus? fo. xxiii [17] Utrum terra naturaliter quiescat in medio mundi? fo. xxiii An idem sit medium mundi et terre? fo. xxiiii An motus gravium sit ad medium? fo. xxiiii Que est causa quietis terre in medio mundi? fo. xxiiii Utrum terra secundum se totam sit mobilis ad medium mundi? fo. xxiiii [18] Utrum terra sit sperice figure? fo. xxiiii. [Questiones tertii de celo et mundo. f. xxvrb has an explanation why Book III is neglected. The Tabula lists nothing under Book III but simply passes over it and continues:] Questiones quarti de celo et mundo. Tabula [1]

[2] [3] [4] [5]

Utrum sit aliquod corpus grave simplex et aliquod leve simplex et aliquod grave et leve in respectu? Utrum gravitas sit forma substantialis gravis et levitas forma substantialis levis? Utrum aliquod elementum in suo loco naturali sit grave aut leve? Utrum corpus quod est gravius in aere altero corpore sit gravius eodem in aqua? Utrum plenum et vacuum sint causae gravitatis et levitatis? Utrum ex parte qualitatum motivarum posset concludi quaternarius numerus elementorum? Utrum levitas aeris et ignis speciei differant? Utrum loca naturalia gravium et levium sint cause suorum motuum? Utrum figure gravium et levium sit cause motuum sursum et deorsum?

fo. xxv fo. xxv

fo. xxv fo. xxv fo. xxvi fo. xxvi fo. xxvii fo. xxvii.

appendix iii

465

Tabula “Incipiunt tituli questionum in libros metheororum Arestotilis. Questiones primi libri metheororum. [1] Utrum corpus simplex mobile ad formam mixti imperfecti prout est in via ad taliter mixtionem sit subiectum huius libri? fo. i [2] Utrum necesse sit hunc mundum inferiorem esse continuum lationibus perioribus ut omnis virtus inde gubernetur? fo. i. [3] Utrum unum elementum sit naturaliter locatum in concavo alterius? fo. ii [4] Utrum motus localis sit calefactivus? fo. ii Utrum ignis et suprema regio aeris naturaliter moveantur motu circulari? fo. iii Utrum lumen sit de se calefactivum? fo. iii [5] Utrum media regio aeris sit semper frigida? fo. iii Utrum in suprema regione aeris possint generari nubes? fo. iii Utrum sub polis generantur nubes? fo. iii Que sit figura medie regionis aeris? fo. iii [6] Utrum unum contrarium sit fortificativum alterius per antiparistasim? fo. iii [7] Utrum omnes impressiones ignite sint eiusdem speciei specialissime? fo. iiii [/ f. 4v–5r / ] Utrum sidera volantia moveantur per continuam extrusionem aut per adustionem? fo. v Utrum sidera volantia sint in celo aut in regione elementari? fo. v Quo tempore fiunt huiusmodi impressiones? fo. v Utrum vapor natus sit ascendere altius quam exalatio? fo. v [8] Utrum de nocte existente serenitate aeris debeant apparere hyatus voragines et sanguinei colores? fo. v Quare dicte impressiones non apparent de die sicut apparent de nocte? fo. v Quare talia apparent in celo cum sint tamen in regione aeris? fo. v Quare talia fantasmata apparent magis tempore serenitatis quam alio tempore? fo. v Quare audiuntur aliquando soni parui quando apparent talia fantasmata? fo. v Utrum exalatio et vapor sint eiusdem speciei cum corpore a quo elevantur? fo. v [9] Utrum cometa sit de natura celesti? fo. v [10] Utrum cometa sit de natura elementari? fo. vi Quo tempore magis generatur cometa? fo. vi Quare cometa diu sic permanet in aere? fo. vi

466

appendices

[f. 6: ] Que sit causa diversitatis colorum comete? fo. et littera(?) eodem Utrum possunt simile apparere plures comete? fo. eodem Que sint signa comete? fo. eodem [11] Utrum gallaxia sit de natura elementari? [“Galaxia” = circulus lacteus (Milky Way).] fo. vii [12] Utrum pluvia generetur in media regione aeris? fo. eodem Que sunt signa pluvie? fo. vii Que sunt accidentia pluvie? fo. vii [13] Utrum ros et pluvia similiter generantur? fo. viii Que sunt accidentia roris? fo. viii Que sunt accidentia nivis? fo. viii [f. 8: ] [14] Que sunt accidentia pruine? fo. viii Que sunt accidentia grandinis? fo. viii [f. 8: ] [15] Utrum aque fontium et fluviorum generentur in concavitatibus terre ex aere in ipsis incluso? fo. viii [16] Utrum ubi nunc est mare aliquando prius fuerit aut posterius erit terra arida aut econtra? fo. ix Questiones secundi libri metheororum. [1] Utrum terra debeat esse totaliter cooperta aquis? [2] Utrum mare in suo loco naturali sit generabile et corruptibile? [3] Utrum mare debeat fluere et refluere? Quare astrologi magis aspiciunt ad orientem in nativitatibus hominum quam ad punctum meridiei? An luna habeat movere mare per lumen suum an per aliquam aliam influentiam distinctam a lumine? Utrum fluxus et refluxus maris sunt maiores in uno tempore quam in alio? Quare aliqua maria solum fluunt in mense et aliqua numquam? [4] Utrum mare sit salsum? Quare aliqui fontes convertunt corpora terrestria in ipsis posita in lapides? Quare alique aque fontales causant strumam in collo? Quare alique aque faciunt nigras ovex ex illis bibentes et alique econverso faciunt albas? Que aque sunt saniores? [5] Utrum ventus sit exalatio calida et sicca laterialiter mota circa terram? Utrum pluvie quandoque faciant cessare ventos?

fo. x fo. x fo. xi fo. xi fo. xi fo. xi fo. xi fo. xi fo. xi fo. xii fo. xii fo. xii fo. eodem fo. xii

appendix iii

[6]

[7] [8]

[9]

Utrum sol sit causa commotionis ventorum et causa efficiens cessationis eorundem? Utrum tantum duodecim sint venti? Quare venti boreales communiter flant in autumpno post tropicum estivalem, et tamen venti australis non flant in vere post tropicum hyemalem? Utrum venti australes flent a polo antarctico nobis manifesto? Utrum plures venti debeant flare a septentrione quam a meridie? Utrum venti debeant reduci ad quatuor principales? Utrum venti contrarii possunt simul flare? Utrum aliqui venti faciunt alios cessare? Que est causa generationis ventorum? Utrum venti distinguantur secundum calidum et frigidum, humidum et siccum? In qua parte anni debent flare etnephei et venti circulares? [sic] Utrum motus terre sit possibilis? [earthquakes, volcanic eruptions, etc.] Que sunt accidentia motus terre? Utrum tonitruum sit sonus factus in nubibus? Unde causatur diversitas sonorum in tonitruo? Que tonitrua sunt magis timenda? Quomodo causatur cuneus fulminis? Utrum tiphones etnephias incensiones et fulmina sint eiusdem speciei et substantie?

Questiones tertii libri metheororum. [1] Utrum radius visualis refrangatur in occursu medii rarioris vel densioris? [2] Utrum halo habeat apparere circularis figure? [3] Utrum colores apparentes in yride sint veri colores? [4] Utrum yris debeat apparere tricolor? Quare per iuxtapositionem viridis et alurgi non apparet unus color sicut per iuxtapositionem viridis et punicei apparet zandros? [5] Utrum quando apparent due yrides superior sit debilior in coloribus quam inferior? An yris possit causari a luna sicut a sole? An duo homines possint eandem yridem in eadem parte nubis videre? Quare est quod quandoque videmus yridem inter nos et arbores vel montes? Utrum yris appareat semper per modum semicirculi? [6] Utrum parelii et virge debeant apparere per reflecionem vel refractionem?

467 fo. xii fo. xii fo. xiii fo. xiii fo. xiii fo. eodem fo. xiii fo. xiii fo. xiii fo. xiiii fo. xiii fo. xiiii fo. xiiii fo. xiiii fo. xiiii fo. xiiii fo. xv fo. xv

fo. xv fo. xvi fo. xvii fo. xvii fo. xvii fo. xviii fo. xviii fo. xviii fo. xviii fo. xviii fo. xviii

468

appendices Que sunt accidentia virgarum et pareliorum? Utrum ad istrum librum pertineat determinare de mineralibus?

fo. xviii fo. xviii

Finis tabule. BJ, Inc. 597, De generatione et corruptione. fol. sig. dir: Tabula fol. sig. dira: “Incipit remissorium librorum de generatione et corruptione in quo questionum dubitationumque effectus assignantur cum foliorum numero. Questiones primi libri de generatione et corruptione. [1] Utrum de corpore mobili ad formam sit scientia tamquam de subiecto attributionis huius libri? fo. i Utrum corruptio sit naturalis et an de ipsa possit scientia naturalis? fo. i Utrum re corrupta possit manere eius scientia in anima? fo. i [2] Utrum ponentes unum materiale principium et hoc in actu possint salvare generationem distingui ab alteratione et aliis motibus? fo. i Utrum generatio secundum quid et alteratio sive motus accidentalis et proprie dictus sint idem? fo. ii [3] Utrum omnium habentium transmutationem adinvicem sit una materia? fo. ii Utrum materia sit una numbero specie genere aut analogia? fo. ii [4] Utrum Democritus ponens corpora indivisibilia esse principia rerum possit salvare distinctionem generationis simpliciter ab alteratione et aliis motibus? fo. iii Utrum corpus componatur ex indivisibilibus? fo. iii [5] Utrum sit aliqua generatio simpliciter? fo. iii Que sit causa perpetuitatis generationis et corruptionis? fo. iiii Utrum ens in potentia ex quo est generatio sit substantia vel accidens? fo. iiii Utrum quicquid generatur ex aliquo corrupto generetur? fo. iiii [6] Utrum verum sit quod generatio unius sit corruptio alterius que quidem questio habetur tam in questiuncula quam etiam inferius in principali questione? fo. iiii Utrum generatio secundum quid que est in accidentibus presupponat corruptionem? fo. iiii Utrum generatio scientie presupponat corruptionem erroris? fo. iiii [7] Utrum generatio differat ab alteratione et ab aliis motibus? fo. v Utrum generatio differat ab aliis motibus? fo. v Utrum eadem qualitas maneat in generato que prefuit in corrupto? fo. v [8] Utrum in corruptione substantiali ex pate formarum substantialium necesse sit resolutionem fieri usque ad materiam primam? fo. v Utrum plurium agentium idem effectus numero a quolibet produci possit? fo. v

appendix iii

[9]

[10]

[11]

[12] [13] [14] [15] [16]

[17]

Utrum ab eodem agente in quolibet plurium instantium possit idem effectus numero produci? Utrum augmentatio et diminutio sint motus distincti ab aliis motibus? Quomodo differunt augmentatio et rarefactio. Utrum augmentatio et diminutio ab invicem distin/ fol. sig. dirb / guantur? Utrum illud quod augetur sit solum in potentia quantum nullam penitus habens quantitatem? Utrum in augmentatione id quod advenit, scilicet cibus vel corpus vel membrum vel utrumque augeantur: Utrum augmentatio fiat adveniente aliquo extrinseco ibi arguitur pro et contra? Utrum in quantitate sit aliqua mutatio proprie dicta? Que sit causa effectiva augmentationis? Utrum tres conditiones augmentationis sint bene assignata? Utrum ad salvandum augmentationem conveniens sit ponere poros? Utrum calor naturalis continue agat in humidum radicale? Utrum nutrimentum sit simile vel dissimile ei quod nutritur? An augmentatio sit ad quantum in communi? An motus nutrimenti quo transmittitur ad singulas partes viventis sit naturalis? Utrum membrum patiatur mixtionem a nutrimento? Utrum augmentatio sit unus motus et continuus? An vivens quam diu vivit nutriatur? Utrum omne agens agat per contactum? Utrum simile agat in sibi simile? Queritur decimoquinto, utrum omne agens in agendo repatiatur? Queritur decimoquinto [sic], utrum actio et passio habent fieri poros? Ibidem vide quatuor opiniones et quinque conditiones quomodo fiunt actio et passio. Utrum mixtio sit possibilis? Ibidem vide pulcra notata in quatuordecim conclusionibus.

469 fo. vi fo. vi fo. vi fo. v [sic] fo. vi fo. vii fo. vii fo. vii fo. vii fo. vii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. ix fo. ix fo. x fo. xi fo. xi fo. xi fo. xi et xii fo. xii

[18] Utrum elementa formaliter maneant in mixto? Ibidem vide opiniones Averrois, Alberti, et Egidii de Roma de illa materia. fo. xii Recapitulatio primi libri de generatione et corruptione. fo. xiii Registrum libri secundi de generatione et corruptione. [1] Utrum qualitates prime sint principium formale elementorum et materia prima sit principium materiale eorundem? fo. xiii [2] Utrum tantum sint quatuor qualitates prime? fo. xiiii Ex quo quodlibet elementum determinat sibi certam

470

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qualitatem in summo quare non sufficiat una qualitas ad constitutionem unius elementi? fo. xv Que sunt loca elementorum? fo. xv An ignis et aqua magis contrarientur quam ignis et terra? fo. xv / fol. sig. div / [4] Utrum cuilibet elementorum primo conveniat una qualitas prima? fo. xv An quodlibet elementum habeat duas qualitates in summo? fo. xv Utrum calor, ignis, et aeris sint eiusdem speciei et similier querendo de aliis qualitatibus? fo. xv [5] Utrum ex quolibet elemento potest immediate generari quodlibet elementum? fo. xvi Ibidem secundo etiam declarat in quibus elementis est facilior transitus et in quibus non, tertio declarat ibidem ex quibus duobus elementis potest fieri tertium. fo. xvi [6] Utrum in genere corporum elementa sint prima? fo. xvii [7] Utrum ad generationem cuiuslibet mixti perfecti existentis circa medium concurrant quatuor elementa? fo. xvii Ibidem agitur de generatione et corruptione elementorum que generantur et corrumpuntur per naturam elementorum. Utrum elementa in equali pondere concurrant ad generationem mixti? fo. xviii Utrum sit possibile qualitates elementorum in mixto equaliter convenire? fo. xviii [8] Utrum tantum sint tria principia generationis et corruptionis mixtorum inferiorum, scilicet, materia, forma, et efficiens? fo. xviii [9] Utrum quatuor elementa per suas virtutes activas et passivas sint agentia sufficientia ad generationem et corruptionem mixtorum? fo. xviii [10] Utrum motus solis sub obliquo circulo factus sit causa perpetuitatis generationis et corruptionis in istis inferioribus? fo. xix Qualiter habet veritatem ista propositio idem inquantum idem et similiter se habens semper natum est facere idem? fo. xix [11] Utrum omne vivens habeat determinatam periodum sue durationis? fo. xx [12] Utrum ex parte finis et ex parte cause moventis possit ostendi perpetuitas generationum et corruptionum? fo. xx Utrum motus capiat suam unitatem a mobili aut a termino? fo. xxi [13] Utrum aliquod corruptum possit idem numero reproduci? fo. xxi Et sic est finis registri questionum et dubitationum huius libri totalis de generatione et corruptione. / f. 21vb / “Et sic est finis questionum Versoris super duos libros Arestotilis de generatione scilicet et corruptione secundum processum burse montis. Anno incarnationis domini nostri M. cccc. lxxx. viii. tertio nonas Martii.”

APPENDIX IV Ficino’s Translation of Parmenides The text in Ficino’s translation (Florence, 1484; Uppsala, Copernicana 31; the Estienne or Stephanus numbers are in brackets) reads, beginning selectively with the context: f. e4va [134b]: “Uerumtamen ipsas species neque nos habere neque circa nos esse posse assenteris. Non profecto. Cognoscuntur ne ipsa scientie specie genera ipsa que singula sunt? Certe. Quam speciem nos haud habemus. Non certe. Nulla igitur species a nobis cognoscitur, cum ipsius scientie particeps minime simus. Non apparet. [134c] Ignotum itaque nobis ipsum pulchrum et ipsum bonus est et omnia denique ut ideas esse supponimus. Uidetur. Consydera et hoc etiam grauius. Quid nam? Num fateris si est ipsum quiddam scientie genus, multo illud prestantius esse hac nostra scientia, et ipsam pulchritudinem ac reliqua eodem pacto. Immo. [134d] Non ne si quid aliud est ipsius scientie particeps, nullum nisi deum dices supremam habere scientiam? Necesse est. . . . [135a] Unde uacillat quisquis hec audit, ac dubitat ne forte idee nihil sint omnino, vel si sint /f. e4vb/ necesse eas esse humane nature ignotos existimat. A deo ut qui ista dicit inferre aliquid uideatur. Et ut paulo ante dixi mirum est quam sit incredibile, et uiri admodum ingeniosi percipere posse quod sit genus quoddam cuiusque, [135b] et ipsa secundum se ipsam essentia, nec non mirabilioris iuri officium est, hoc postquam inuenerit alios docere posse sufficienter omnia discernentem. Assentior. Parmenides inquit Socrates . . . [135d] Ante quam exercitatus sis o Socrates, definire aggrederis, quid pulchrum, iustum, bonum, et aliarum quelibet specierum, hoc enim pridem animaduerti, hic te audiens una cum hoc Aristotele disputantem, pulcher sane atque diuinus mihi crede impetus iste tuus, quo ad rationes aduolas. Ceterum collige te ipsum diligentusque te in eo facultate exerce, que in utilis esse uidetur, et a multis nugatio siue garrulitas nuncupatur dum iuuenis es, alioquin te ueritas fugiet. Quis exercitationis huiusce modus est Parmenides? [135e] Iste inquit quem a Zenone audisti. Sed etiam illud tuum aduersus hunc dictum miratus sum cum diceres non in iis que oculis percipiuntur eorumque errore cogitationem sistere oportere, sed ad ea conscendere quae quis maxime ratione comprehendere ac species esse putaret. Neque in hunc modum arduum esse uidetur, similia utrum atque dissimilia cetera ue quae rebus existentibus competunt explicatur. Et probe quidem disiste. Est autem propter hoc, illud etiam obseruandum, [136a] ut non modo si est aliquid supponas, ac deinde que proueniunt ex suppositione consideres uerum etiam si non sit id ipsum supponas si perfectius exercitari uoleris, quo pacto id ais. Uerbi causa si uelis circa istam suppositionem /f. e5ra/ [Copernicus’s annotation is directly above the following words through ‘euentu’:] quam Zenon inuexit, si multa sunt quid euenturum est ipsis multis ad se ipsa et ad unum, et uni ad se ipsum et ad multa. Ac rursus si non sunt multa, iterum consyderandum

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quid accidat uni atque multis, tum ad se ipsa, tum inuicem. Et rursus si supposuerit esse similitudinem, vel non esse, quid potissimum ex utraque suppositione contingat, tam iis que supposita sunt quam ceteris omnibus, ad se ipsa pariter atque inuicem. [136b] Eadem quoque de dissimilitudine ratio est, de motum statu, generatione, corruptione, esse, atque non esse, et ut uno uerbo completar, de quocunque supponitur, aut esse, aut non esse, siue quamuis aliam passionem suscipere, consyderanda sunt que ex suppositione proueniant ad se ipsum, et ad quodlibet aliorum, quodcunque elegeris, et ad plura et ad uniuersa similiter, [136c] et alia rursus ad se ipsa atque ad aliud, quodcumque adsumpseris siue ut existens siue ut non existens ipsum posueris, si modo absolute exercitatus, ueritatem sis penitus inspecturus. Arduum inquit opus adducis nec te omnino intelligo. Sed cur ipse non supponis aliquid illud eo modo percurrens, ut clarius intelligam? [136d] Grande o Socrates onus seni imponis. Tunc Socrates cur non ipse o Zenon hanc rem discutis? Cui Zeno subridens respondit, ipsum o Socrates oremus Parmenidem neque enim leue quiddam est quod ait. an non uides quantum sit negocium quod iubes? Quod si plures essemus haud sane id postulare deceret. Indecorum nanque huiusmodi quedam in conspectu multorum tractare, atque id seni precipue. Ignorant enim multi quod absque hoc discursu ac peruagatione per omnia impossibile sit mentis ueritati coniuncte compotem fieri. [136e] Ego igitur o Parmenides una cum Socrate precor, ut et mihi etiam liceat tanto tempore transacto hec audire. Cum uero hec intulisset Zenon retulit. Antiphon dixisse Pythodorum, se quoque et Aristotelem ac reliquos omnes obsecrauisse Parmenidem, ut quod dixerat, demonstraret, neque aliter faceret. [137a] Tunc demum Parmenides necesse est inquit obtemperare, et si mihi uideor in id quod passus est ibicius equus incidere. Cui profecto equo athlete seniori curruum subituro certamen et propter experientiam euentum ex /f. e5rb/ timescenti ibycus ipse se conferens inuitas inquit et ipse tam senex ad amores aggredi cogor. Eadem ratione ego mihi admodum trepidare uideor, cum cogito quo pacto possim iam grandis natu tam profundum differendi Pelagus transnatare. Obsequendum tamen cum et Zenon ipse roget, iidem enim sumus. Unde igitur incipiemus? Quid ue primum supponemus? An multis postquam negociosum ludum ingressi sumus a me ipso meaque suppositione in primis exordiar? [137b] De ipso uno supponens, siue unum sit siue non, quid accidat? Prorsus inquit Zenon. Quis igitur mihi respondebit? An iunior est minus enim negocii prebebit, et que ipse sentit maxime respondebit ut eius responsio minus me defatiget paratum sum o Parmenides. [137c] Aristoteles inquit me namque significas dum iuniorem respondere iubes. Sed age ut lumet interroga me, tanquam libentissime responsurum. “Age igitur si unum est, non utique multa erit ipsum unum. At quo modo? Neque igitur partem esse illius aliquam, neque totum esse ipsum oportet. Cur nam? Pars utique totius pars est. Est. Quid vero? Non se totum est, cui nulla pars deest? Prorsus. Utrinque igitur ipsum unum ex partibus esset, totumque existens ac partem habens. Necesse est. Utrinque rursus ipsum unum multa potius quam unum esset. Uerum. [137d] Oportet autem non multa, sed unum ipsum existere. Oportet, sane. . . .”

APPENDIX V Summary of Plutarch’s De facie1 Here I emphasize only those ideas that are the most relevant to Copernicus’s critical evaluation of Aristotelian and Ptolemaic geocentrism. In Plutarch’s dialogue, the narrator, Lamprias, is a supporter of the Platonic Academy who elsewhere is described as an Aristotelian, but one who criticizes him usually by adopting a Platonic doctrine. The issue that the dialogue addresses is how there can be dark spots on the Moon if it is the sort of perfect celestial body maintained by Aristotle. The Platonists had come to the conclusion, supported here, that the Moon must be an Earth-like spherical body possessing weight and solidity. It does not fall towards Earth because its circular motion generates a centrifugal tendency that remains circular and stable because a natural motion preserves itself unless it is diverted.2 In holding the view that Earth is in the middle, Stoics maintained that all weights in their natural inclination press against one another and towards which they move and converge from every direction. In response to objections to the sphericity of Earth, Lamprias argues as follows: If all heavy body converges to the same point and is compressed in all its parts upon its own centre, it is no more as centre of the sum of things than as a whole that the earth would appropriate to herself the heavy bodies that are parts of herself; and of falling bodies proves not that the is in the centre of the cosmos but that those bodies which when thrust away from the earth fall back to her again have some affinity and cohesion with her. For as the sun attracts to itself the parts of which it consists so the earth too accepts as own the stone that has properly a downward tendency, and consequently every such thing ultimately unites and coheres with her. If there is a body, however, that was not originally allotted to the earth or detached from it but has somewhere independently a constitution and nature of its own, as those men would say of the moon, what is to hinder it from being permanently separate in its own place, compressed and bound together by its own parts? For it has not been proved that the earth is the centre of the sum of things, and the way in which things

1 See Plutarch, Moralia, Vol. 12 (Cambridge: Harvard University, 1957), Concerning the Face Which Appears in the Orb of the Moon, tr. Harold Cherniss, 67–71, 924 D-F. I have quoted the text at length because Copernicus’s later arguments display familiarity with the notions represented here, and his language even echoes some expressions, suggesting that he adopted Neoplatonic doctrines on the elements, motions of elemental bodies, and the like. He believed that Aristotelian views could be adapted, however, to accommodate these Neoplatonic doctrines. 2 The similarity to a “circular” inertia is at hand.

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appendices in our region press together and concentrate upon the earth suggests how in all probability things in that region converge upon the moon and remain there. The man who drives together into a single region all earthy and heavy things and makes them part of a single body—I do not see for what reason he does not apply the same compulsion to light objects in their turn but allows so many separate concentrations of fire and, since he does not think that there must also be a body common to all things that are fiery and have an upward tendency.

In the dialogue Lamprias reports the view of some mathematicians who place all of the planets above the Sun (the Platonic opinion, although not explicitly identified here as Platonic), which Lamprias uses to argue explicitly for the Platonic assimilation of the Moon to Earth. In other words, with the Moon separated from the other planets by the Sun, there is even greater reason to consider the Moon Earth-like.3 Arguments about the size of the universe and Earth in the middle are shown to be fraught with a number of difficulties, all pointing to the dialectical nature of the arguments. So also are the principles “natural” and “unnatural” that, if improperly applied, would rather result in a dissolution of the cosmos thus leading to disorder by insisting on the absolute separation of what is heavy from what is light.4 The relation of part to whole also does not support conclusions about what is natural in any absolute sense but is rather a matter of relative wholes and how as related to one another they constitute the whole ordered cosmos.5 This is clearly an argument directed at the Aristotelian (and Stoic) assumption that is used abruptly to support the conclusion that as a principle of order in nature, Nature established directionality by means of the absolute separation of the light from the heavy. This is why the Platonic Academy placed emphasis on a universe controlled by a rational principle rather than one under the direction of Nature.6 We may comment that scholastic Aristotelians seem not to have realized to what extent they had substituted Platonic principles for Aristotelian ones that they nonetheless continued to call “Aristotelian.” It is little wonder that late medieval scholastics defended Aristotle as they did, for they blended their Platonized Aristotle with what they had come to accept as Aristotle rightly understood.7 The remainder of the genuinely philosophical portion of the dialogue returns to the argument that the Moon is Earth-like. The text appeals to optical phenomena and eclipses, all of which support the conclusion that the

3

De facie, 71–73, 925 A-C. Ibid. 77–83, 925 F-926 E. Compare with Copernicus’s arguments from De revolutionibus I, 4–10, which are examined in chapter nine. 5 De facie, 89–91, 927 D-928 A. 6 Ibid. 91–95, 928 A-D. 7 Di Napoli, 346–347, points out that Ficino too oriented Aristotle to Plato, meaning that he interpreted Aristotle in a Platonic way. See also Monfasani, “Marsilio Ficino,” 195–196. 4

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Moon must have the same consistency as Earth, for the same effects must be produced by similar agents.8 A little later, the possibility of habitation on the Moon is discussed, leading to the speculation that if the Moon moves and rotates, then it would have to be gentle and smooth enough so as not to pose any danger to those on it. The rotation “smooths the air and distributes it in a settled order, so that there is no danger of falling and slipping off for those who stand there.”9

8

De facie, 99–121, 929 A-932 C. Ibid. 157–167, esp. 167, 938 F-939A. Note the implication that if the Moon rotates, then rotation must be natural to it. 9

APPENDIX VI EXCURSUS ON TRANSMISSION This is a difficult subject to discuss in the current environment. There is no doubt that Islamic astronomers and mathematicians of the Middle Ages and well into the fifteenth century were far ahead of their western Latin contemporaries.1 The appearance of several mathematical solutions in the Latin West from the fourteenth to the sixteenth century that seem to descend from Islamic predecessors has inspired a perfectly legitimate hypothesis, namely, that there must have been a connection and that these solutions and models were transmitted by Byzantine or Latin intermediaries that have either disappeared or have not yet been discovered. Some scholars speak of the hypothesis as if it were a certainty. A recent example confirms the extent to which even knowledgeable and highly regarded scholars have adopted the hypothesis as fact: We should not be surprised, then, that Nicolaus Copernicus (1473–1543) gained insight into the mathematical problems concerning the motions of the planets from the work of the astronomers at the Maragha observatory, in particular that of Nasir al-Din al-Tusi (d. 1274).2 All I wish to emphasize is that even a highly likely hypothesis is still just that until the missing link is found, and that in the meantime we ought to entertain other possible hypotheses. What follows is less a fully articulated hypothesis than a series of observations and questions that suggest how certain problems may have inspired solutions that were similar, so similar in fact that it did not seem possible that they could have been discovered independently. Of course, they may not have been constructed independently, but post hoc ergo propter hoc is a fallacy, and the contrary claim that it is impossible for them to have been discovered independently in the absence of the hypothesized source is also fallacious. How, then, would the story go? It is striking to read all of the articles describing the problems and solutions. In mathematics there are probably no unique solutions to a problem, although some are certainly more elegant than others. Still, there is a selection. We have been introduced to solutions that are similar. Now, what is there about these problems that “led to” specific kinds of solutions? These kinds of solutions began to appear in the Latin West in the fourteenth century. Part of the background here includes either rejection or

1 Endress, “Mathematics”; King, In Synchrony; and Sabra, “An Eleventh-Century Refutation” are representative and exemplary. 2 Smith, “Science on the Move,” 370–371.

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neglect of Aristotelian/Averroist prohibitions that restricted the application of mathematics to analyzing problems. Although the applications were mostly in hypothetical, theoretical, or imaginary contexts, they challenged standard philosophical solutions. Because natural philosophy and astronomy were primarily speculative or theoretical sciences, the “practice” of natural philosophy and astronomy meant carrying out thought experiments and evaluating them for their logical consistency and coherence.3 In responding to Averroes’s objections to Ptolemaic models, some astronomers distinguished between the considerations proper to philosophy from those proper to astronomy. Philosophers regard spheres as concentric because they refer all of the motions to the prime mobile or the starry vault, the proper motion of which is diurnal, and it carries or influences all of the motions below it. Astronomers consider this motion, of course, but they also consider the proper motions of lower spheres, and these motions are proper to astronomy. The motions of lower spheres compelled astronomers to develop mathematical models, mechanisms, or devices to account for these motions. These considerations usually generated eccentric, epicycle, and equant models. On the other hand, some philosophers or astronomers who treated the proper motions of the lower spheres attempted to find solutions that minimized the inconsistencies between the models and the philosophical axiom about the uniform, circular motions of the spheres concentric to Earth. Turning now to the history of the transmission of models, we may observe that in several seminal and otherwise important articles on the resonance of Islamic solutions in the Latin West we find the same pattern. Authors recognized problems with the Ptolemaic models or accuracy of predictions, and they proposed solutions that involved generating a variety of devices. These devices are mechanisms that solve the problems by means of circles that generate a harmonic motion. These are the devices that apparently derive from the Islamic sources by way of a supposed Byzantine or Latin intermediary that has yet to be found. We cannot recite all of the details here, but it is the sketch that is suggestive. One version of this story begins with Ibn al-Haytham’s physical interpretation of Ptolemy’s planetary theory.4 Ibn al-Haytham (965–ca. 1040) proposed a physical mechanism of two concentric solid spheres (a Eudoxan device) to account for Ptolemy’s assumptions in the Almagest. In the thirteenth century, Nasir al-Din al-Tusi (1201–1274) criticized and modified Ibn al-Haytham’s solution by proposing his own that used a spherical version of his “couple.” As Mancha summarizes it, al-Tusi proved “that the spherical version of his ‘couple’ may also be applied to three similar problems involving an oscillatory motion of a point along an arc of a sphere: the oscillation of the inclined planes of the eccentrics of Venus and Mercury, the change in the obliquity of the ecliptic between a maximum and minimum value,

3 4

Podkoński, “Charm.” Sabra, “Refutation,” 121; Mancha, “Homocentric Epicycles,” 70–73.

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and trepidation.”5 Three astronomical texts of the fourteenth and fifteenth centuries describe physical arrangements of two concentric spheres describing the epicycle or eccentric similar to that of Ibn al-Haytham. Henry of Hesse, magister Julmann, and Albert of Brudzewo describe arrangements of two concentric spheres. Brudzewo explicated a passage in Peurbach’s Theoricae. Peurbach’s own description is unclear, but Brudzewo attributes the arrangement to some unknown author. Because Hesse’s text also suggests dependence on some unknown source, it seems likely that Hesse, Julmann, Brudzewo, and possibly Peurbach took the Eudoxan device from a source that described Maragha planetary theory. In any case, these three and possibly all four authors used two homocentric spherical devices to provide a physical mechanism to account for “the different oscillatory motions of the Ptolemaic epicycle diameters required by the equant and latitude theory.”6 Now, Brudewo seems to have known Hesse’s argument,7 and Regiomontanus certainly knew it.8 Julmann seems to provide additional evidence that the device circulated, as it were, among late fourteenth-century authors, and, in any case, his elaborations seem to depend on Hesse.9 In short, the intermediary may have been a text on which Hesse drew. And here I suggest that we insert Oresme’s “rolling device.”10 The context of Oresme’s discussion is the question whether any heavenly body moves circularly? After presenting several observational reasons supporting a negative answer, Oresme responds to the Aristotelian and Averroist objections that the heavens move regularly. His first conclusion is that a planet can move naturally with rectilinear motion that is composed from several circular motions. To my knowledge there are only two editions and explications of Oresme’s text, one published and the other an unpublished doctoral dissertation. I quote the principal sections here:11

5

Mancha, 82. See also Sabra, 122–124. Mancha, 81. 7 Mancha, 86–87, n. 20. 8 Mancha, 82, n. 4. 9 Mancha, 78. 10 Droppers, Questiones; and Kren, “Rolling Device.” 11 Oresme, Questiones de spera, ed. Droppers, Q. 13: “Utrum quodlibet corpus celeste moveatur circulariter. Et arguitur quod non primo de luna quia per experientiam videmus lunam moveri tardius motu proprio quando est in oppositione et coniunctione et velocius quando est in quadraturis et e contrario est de motu diurno. Secundo, dies naturales sunt longiores in illo tempore et in alio breviores. Ergo sol movetur irregulariter. Consequentia tenet quia dies naturalis est revolutio solis super terram. Et antecedens patet per auctorem de Spera, et per omnes astrologos. Unde repertum est quod dies naturales sunt longiores in estate quam in yeme et quod una medietas anni est maior quam alia. Tertio, sol aliquando describit minorem circulum in uno tempore quam in alio. Ergo sol movetur irregulariter. Consequentia tenet ex diffinitione irregularitatis. Antecedens patet quia circulus tropici est minor quam circularis equinocialis ut dicit auctor in littera et tamen sol describit tropicum in uno die naturali et in alio describit equinocialem. Quarto, auctor de Spera dicit quod signa 6

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Whether any heavenly body moves in a circle? Some argue that it does not, because we observe in ordinary experience that the moon moves more slowly in its proper motion when it is in opposition and conjunction, and more quickly when at quadrature, and it moves in a contrary manner in its diurnal motion. Second, the natural days are longer at one time of the year and shorter at another; therefore, the Sun moves non-uniformly. The consequence holds because a natural day is the revolution of the Sun around the Earth. The antecedent is evident [because] supported by the author of the Sphere and by all astronomers. Hence, we find that the natural days are longer in the summer than in the winter, and that one-half of the year is greater than the other half. Third, the Sun sometimes describes a smaller circle at one time than at another; therefore, the Sun moves non-uniformly. The consequence holds by virtue of the definition of “non-uniformity.” The antecedent holds because the tropic circle is smaller than the equinoctial circle, as the author says in the text; nevertheless, the Sun describes the tropic circle in one natural day and the equinoctial circle in another. Fourth, the author of the Sphere says that the signs rise non-uniformly, for some rise more quickly and some more slowly. Fifth, astronomers maintain that certain planets are sometimes retrograde and sometimes stationary, for the planets are said to be stationary when they seem to stand still and delay their initial motion because they do not move as quickly as they did before. . . . Aristotle and the Commentator (On the Heavens, Book II, comment 39) hold the opposite, maintaining that heaven does not accelerate at some times or decelerate at other times.12 In answer to this question I propose three elegant conclusions. First, it is possible for a planet to move perpetually according to its own nature with a rectilinear motion composed of several circular motions. This motion can be accomplished by several intelligences, any one of which may endeavor to move with a circular motion without being frustrated in its purpose. To prove this, let us suppose by imagination, as the astronomers do, that A is a deferent circle of some planet, or its center, B is the epicycle circle of the same planet, and C is the planetary body or its center—I take these to be the same.

oriuntur irregulariter. Unde quedam oriuntur velocius, quedam tardius. Quinto, per astrologos qui ponunt quasdam planetas aliquando retrogrades, aliquando stationarios, planete enim dicitur stationarius eo quod videtur stare et cessare a primo motu quia non movetur ita velociter sicut ante. . . . Oppositum patet per Aristotelem et Commentatorem Secundo Celli, commento 39, ubi point quod cellum non vigoratur aliquando in motu nec aliquando tardatur.” The translation is mine. 12 From this point on, the Latin text is available in Kren, “Rolling Device,” 491–492.

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appendices Let us further imagine that the line BC extends from the center of the epicycle to the center of the planet, and that the line CD is a line on the planet on which BC falls perpendicularly. Let circle A move on its center toward the east, and circle B toward the west, while the planet C revolves on its center toward the east. Therefore, because line BC is always equal (for it is a radius), I maintain that the distance that B descends with the motion of the deferent is the distance that point C ascends with the motion of the epicycle. From this it follows evidently that point C will move in a certain time on a straight line. Further, I maintain that as point B ascends on its circumference so will the planet ascend. It is evident that the point D will move continuously on the same line. Therefore the whole planetary body moves with a rectilinear motion to some point and returns again with an entirely similar motion.

Skipping over the responses to objections, I now turn to the four corollaries: First, at least three circles are required for such a rectilinear motion. Second, circular motion never arises from rectilinear motion, nor does rectilinear motion result from rectilinear and circular motions, but a rectilinear motion can result from several circular motions. Third, the conclusion drawn by Aristotle and the Commentator that no rectilinear motion of heaven is possible is false. . . . Fourth, it is possible to imagine a rectilinear motion that is eternal with the exception that at the point of reflection the moving body would not be said to move or rest. None of the manuscripts provides a figure, leaving readers to construct their own. The first explication, by Claudia Kren, does not fit Oresme’s description very well. In her figure 1, she provides a version of al-Tusi’s rolling device, and supposes that Oresme produced a garbled description of the Tusi couple.13 This interpretation is implausible. Even if by “deferent circle” Oresme means a sphere on the inside surface of which an epicycle is rolling, he says explicitly that the solution requires at least three circles, but the rolling device has only two circles, or one circle rolling inside a sphere. Next, Oresme says nothing about having relied on a source. On the contrary, he suggests that the idea that circular motions can be combined to generate a rectilinear motion is obvious. Now, the text does not support that claim, but the idea of constructing a rectilinear motion by combining circular motions is explicit, and Oresme does not suggest an application other than an astronomical one, as his examples and references indicate. In his explication and more detailed illustration, Droppers makes an additional assumption, namely that the radius of the epicycle carrying C must be

13 Kren refers to Droppers’s dissertation, but she does not comment on or criticize his reconstruction.

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A = center of deferent. B = center of epicycle. C = center of planet. C2 and C4 = extremes of straight-line path of center C. CD = line in planet ⊥ to CB.

Figure 5—Droppers’s representation of Oresme’s Reciprocation Device. (From Droppers, p. 287) twice the length of the deferent carrying B. Oresme says nothing about the length of the radii, yet Droppers assumes here that there must be a 2:1 ratio, and supplies the following illustration: The motion of C around its center B is non-uniform because as B sweeps out angle α in some uniform time, C sweeps out angle α + β. Angle β continuously varies, and when angle α = 180o (at B3), angle β = 45o. Perhaps a simpler mathematical solution can be seen in the following illustration, although it is a figure interpreting the Tusi couple. In sum, Oresme describes a reciprocation device, and he employs an epicycle model. The likeliest interpretation is that he hit on a solution similar to the Tusi couple, but there is no indication that Oresme was directly concerned with the physical characteristics of the bodies or the mechanisms. In fact, he takes it for granted that the motion proceeds from several intelligences. He presents it simply as a geometrical solution of a geometrical problem, albeit in the context of a discussion about the circular motions of heavenly bodies. It is very likely that Hesse was familiar with Oresme’s works, a likelihood that extends to Julmann. Almost no one has doubted Oresme’s originality or ingenuity. Still, it may be that Oresme saw some Islamic solution, but his version constitutes hardly more than a hint, which might explain Hesse’s silence. If Hesse and Julmann elaborated on a suggestion in Oresme, then we

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A = center of a deferent circle. B = epicyclic circle revolving on circumference of A to the west. C = center of the planet to east. D = point on circumference of planet such that CD ⊥ BC (not drawn; see Figure 5). B1B2B3B4 = successive positions of B. C1C2C3C4 = successive positions of C corresponding to those of B. R = radius and RB = 2RA. ∠ α = ∠ described by B revolving on A. ∠ β = ∠ described by C around B (and it varies as explained).

Figure 6—Droppers’s Interpretation of Oresme’s Reciprocation Device. (From Droppers, p. 461)

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A combination of uniform circular motion can be devised to produce motion in a straight line. a. First, imagine (above) a circle of diameter d rolling on a flat surface. A planet fixed to the circle moves halfway around the circle as the circle rolls a distance of half its circumference (πd/2), and completes a circuit as the circle rolls a distance πd. b. Next (above), curve the flat surface into a circle of diameter D, with D = 2d. (The new circle is twice the size of the original circle.) Roll the small circle inside the large circle. A point on the small circle will come back into contact with the circumference of the large circle after one complete turn of the small circle. This occurs after the small circle moves a distance πd (its circumference) around the large circle, or halfway around the large circle (πd = πD/2). c. Finally, as the small circle rolls around the inside of the large circle, a point (planet) on the small circle constantly falls along a straight line, which is also a diameter of the large circle (in this case, the vertical diameter). Three positions of the small circle are shown above. Intermediate positions also place the planet on the same straight line. The net result is to convert uniform circular motion into seemingly straight-line motion.

Figure 7—Straight-line motion from circular motion. (From Hetherington, p. 79)

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may suppose that Oresme may be either the Latin intermediary who saw or heard of the Maragha mechanism, or that Oresme himself produced it while contemplating a geometrical problem. As for double-epicycle models, as we saw in chapter five, Sandivogius proposed one as a solution to account for the observations of the Moon; it was adopted by Brudzewo, and Copernicus certainly could have heard about Brudzewo’s double-epicycle model even if he did not know the Commentariolum directly.14 None of this sketchy reconstruction is intended to minimize the originality of Islamic astronomers.15 Copernicus’s use of these devices, however, seems to derive from his critical evaluation of the work of his teachers and Regiomontanus’s Epitome. From the former he may have adopted double-epicycle models, and from the latter his acquaintance with Hesse’s use of two concentric spherical mechanisms. It would follow, then, that Copernicus did not invent or discover these solutions independently, but that he adopted and modified solutions deriving immediately from Brudzewo and Regiomontanus, and indirectly from Oresme and Hesse. Di Bono has offered an alternative reconstruction. I am persuaded by his critique of the usual scenario, but the dependence of his argument on the homocentric astronomy of the Paduan school, while plausible—especially the return to Eudoxus and Callippus—remains as nebulous as the supposed missing textual link. Still, as di Bono pointedly emphasizes,16 when Copernicus took up the demonstration of the harmonic linear motion in De revolutionibus, he elaborated it independently. Why would he have done so if he had just copied it? Di Bono’s second hypothesis seems even likelier, namely, that from critical reflection on problems with the Ptolemaic system, Copernicus followed the same path more or less to results very similar to those obtained by his predecessors. Di Bono’s dismissal of textual or pedagogical precedents at Cracow leaves him without a textual basis for Copernicus’s initial versions in Commentariolus. Copernicus’s recognition of problems with the Ptolemaic system, his likely familiarity with the mechanisms described at Cracow, his reliance on Regiomontanus’s Epitome, and the internal logic of the methods employed by the Islamic astronomers and Copernicus—all together may be sufficient to explain Copernicus’s derivation of the reciprocation device. I conclude this excursus with some consideration of Dobrzycki’s and Kremer’s comment on di Bono’s argument.17 They assert that their reconstruction of Johannes Angelus’s tables weakens di Bono’s claim “that Copernicus rein-

14

Rosińska, “Al-Tusi and al Shatir.” Ragep, “Ali Qushji,” 363, shows that there was also a fifteenth-century Islamic precedent for Regiomontanus’s use of eccentric models to account for the motions of Mercury and Venus, and again there is a striking similarity between the geometrical figures. Ragep finds parallel developments implausible, but if the scenario developed here is correct, then some of the solutions in the West appear already in the fourteenth century and not just “in a fifty-year span in the last part of the fifteenth century.” 16 Di Bono, “Copernicus,” 147. 17 “Peurbach,” 33, n. 55. 15

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vented the Tusi couple rather than borrowing it from Islamic traditions via unknown sources.” The logic of this assertion eludes me. Their reconstruction is ingenious, but, first, even if their claim that Angelus’s parameters for longitudes cannot be reproduced by modifying the geometry of Ptolemy’s models in obvious ways—asserted and not proved with only one alternative actually eliminated—and their further claim that their reconstruction is a unique solution are true, they do not prove that mechanisms of harmonic motion rely on an Islamic source or an intermediary. They simply repeat the usual assumption. Di Bono does not deny that the hypothesis about an Islamic intermediary may be correct; his argument is that the hypothesis remains unconfirmed, and that it does not explain Copernicus’s independent elaboration of some of the mechanisms. Second, how can a hypothetical reconstruction based on a still unconfirmed hypothesis weaken a reconstruction that demonstrates the differences between Copernicus’s versions and the Islamic solutions? It is in such contexts that hypotheses about Maragha have taken on the status of dogma. It remains a hypothesis, and one that may turn out to be based on a ghost. From someone who regards the connection as likely, Emilie Savage-Smith offers an important reminder:18 As for the hypothesis that there was a causal link between the activities of the later Islamic astronomers and the development of Copernican astronomy, it remains only a hypothesis until the mechanism for such borrowing can be found. Yet the evidence is mounting for some form of connection, especially given the sudden appearance in Europe of technical geometric innovations that had a centuries-long tradition in Islam. All of that said, scholars convinced of the hypothesis should continue to search for the intermediary link. It may yet turn out to be correct, and the fact remains that the Maragha hypothesis still provides the most complete version of the models that Copernicus could have adapted both in the Commentariolus and De revolutionibus. I would welcome the discovery for it would finally put all of the speculation, including mine, to rest. In the meantime, however, I urge others to read the literature on Oresme, Hesse, Julmann, Sandivogius of Czechel, Albert of Brudzewo, Peurbach, and Regiomontanus, and consider all of it with the following consideration in mind. Historians have long recognized Oresme’s ingenuity and precociousness as compared with his contemporaries. Scholars, Marshall Clagett in particular, have questioned his influence beyond the early fifteenth century.19 What I am suggesting here is the possibility that Oresme’s cryptic geometrical proposal of a reciprocation device along with an epicycle model in De sphera was the Latin source for some of the later elaborations of these techniques. The path to Copernicus would have proceeded from Oresme to Hesse, Julmann, and Sandivogius, and from them to Peurbach, Brudzewo, and Regiomontanus. On the basis of what we find in both Brudzewo and Regiomontanus, we can try to reconstruct

18 19

“Islamic Influence,” 540. Clagett, Nicole Oresme, 3.

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Copernicus’s elaboration of the models, and in these cases, at least, we have reasonable grounds for believing that Copernicus knew them. The weakest connection is his knowledge of Hesse’s treatise, leaving us to speculate that Copernicus may have been acquainted with the version of it that Regiomontanus had preserved, or that Novara saw the treatise and communicated its solution to Copernicus.

APPENDIX VII EXAMPLES FROM CHAPTER 8, SECTION 7 Example 1: (Ia) If hypotheses (A) should be relevant to the consequent (B), then astronomical hypotheses (A) should be relevant to the structure of the universe (B). (II) Hypotheses should be relevant to the consequent; therefore, (III) Astronomical hypotheses should be relevant to the structure of the universe. Example 2: (Ia) (Ib) (II) (III)

If the efficient cause is good, then what God creates is good. What is good is well ordered. The efficient cause is good; therefore, What God creates is well ordered.

Example 3: (IA) If the whole is well ordered, then the parts are linked together. (IB) If parts are linked together, then the parts cannot be shifted without disruption of the whole. (II) The whole is well ordered; therefore, (III) The parts cannot be shifted without disruption of the whole. Example 4: (IA) (IB) (II) (III)

If a form is spherical, then circular motion is proper to the form. What is proper to the form is proper to the sphere. The form is spherical; therefore, Circular motion is proper to the sphere.

Example 5a: (Ia) If the distances between one part and the whole vary, then either the part moves or the whole moves. (Ib) From the observation of motion alone without a third fixed reference point we cannot tell whether the part moves or the whole moves (the principle of relativity of motion). (II) The distances vary; therefore, (III) We cannot tell whether the part moves or the whole moves. Example 5b: (Ia) If the part does not move, then the whole may or may not move. (Ib) From the non-motion of the part, we cannot infer the motion of the whole (topic from the part).

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(II) The part does not move; therefore, (III) The whole may or may not move. Example 6: (Ia) If Earth is located and enclosed, then its rotation accounts for the observation of daily rotation of the celestial sphere. (Ib) Rotation should be attributed to the located and enclosed rather than to what locates or encloses (a topic proper to metaphysics). (II) Earth is located and enclosed, heaven locating and enclosing; therefore, (III) Earth’s rotation accounts for the observation of the daily rotation of the celestial sphere. Example 7: (Ia) If Earth’s eccentricity and distances in relation to the Sun and planets vary, then Earth approaches to and withdraws from the Sun and other planets. (Ib) The variable eccentricities and distances of a body with respect to other bodies can be explained more naturally and more simply by the motion of the one body relative to the other bodies (topic from the whole and the principle of simplicity). (II) Earth’s eccentricity and distances relative to the Sun and planets vary; therefore, (III) Earth approaches to and withdraws from the Sun and other planets. Example 8: (Ia) If rotation is natural to a sphere, then Earth’s rotation is a natural effect. (Ib) What is natural has natural effects. (II) Rotation is natural to a sphere; therefore, (III) Earth’s rotation is a natural effect. Example 9: (Ia) If planets move away from and towards Earth, then Earth is not the center of their motions. (Ib) Circular motions around the center exclude motions away from and towards the middle. (II) Planets move away from and towards Earth; therefore, (III) Earth is not the center of their motions. Example 10a: (Ia) If Earth orbits the Sun, then the observed retrograde motions of the planets are an optical illusion. (Ib) An optical illusion is caused by the proper motion of one body relative to the proper motions of other bodies (a warrant or topic proper to optics). (II) Earth orbits the Sun; therefore,

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(III) The observed retrograde motions of the other planets are an optical illusion. Example 10b: (Ia) If Earth and the planets orbit the Sun, then the Sun is the body near the center of the planetary motions. (Ib) The body near the center of the planetary orbits is the mean center of their motions. (II) Earth and planets orbit the Sun; therefore, (III) The Sun is the mean center of the planetary motions. Example 11a: (Ia) If Mercury and Venus are arranged around the Sun according to their bounded elongations, then they are arranged according to their distances from the Sun. (Ib) The distances of planets correspond to the duration of their orbits (calculated by Copernicus and the principle was adapted from the standard view of the orbits of Mars, Jupiter, and Saturn). (II) Mercury and Venus are arranged around the Sun according to bounded elongations; therefore, (III) Mercury and Venus are arranged according to the duration of their periods. Example 11b: (Ia) If Mercury and Venus are arranged according to the duration of their orbits, then all of the planets are arranged according to their sidereal periods. (Ib) The position of Earth’s orbit outside the orbits of Mercury and Venus explains the bounded elongations of Mercury and Venus and why we see the remaining planets in opposition (natural explanation of observations). (II) Mercury and Venus are arranged according to the duration of their orbits inside Earth’s orbit; therefore, (III) All of the planets are arranged according to their sidereal periods.

APPENDIX VIII SUIDAE LEXICON, ED. THOMAS GAISFORD AND GOTTFRIED BERNHARD (1853, REPR. OSNABRÜCK: BIBLIO VERLAG, 1986) Kinesis. Motus localis in hominibus causa est mens (ipsa enim animal movet), in brutis vero sensus. Est etiam alia praeter has motus localis causa; nimirum appetitus, qui varius est, et tam facultatibus ratione praeditis quam brutis inest.—Motus etiam existit, cum res alium ex alio locum mutant.—Quae per orbem aguntur interitu vacant.—Aliter de motu. Non est, inquit [Aristoteles,] glebae naturale moveri deorsum, neque igni sursum ferri: neque enim talis motionis principium in se habent, sed extrinsecus ab alio moventur. unumquodque enim elementum in suo toto quiescit: quippe tota vel stare volunt vel in orbem moveri: est autem motio in orbem quies quaedam. Iam secundum naturam suam gleba cum movetur, in suo toto manet immobilis; quemadmodum hic ignis in sua sphaera. cum vero gleba vel aqua vel hic aer extra locum naturalem existit, singula ad totum suum tendunt, et quieti naturali restitui cupiunt. nam ab vi quadam externa ex loco naturali pulsa moventur ea via, quae est secundum naturam. quando quidem sic moventur, ut quae in alieno loco existant, et toto suo contra naturam privata sint. Non igitur motus ille secundum naturam est, quo res ad locum naturalem tendunt (alioquin enim ipsa tota sic moverentur), sed viae ad id quod est secundum naturam. Potest tamen etiam motus ille naturae consentaneus dici: eo nimirum sensu quo dicimus sanitatem esse secundum naturam, morbum vero contra naturam. illa ducit ad id quod est secundum naturam hic vero ad id quod est contra naturam. id enim quod primum movet, si quidem corpus sit, ipsum etiam movetur. movet enim baculum ianuam, et baculum manus, quae non manet immota, sed ipsa movetur. quod si primum movens sit incorporeum, nihil necesse est ipsum quoque moveri, dum alterum movet. nam deus, qui universum movet, ipse est immotus, utpote stabilem habens essentiam et facultatem et actionem. praeterea nihil eorum quae appetuntur, quamvis moveat, ideo movetur: ut neque pulchritudo movetur, quamvis amatorem saepe moveat; neque imago, quae intuentem movet; et id genus alia.—Plato cum animam dicit per se moveri, non intelligit motum localem.—Anima saepe mutationem subit, a potentia ad actum transiens: velut ab ignoratione rei ad eius scientiam. quod si mutationem subit, eadem movetur. huiusmodi autem motus et mutatio generatio quaedam est; sed non simpliciter essentiae generatio.—Differt motio ab actione, nam motio est actio imperfecta, cum actio sit perfecta. quare etiam in deo actio est sine potentia. Quaeritur autem, utrum duae sint motiones in eo qui movet et movetur, an una? et utrius sit motio, moventisne an eius qui movetur? Affirmant autem eius esse qui movetur. is est enim qui ab imperfecto progrediatur ad perfectum, non qui movet: uti se res habet in discipulo et magistro. unus est enim in utroque motus, qui a magistro profectus in discipulo desinat. Ita anima quoque movetur. nam ab imperfecto transit

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ad perfectum, neque habet actionem omnino perfectam, neque caret potentia. accedit ut in quibus prius et posterius, in iis etiam sit tempus; in quibus vero tempus, in iis etiam motio. haec enim inter se reciprocantur. quamobrem in quibus est motio, in iis etiam est tempus. in anima autem est prius et posterius; est igitur motio. esse autem in anima prius et posterius manifestum est. nam a propositione ad conclusionem transit; neque omnia simul cognoscit, sed aliud ante aliud; neque omnia quae novit, simul tractat, sed aliud quidem prius, aliud posterius; et, ut universe dicam, ab virtute ad vitium, ab ignorantia ad scientiam transit. itaque recte Plato eam per se moveri affirmat. accedit etiam Aristoteles, qui cum animam moveri negat, non hanc motionem ab ea abiudicavit, sed qualemcunque motionem naturalem nobisque cognitam. neque enim ea augetur aut imminuitur; neque qualitatis aut quantitatis mutationem subit, sed alias habet motiones, quae intellectuales sunt et maxime vitales. Movetur autem anima, cum mutationem subit: ut cum a dispositione transit ad habitum, ab ignorantia ad scientiam. Aristoteles autem eam moveri negat, ad corporeas motiones respiciens. si enim anima, inquit, non movetur per accidens, natura habebit motum; si hoc, etiam locum. omnes enim motiones corporum in loco fiunt. quicquid est enim in loco, corpus est.

APPENDIX IX COPERNICUS’S UNDERSTANDING OF PTOLEMY Following Kepler’s comment that Copernicus modeled Ptolemy rather than nature, several historians have rightly concluded that no one understood Ptolemy as well as Copernicus did.1 On the whole I agree with this judgment. There is, however, one respect in which Copernicus’s understanding of Ptolemy may have been based on a mistake or on an assumption that Ptolemy did not share. In Copernicus’s interpretation of Ptolemy’s geometrical models he adopted a “mechanical” understanding of the motions of celestial spheres that conditioned his reaction to the so-called equant model. Copernicus did not consider the possibility that Ptolemy adopted Aristotelian-like intelligences as movers of the planets, calculating and adjusting their motions as the models represented them, or simply willing them to move as needed. In his explanation of Ptolemy’s exposition of spherical mechanisms in Planetary Hypotheses, Olaf Pedersen describes a typical mechanism and comments:2 We notice that there is no sphere corresponding to the equant circle, and therefore no body revolving with uniform mean angular velocity. Thus the non-uniform motion of the deferent sphere . . . is not produced by any kinematical device, but is caused directly by the vital force of the whole system. No wonder that this force has to be conceived as an ‘intelligence’. Likewise, Bernard Goldstein emphasizes the point that Ptolemy was more concerned about periodic mean motion than uniform motion, and adds that Ptolemy understood the nature of the gods to be different from what Geminos and others believed.3 If Pedersen and Goldstein are correct, then it would mean that Copernicus misunderstood the relation between the celestial movers and the mathematical models that account for the observed motions, or, at least, that he rejected Ptolemy’s view about the movers of the spheres and planets. Copernicus’s reading of Ptolemy in this way may have been conditioned by Albert of Brudzewo’s interpretation of the equant model. Brudzewo maintained that the model could not refer to the motion of an orb, which led him to interpret the model as a mathematical fiction.4 Of course, neither of them knew the Planetary Hypotheses. Copernicus, however, drew a different conclusion, namely, that if an orb cannot move in the way described, then

1 2 3 4

For example, Swerdlow, “Copernicus,” 167; Evans, History, 425–427. Pedersen, Survey, 397. Goldstein, “Saving,” 6–10. Brudzewo, Commentariolum, 85–92.

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the model violates the fundamental axiom about uniform, circular motion. In both cases, the Averroistic objections to Ptolemy’s models may have influenced them to focus on strictly mechanical issues, thus accounting for their interpretations of the models. The distinction between instrumentalist and realist interpretations of astronomical models was falsely attributed to ancient authors. Later authors did make a distinction, attributed it to earlier authors, and thus fabricated a non-existent problem that many continued to perpetuate. The tradition also created another problem when some authors reduced causal explanation of celestial motions to strictly mechanical principles without the agency of Aristotelian intelligences or vital forces. As a result, Copernicus attributed the axiom about uniform, circular motions to Ptolemy, and then, implausibly, accused him of having violated it because he was content to solve the problem only mathematically. If Copernicus did begin his critique of Ptolemy with a mistake, the result is not as unfortunate as it might seem. The reason is that he did not stop there. The “problem” with the equant merely motivated him to look for other problems, and in most other cases he did find genuine problems with or puzzles in Ptolemy’s models that led him to seek the kind of solution out of which his hypotheses about the motion of Earth around the Sun emerged.

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Abbreviations DSB JHA PSB Rc Sc SPS ZGAE

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INDEX OF NAMES Pre-1800 Achillini, Alessandro viii, 184–188, 219, 238–243 Aelius Donatus 8 Aeneas Sylvius Piccolomini, Pius II, Pope 13, 138 Aëtius Amedinus (see also PseudoPlutarch) viii, 196, 229–230 Agricola, Rudolf 181, 281–284, 304 Albert Caprinus of Buk 18, 49 Albert (also Adalbertus) of Brudzewo viii, xxii, 15, 23, 31–36, 41, 44–49, 135, 141, 144, 148, 150, 153–156, 159–162, 218, 244, 248, 370, 376, 478, 485, 492 Albert of Pnyewy 29–32, 41, 46, 48, 161 Albert of Saxony vii, 42, 47–48, 100–104, 111–112, 128–132, 148 Albert of Szamotuli (also Schamotuli and Szamotuły) 32, 46, 48, 160–161, 191 Albert Piotrokow of Swolszowice 31, 42, 140 Albert the Great 15–16, 36, 42, 47, 54, 72, 74, 95–96, 100, 103, 107, 109, 111, 446, 449, 469, 514 Al-Bitruji 219 Albohazen Haly 191, 211 Albrecht of Prussia, Duke 293 Alciato, Andrea 178 Alessandro Piccolomini 391 Alexander of Aphrodisias 61, 449 Alexander of Hales 10, 47 Alexander of Villa Dei 9, 25 Alfonso de Corduba Hispalensis 250 Alhazen (Ibn al-Haytham) 145, 156, 382, 477–478 Alidosi, Giovanni 179, 181, 183 Ambrosius Regius 211 Amico, Giovanni Battista 262, 267–268 Andrew of Kokorzyna 111 Andrzej Grzymala 150 Antiphon 472 Antonius Andreae 42 Aratus 211 Aretino, Pietro 13

Aristarchus of Samos 202, 234–236 Aristotle ix, 10, 25, 46, 52, 55–60, 69, 72, 75, 80, 90, 92, 98, 107, 110, 112, 116, 118, 122–125, 142, 148, 171–172, 185, 187, 192, 198–199, 216, 220, 223–224, 229–233, 238–239, 242, 262, 277, 284, 289–290, 303–304, 320, 323–325, 328, 334, 336, 338, 343–347, 352, 354, 358–360, 374–375, 408, 411–417, 421, 423, 432, 435, 437, 444–460, 471–474, 480 Categories 26, 30, 53, 63, 102 De anima 26, 35, 43, 115, 350 De caelo vii, 26, 32, 37–38, 49, 95, 100, 111–114, 117, 119, 124, 126, 128, 250, 288, 311, 318, 332, 335, 339–342, 348–353, 357, 389, 392–399, 402–403, 412, 456, 479 De generatione animalium 400 De generatione et corruptione vii, 26, 32, 37–39, 95–96, 100, 114–115, 119, 127, 403 De interpretatione 26 Meteorologica vii, 26, 28, 32, 39, 95, 100, 114, 119–121, 126, 346, 389, 394, 396, 402–403 Metaphysics vii, 26, 28, 35–36, 43, 45, 49, 88, 91, 114, 121, 133–134, 222, 276, 286–287, 318, 321–322, 332–333, 389–391, 400–402, 412 Nicomachean Ethics 86–87, 135, 276, 321, 390 Parva naturalia 26, 28, 32, 37, 40–41, 115, 461 Physics vii, 26–27, 30, 35, 41–42, 45, 49, 77, 89, 91, 94–95, 99–109, 114, 117, 128, 318–319, 332, 337, 356, 376, 399–400 Posterior Analytics 26, 35, 41, 43, 51, 54, 64, 87, 337, 391, 399 Prior Analytics 26, 35, 51, 54, 64, 86–87, 135, 276, 390 Rhetoric 55, 303 Topics 26, 32, 52–55, 58–59, 61–62, 64, 73, 281, 286, 292, 296, 303 Augustine of Hippo 10, 45, 97, 224

526

index of names

Aurifaber, Johann 410 Averroes (also Ibn Rushd) 49, 86–87, 94, 100–105, 124, 134–135, 143, 148, 155, 157, 163–166, 184–186, 239–241, 250, 373, 391, 400, 413, 422, 449–452, 469, 477 Avicenna 100–101, 199, 201, 444, 449 Bacon, Francis 194 Barbaro, Ermolao 140 Bardella, Philippo 203–204 Bartholin, Caspar 425 Bartholomew of Lipnica 29, 40 Bartholomew of Oraczew 46, 160 Beldomandi, Prosdocimo 153, 162 Bellarmine, Robert, Cardinal 407, 417 Bernard of Biskupie 40, 48, 161 Bernard of Verdun 148 Beroaldus, Philip 140, 184 Bessarion, Cardinal viii, xxiii, 167, 188, 196, 208, 211–216, 220–229, 243, 251, 271, 297, 318, 390, 412 Bianchini, Johannes 25, 151, 162, 188 Biondo, Flavius 141 Blasius of Parma 98 Boccaccio 141 Boethius, Anicius 10, 26, 30, 42–44, 52–56, 59–64, 160, 181–182, 281–284, 288–289 Bonaventure, St. 10, 42, 47 Boniface VIII, Pope 177 Boniface IX, Pope 14–15 Bracciolini, Poggio 13, 139 Brahe, Tycho 166, 243, 254–255, 271, 369, 376, 381, 407, 427–434 Brożek, Jan 37, 49, 424 Bruni, Leonardo 139 Bruno, Giordano 356 Caccini, Thomas 414 Caesarius, Johannes 281–284, 304 Cajetan of Thienne 407 Callimachus (also Buonacorsi), Philip 140–142, 225 Callippus 122, 240, 244, 267, 484 Campanus of Novara 143, 147–148, 217–218 Campeggi, Giovanni 183 Capuano da Manfredonia, Giambattista 186–187 Casimir III 14 Casimir IV Jagiellon 7 Caspar Salionis Cervimontani 237 Cato the Elder 9, 102

Celtes, Conrad 26, 37, 43, 140–141, 159–160, 167 Cicero, Marcus Tullius 26, 45, 102, 140, 181–182, 214, 238, 250, 282, 284, 288–289, 345, 347–348, 374, 392 Chalcidius 237 Clavius, Christopher 391 Cleanthes 345 Cleomedes 229 Conrad Gesselen 9–10 Copernicus, Andrew 11, 19 Copernicus, Barbara 6, 19 Copernicus, Nicholas vii–viii, xiii–xiv, xvii, xxi, 1, 5–6, and passim Commentariolus xxiii–xxvi, 16, 29, 154, 157, 187, 212–216, 219, 221, 226–229, 233–243, 251–257, 261, 264, 267–272, 275, 291, 294–295, 307, 364, 375, 378–383, 388, 391, 409, 484–485 De revolutionibus xi, xxiii–xxv, 29, 37, 85, 92, 122, 124, 127, 132, 134, 144–145, 154, 165, 172, 185–188, 190, 192, 202, 206–219, 221–229, 234–235, 237–238, 242–243, 249–260, 264, 266–271, 275, 278, 292–313, 322, 326–330, 333, 336, 339, 341, 351, 355–363, 371–378, 382, 386, 388, 391–392, 396–403, 408, 411–414, 417, 420–422, 425, 474, 484–485 Letter Against Werner 47, 242, 318, 400 Letters of Theophylactus Simocatta 143, 194–196, 206, 211 Uppsala Notes xi, 146, 150–151, 249–250, 257–259, 381 Copernicus, Nicholas Sr. 19 Corvinus, Lawrence 31, 43–44, 48, 140–141, 167 Crastonus, Johannes 195–197, 211, 235 Da Montagnana, Bartholomaeus 199, 201 Da Montagnana, Bartholomaeus Jr. 201 Dantiscus, John, Bishop 213, 409, 414 D’Aquila, Johannes 199 Del Ferro, Scipio 193 Della Mirandola, Pico xxiii, 185–187, 191 Della Torre, Marcus Antonius 199 Democritus 231, 234, 468 De Sala, Antonio 183 D’Estouteville, Cardinal 73

index of names Digges, Thomas 356 Diogenes 232 Epicurus 230–232 Euclid 10, 26, 32, 45, 146, 157, 160, 191, 195, 211, 214 Eudoxus 122, 240, 244, 267, 269, 401, 484 Eugenius IV, Pope 139 Fantuzzi, Giovanni 181, 183 Ficino, Marsilio viii, 141–142, 195–196, 208–215, 221, 224–228, 235, 243, 278, 314, 318, 323, 349, 358, 471–474 Foscarini, Paolo Antonio 407, 417 Fracastoro, Girolamo (also Hieronymus) 186–187, 262, 268, 294 Francis of Meyronnes 47 Frisius, Gemma 414 Gabriel Biel 47 Gabriel Zerbus of Verona 106–107 Galen 199, 421 Galilei, Galileo 58, 166, 199, 318, 325, 407, 414 Gammaro (also Gambari and Gambarinus de Casali), Pietro 181, 183, 284 Ganfredum 29 Geminos 492 George of Trebizond 222 Gerard de Monte 134 Gerard of Cremona 147–148 Gerard of Harderwyck 42 Gerard of Sabionetta 147 Gertner, Bartholomew 19 Giese, Tiedemann xvii, 13, 37, 134, 293–294, 321–322, 400, 413–414 Gilbert, William 189, 433 Giles (Aegidius) of Rome 15–16, 47, 72, 96, 100, 103, 106–107, 241, 444, 449, 469 Gratian 176–177 Gregory of Rimini 47 Gregory of Sanok 138–139 Gregory the Great 13 Gregory IX, Pope 177 Gualterus de Vino Salvo 25 Gustavus Adolphus, King 208 Grynaeus, Simon 228 Haller, Jan 100 Henry of Hesse (also Langenstein) 127, 144, 155–159, 478, 481, 484–486

527

Hermes Trismegistus 223, 358 Hipparchus 211, 222 Hippocrates 199 Horace xvii, 25 Hugh of St. Victor 10 Ibn al-Shatir 157, 384 Ibn Rushd (see Averroes) James of Gostynin 29–30, 35, 38, 47–49, 74, 86 James of Iłzy (also Iszla) 46, 160 James of Szadek 29, 45–46 Jan Długosz 138 Jan of Dąbrówka 138 Jan of Ludzisko 138 Jan of Szamotuły (also Schamotuli and Szamotuli) 160–161 Jan Ostraróg 138, 140 Jerome, St. 13 Johannes Angelus 484 Johannes de Muris 26, 160 Johannes Peckham 26 Johannes Versoris (also John Versor) vii, 47, 72–74, 95–96, 100, 111, 122–128, 134, 322, 333, 345, 398, 402, 461–462, 470 John Argyropulos 44 John Buridan 15–16, 41–42, 47–48, 72–73, 93, 99, 107, 128, 148, 335, 340–341, 348, 373 John Duns Scotus 15, 39, 42, 72, 74, 107 John Gerson 10, 13, 47 John Gromaczky (also Gromaczki) 29–30, 46, 160 John Isner 42 John Magister 39 John of Cracow 29 John of Glogovia vii, xvii, xxii, 27–32, 35–39, 44–53, 57, 73–86, 97, 100, 103–109, 112, 128, 132–133, 150, 158–161, 219, 281–282, 373, 446, 456 John of Jandun 111, 457 John of Lesznica 29 John (also Jan) of Ożwięcimia 44 John of Sacrobosco 26, 32, 35, 41–42, 123, 147, 214, 240, 370 John of Seville 147 John of Slupy (also Słupczy) 29, 46 John of Stobnicy 40 John of Zanau 172 John Philoponus 92, 348 John Premislia 29

528

index of names

John Stöffler 269 John Teschner 11 John Wohlgemuth 10 John XXI, Pope 26 John XXII, Pope 177 Joshua 410, 415 Julmann, Magister 155–156, 478, 481, 485

Michael Falkener of Wrocław) 32, 38–40, 47–49, 73–75, 96, 98, 107, 161 Michael of Oleśnica 140 Michael Parisiensis of Biestrzykowa 29–30, 39, 47–49, 74, 82–84, 142 Michael Stanislaus of Wratislavia 18 Montaigne, Michel de 391

Kepler, Johannes xiii–xiv, xxvii, 166, 235, 277, 291, 323, 369–370, 384, 404–405, 411, 422–425, 435, 492

Nasir al-Din al-Tusi xi, 144, 154–157, 248, 261–267, 476–477, 480–481, 484–485 Newton, Isaac 90, 325–326, 427 Nicholas de Orbellis 39, 42 Nicholas Labischin 160–161 Nicholas of Cracow 45 Nicholas of Lyra 10 Nicholas of Marienwerder 12 Nicholas of Pilcza 29, 43 Nicholas Wodka of Kwidzyn 12 Nicholas V, Pope 73, 224 Nicolaus Cusanus (also Nicholas of Cusa) 341, 348–349, 356 Nicole Oresme xi, 47, 98, 112, 128, 131, 148, 155–156, 299, 334–335, 349, 478–485 Nifo, Agostino 185, 198–199, 391 Novara, Domenico Maria viii, xxiii, 152, 159, 173, 184, 187–193, 197, 202–205, 216, 219–221, 240, 370, 411, 419, 486

Lactantius 297 Laetus, Pomponius 141 Lambert of Auxerre 181 Lambert of Monte 42, 461 Lamprias 473–474 Lauterbach, Anton 410 Lawrence of Lindores 111 Lawrence of Raciborz 152 Leibniz, Gottfried 408 Leo I, Pope 13 Leoniceno, Niccolò 199–200 Leonard Vitreatoris of Dobzyc 44–45 Leutus, Antonio 203–204 Livy 138 Louis XI, King 73 Luther, Martin 276, 279, 299, 302, 406, 410 Lysis 211, 222 Macrobius 159, 238 Mästlin, Michael 291, 295, 383–384, 405, 411, 422–428, 432 Marsilius of Inghen 26, 39, 47 Martianus Capella 144, 159, 238, 250, 253–257, 313, 381–385 Martin (also Marcin) Biem of Olkusz 40–41, 48, 269 Martin Bylica of Olkusz xvii, 15, 153, 161–162 Martin Król of Żurawica 15, 40, 150, 153, 162 Martin Kułab of Tarnowiec 42, 48 Martin of Szamotuli 31 Martin of Zeburk (also Martin Jezioran) 46, 160–161 Matthew of Kobylina 30–31, 41–42, 48 Matthew of Miechów 244 Melanchthon, Philipp 181, 214, 304, 421 Metrodorus 231–232 Michael Falkener de Wratislavia (also

Offusius, Jofrancus 420 Oleśnicki, Zbigniew, Cardinal 138 Osiander, Andreas 277, 279, 315, 365–366, 410, 414–415, 418, 420, 424–425 Ovid 25 Pappus of Alexandria 10 Parmenides 228, 471–472 Paul of Venice 47, 56 Paul of Zakliczew 29, 46, 96 Paul III, Pope 223, 276, 293, 295, 321, 327, 406, 409, 411, 414 Peckau, Catherine 19 Peter Damian 13 Peter John Olivi 98 Peter Lombard 45 Peter of Spain 26, 29–30, 35, 42–46, 53, 56, 58, 62–83, 179, 181, 280–284, 289, 292, 296, 427, 441 Peter of Żnanow 152 Peter Tartaret 39

index of names Petrarch 139 Petrus Roselli 39 Peurbach, Georg 139, 143–144, 148–151, 154–155, 158–167, 172, 188, 215, 217, 220–221, 244, 370, 375–376, 478, 485 Pierre d’Ailly 148 Philolaus 233–234, 308 Plato 97, 101, 113, 119, 132, 135, 141, 144, 172, 208–215, 220–235, 243, 250–253, 256, 271, 275, 278–279, 286, 305, 312, 314, 323, 327–328, 337–338, 345, 347, 351, 357–358, 388–389, 396, 400–401, 408, 419, 449, 456, 474, 490–491 Plautus 25 Pliny the Elder viii, 121, 132, 189, 196, 199–200, 210–215, 237–238, 243, 249–250, 347–348, 355, 374, 392, 402–403 Plotinus 214 Plutarch viii, 196, 212, 227–236, 347, 395, 473–475 Poliziano, Angelo 140, 195 Pomponazzi, Pietro 184 Pontanus, Johannes 211, 271 Proclus 92, 157, 195, 214, 250, 267, 288 Profatius (Jacob ben Nahir) 153 Pseudo-Plutarch (see also Aëtius Amedinus) viii, 196, 212, 227–236, 347 Pseudo-Scotus 185 Ptolemy of Alexandria xi, xvii, 23, 32, 35, 37, 45–49, 124, 133, 143–144, 148, 153–161, 166, 174, 184, 187–188, 191–197, 206, 212–221, 225–238, 242–245, 248, 253, 257, 260, 272, 295, 300, 303–306, 309, 312, 318, 327–328, 341–342, 353, 364, 381, 384, 388, 391, 393, 398, 407–409, 412–413, 417–421, 428, 431, 434, 477, 485, 492–493 Pythagoras 231 Pythodorus 472 Quintilian

xvii, 181

Ramus, Peter 181, 391, 419 Regiomontanus, Johannes xvii, xxiii–xxiv, 15, 26, 41, 107, 127, 139, 144–146, 150, 154, 159–162, 166–167, 172–173, 187–193, 196, 205–208, 211, 214–221, 243, 248, 250, 255, 259, 261, 271, 295, 364, 478, 484–486

529

Reinhold, Erasmus 375, 421, 425 Rheticus, Georg Ioachim xvii, 88, 152, 157, 172–173, 184, 186, 188, 191, 193, 195, 197, 202, 210, 219, 228, 252, 256, 271, 276, 278, 293–294, 300, 302, 311, 314, 318, 321, 355, 390, 392–401, 404, 406–414, 418–422, 425–426, 428 Richard of Mediaevalia 47 Richard of Wallingford 164 Ristoro d’Arezzo 127 Robert Grosseteste 86, 92 Robert Holcot 47 Robertus Anglicus 375 Sabellius, Marcus 140 Sandivogius of Czechel 144, 153–156, 484–485 Schilling, Anna 409 Schönberg, Nicholas, Cardinal 409 Schöner, Johannes 172, 293, 422 Schreiber, Jerome 422 Scultetus, Alexander 409 Seleucus 232 Simon of Sierpc 31, 46, 48, 160–161 Simplicius 124 Sinclair, David 424 Spina, Bartolomeo 405, 414 Socrates 228, 471–472 Sommerfeld, Jan (also John of Sommerfelt) 29–30, 140–141 Sophocles 196 Sosigenes 377 Stanisław Biel 30, 161 Stanisław Bylica (also Stanisław of Ilkusch, Stanislaus Bylica) 30, 32, 41, 48, 160–161 Stanisław Gorky 29 Stanisław (also Stanislaus) Kleparz 32, 46, 160–161 Starowolski, Szymon 18, 36–37, 49, 269 Statius 25 Stobner, John 15, 41, 152–153 Terence 9, 25 Thales 231 Themistius 64, 103, 449 Theon 195, 211, 214 Theophrastus 61, 230 Theophylactus Simocatta 43, 194, 196, 206, 211 Thomas Aquinas 10, 15–16, 35–36, 42–47, 72, 97, 100–107, 110, 114, 116, 125, 127, 134, 241, 276, 319, 373, 387, 391, 394, 415, 417, 449

530

index of names

Thomas Cajetan de Vio 47 Thomas of Strasbourg 47 Thomas of Sutton 127 Tolosani, Johannes (also Giovanni) Maria 405, 414 Trapolini of Padua, Petrus 199 Urceo da Forlì, Antonio (also Codro) 140, 184, 195–196 Ursus, Nicolaus 425, 427 Vaclav, Saint 436 Valla, Giorgio viii, 196, 212, 227–236, 243, 247, 250, 349 Valla, Lorenzo 140, 281–282, 304 Vergil 25, 29, 44 Vitruvius 124, 238, 250 Vitus de Brunna 29

Walter Burley 47 Walther, Bernard 152, 166, 172, 192 Wapowski, Bernard 47 Watzenrode, Barbara 6 Watzenrode, Lucas, Bishop 8, 11–12, 18–19, 22–23, 207–208, 225, 270–271 Werner, John 47, 242, 318, 322, 400, 419 William of Ockham xiii, 47, 97, 185, 319 William of Sherwood (also Shyreswood) 64, 83, 181 Władisław Jagiello 14 Zabarella, Giacomo 58 Zeno 471–472 Zimara, Marcantonio 86–87, 422–423

Post-1800 Achinstein, Peter 277 Aiton, E. J. 149, 376–377, 383 Ameisenova, Zofia 141 Ashworth, E. Jennifer xv, 51, 56–57, 63, 71, 73, 78, 82, 84, 185, 203, 281–282 Aurivillius, P. F. 209 Babicz, Józef 144 Baldner, Stephen 107 Baldwin, Martha xvi Barker, Peter 149, 160, 184, 239, 293–294, 369, 371, 381, 385 Baroncini, Gabriele 297 Barone, F. 239 Barwiński, Eugeniusz 213, 226 Barycz, Henryk 38, 40, 43–44 Bayer, Greg 54 Benjamin, Francis 143, 147, 158, 217 Berger, Harald 128 Berman, Harold 173, 177 Bernhard, Gottfried 490 Bianchi, Luca 90 Biliński, Bronisław 188, 191, 225 Bird, Otto 51–52, 280 Birkenmajer, Aleksander 13, 40, 94, 134, 145, 157, 160–161, 192, 211, 345, 348, 352–353, 384, 391, 394–403 Birkenmajer, Ludwik Antoni xiv, 12, 36, 140, 146, 151, 158–162, 165, 187–193, 196, 201, 206, 208–209, 212–216, 218–219, 222, 225–226, 237–240, 244, 248, 327

Biskup, Marian 5–12, 17, 19, 21, 161, 173–175, 192, 197–200, 202, 204, 244, 248, 269, 271, 361, 409 Blair, Ann 143, 178, 237 Blake, Ralph 412 Boh, Ivan 75–81, 84, 282 Boncompagni, D. 203 Booth, Wayne 292 Bostwick, David 91 Braakhuis, H. A. G. 73 Brachvogel, Eugen 210, 212–214, 226, 236 Brown, Stephen xiv Bulmer-Thomas, Ivor 327 Burkhardt, Hans 84, 285–286, 298 Burmeister, Karl 294, 411 Busard, H. L. L. 155 Buzzetti, Dino xv Carmody, Francis 144 Caspar, Max 428–434 Celano, Anthony xvi Chabás, José 150–151 Charles-Saget, Annick 288 Charlton, William 91 Cherniss, Harold 473 Chojnacki, Piotr 52 Clagett, Marshall 155, 485 Cleary, John xiv Clutton-Brock, Martin 253–254 Cochrane, Eric 199 Cohen, I. B. 326, 435

index of names Collijn, Isak 134, 208–216, 226, 229, 236, 461 Colomb, Gregory 292 Conroy, Kathy xvi Copleston, Frederick 185, 199 Costabel, Pierre 403 Cranz, F. Edward 387 Crombie, A. C. 391, 404 Crowe, Michael xiii, 158, 302 Curtze, Maximilian 151, 195, 302 Czacharowski, Antoni 6 Czajkowski, Karol 436 Czartoryski, Paweł 146, 191, 195–196, 200, 202, 208–212, 226–227, 249 Daiber, Hans 230 Dales, Richard 92, 335 Dallari, Umberto 179, 181, 183, 192–193 Danielson, Dennis 302, 414 De Bustos Tovar, Eugenio 404 De Haas, Franz xiv Denifle, Heinrich 173 De Pace, Anna 228, 279 De Rijk, L. M. 30, 64 Derolez, Albert 146, 209 Desrosiers, Nathaniel xvi, 350 Dianni, Jadwiga 145 Di Bono, Mario xix, 143, 154–157, 184, 239, 261–269, 484–485 Diels, Hermann 230 Dijksterhuis, E. J. 144, 159 Dilg, Peter 201 Di Napoli, Giovanni 222, 224, 474 Dinneen, Francis 63 Dobrzycki, Jerzy 5, 8–12, 24, 146, 150–151, 155, 161, 197, 206, 216, 244, 381, 404, 484 Domenkos, Leslie 162 Donahue, William 404, 428, 432–434 Drake, Stillman 338 Dreyer, John 262 Droppers, Garrett xi, xix, 155, 478, 480–482 Dufour, Carlos 84, 285–286, 298 Duhem, Pierre 327, 361, 373 Dunne, Michael xiv Eastwood, Bruce 159 Ebbesen, Sten 51–52, 61–62, 80 Egan, Regina xvi Eisenstein, Elizabeth 180, 182 El Bouazzati, Bennacer xiv Endress, Gerhard 476

531

Estreicher, Karol 39 Evans, James 130, 206, 260, 327–329, 383–384, 428, 492 Everett, Glenn xvi Farndell, Arthur 228 Favaro, Antonio 199 Finocchiaro, Maurice 407, 417 Freeman, James 292 Friedberg, Helena 45 Funkenstein, Amos xiii, 335 Furley, David 104 Gaisford, Thomas 490 Gardenal, Gianna 230 Gariepy, Thomas xvii Garin, Eugenio 196, 276, 414–418 Gąssowski, Jerzy iv, 436 Genequand, Charles 143 Geyer, Bernhard 100, 159 Ghisalberti, Alessandro 107 Gilbert, Neal 203 Gill, Mary Louise 228 Gilson, Étienne 144 Gingerich, Owen xiii–xv, xxvi, 7, 150–151, 206, 254, 362, 409, 421–425, 433–434 Goddu, André 47, 55, 69, 72, 76, 79–84, 89, 93, 100–101, 107, 110, 122–128, 131, 142, 146, 187, 209–212, 226–227, 238, 244, 248–249, 253, 255, 275, 277–278, 282, 285, 296, 319, 326, 333, 338, 345, 388, 415, 426–427, 436 Golden, John xvi Goldstein, Bernard 124, 149–150, 215, 219, 249–250, 255, 293–294, 327, 369, 377, 381, 492 Golińska-Gierych, M. 201 Górski, Karol 5, 8, 13–14, 18 Grässe, Johann 237 Grafton, Anthony xxvi, 143 Granada, Miguel 143, 187, 239–240, 294–295, 356, 414, 433 Grant, Edward 90, 92, 97–98, 104, 143, 149–150, 358–359, 370, 373–376 Green-Pedersen, Niels 52, 59, 62, 64, 80, 282–283 Grendler, Paul 174–179, 198–200 Grootendorst, Rob 292 Guthrie, W. K. C. 288, 392 Hajdukiewicz, Leszek 24 Halecki, O. 138 Hamel, Jürgen 6, 20, 271

532

index of names

Hamesse, Jacqueline 81, 116 Hankins, James 222 Hartner, Willy 154 Hartwig, Otto 159 Heiberg, J. L 230 Heilbron, John 404 Heninger, Jr., S. K. 159 Henry, Desmond Paul 285, 289 Herbst, Stanisław 9 Hetherington, Norriss xi, xix, 483 Hilfstein, Erna 18, 36–37, 49, 269 Hipler, Franz 5, 8, 10, 20, 36, 152, 187, 195, 208, 210–213, 226, 341 Hooykaas, Reijer 344, 351 Hope, Richard 286–287, 402 Horne, Michael xvi Hoskin, Michael xix Houtlosser, Peter 303, 323 Hugonnard-Roche, Henri 276, 371, 390 Hussey, Edward 94, 320, 337 Ingarden, Roman 373 Ingram, David 351 Jacobi, Klaus xvi, 83 Janik, Allan 292, Jardine, Lisa 280–282 Jardine, Nicholas 158, 372, 376, 378, 380, 404–405, 427, 433 Jarrell, Richard 254, 422, 433 Jarzębowski, Leonard 210 Jervis, Jane 360 Johnson, Monte 93 Jordan, Mark 95, 387 Jung, Elżbieta xiv Jurkiewicz, Beata 436 Juznic, Stanislaw 404 Karliński, Franciszek 11, 25, 28–33, 36, 38–46, 96, 160 Kempfi, Andrzej 414 Kennedy, E. S. xix, 154, 264–265 Kiełczewska-Zaleska, Maria 8 King, David 476 King, Peter 285–286, 288–289 Kirschner, Stefan 200–202 Kiryk, F. 46 Knoll, Paul 137–140, 142, 158 Knorr, Wilbur 243, 327 Knox, Dilwyn xv, 91–92, 97, 102, 107, 117, 132, 195–196, 214, 225–227, 234–238, 250, 256, 288, 330, 333, 335,

339, 342–345, 347–353, 357, 360, 392, 394, 396, 401–403 Koczy, Leon 138 Kokowski, Michał xiv, 95, 300, 333–335, 338–343, 345, 347–348 Kolberg, Anton 213 Kolberg, Joseph 187, 210, 212–213 Korolec, Jerzy 39 Koutras, Demetrios 59, 277 Krafft, Fritz 235–236, 347, 383 Kremer, Richard 152–153, 155, 192, 419, 484 Kren, Claudia 155, 159, 478–480 Kristeller, Paul 209 Krohn, Knut 436 Krókowski, Jerzy 141 Kruiger, Tjark 292 Kubach, Fritz 7 Kuhn, Heinrich 387 Kuhn, Thomas xiii Kühne, Andreas 173, 200–202 Kuksewicz, Zdisław 89 Kurdziałek, Marian 89 Lai, T. 356 Laird, Walter Roy 58 Lakatos, Imre 90 Lang, Helen 89, 93, 101, 111, 335 Lee, H. D. P. 346 Leijenhorst, Cees 387 Lemay, Richard 147, 159, 191 Lerner, Michel-Pierre 143, 149, 218, 276, 369, 372, 376–378, 385, 390, 413–418 Lesnodorski, Bogusław 8 Lewicka-Kamińska, A. 461 Lhotsky, Alphons 141 Lines, David 174–175 Litt, Thomas 375–376 Lloyd, G. E. R. 327 Lohr, Charles 79, 87, 89, 423 Longeway, John Lee 185 Lüthy, Christoph xiv Łoś, Jan 213 Mack, Peter 281–282 Maclean, Ian 203 McMenomy, Christe 32, 149–150, 369, 376 McMullin, Ernan xiv, 94, 300, 319 Madyda, Władysław 138 Magee, John 288 Mahoney, Edward 185

index of names Maier, Anneliese 89, 93, 98, 111 Maierù, Alfonso xv Malagola, Carlo 140, 173–175, 187–188, 192–194, 196 Małłek, Janusz 9 Malmsheimer, Arne 228 Mancha, José Luis 145, 156, 477–478 Mandosio, Jean-Marc 195 Markowski, Mieczysław 12, 15–16, 21–22, 35–42, 46–49, 52–53, 72–75, 80, 82, 86, 89, 94–100, 106, 111–112, 122, 128, 142, 144–145, 149, 153, 158–162, 343, 358, 373, 456 Martens, Rhonda 435 Martin, Craig 120 Matsen, Herbert 185 Methuen, Charlotte 405 Mett, Rudolf 162 Metze, Gudula 436 Meyer, Christoph 177 Mignucci, Mario 54 Mikulski, Krzystof 18, 138 Mincer, Franciszek 207 Moesgaard, Kristian 408, 425 Mohler, Ludwig 221–222, 224 Monfasani, John 224, 474 Mooney, Susan xvi Moraux, Paul 326, 332, 341, 348, 372, 394–397, 400–403 Moraw, Peter 13–18, 22, 49, 138 Morawski, Casimir 17–18, 29, 138, 140 Mortari, Vincenzo 180–183 Morysiński, Tadeusz 436 Moss, Jean Dietz 280, 301 Muczkowski, Jósef 26, 29 Müller, Rainer 173 Murdoch, John xiv Musiatewicz, Mikołaj 436 Naas, Valérie 237 Nardi, Bruno 185 Neugebauer, Otto xxvi, 6, 144, 151, 154–155, 194, 216–219, 260, 269, 302, 328–329, 333, 365, 371, 374, 377, 381–384 Nobis, Heribert 187, 192, 230 Norlind, Wilhelm 299, 302, 410 North, John 150 Nowak, Zenon 5, 8–13 Obrist, Barbara

347

Pacanowski, Grzegorz Pakulski, Jan 36

436

533

Palacz, Ryszard 15–16, 25–26, 36, 38, 73, 75, 89, 100, 111, 159, 373, 444, 448 Pantin, Isabelle 404–405 Papritz, Johannes 18 Patar, Benoît 340 Pawlikowska-Brożek, Zofia 36 Pedersen, Olaf 135, 143, 147, 156, 158, 166, 326–327, 492 Pennington, Kenneth 177 Pepe, Luigi 204 Perlbach, Max 17 Perry, Heather xvi Piasecki, Karol 436 Pihl, Mogens 143, 326–327 Pinborg, Jan 52, 55, 60–61, 65 Pociecha, Władysław 134, 321 Podkoński, Robert xiv, 477 Poschman, Brigitte 7 Poulle, Emmanuel 6, 150, 152, 160 Price, Derek de Sola 150, 153 Prowe, Leopold 5, 8, 10–12, 43–44, 151, 173, 175, 184, 188–198, 203, 208, 211, 244, 361 Pruckner, Hubert 159 Rabin, Sheila 6, 191 Ragep, F. Jamil 154, 262, 484 Randi, Eugenio 90 Rashed, Roshdi xix Read, Stephen 82, 277 Reeds, Karen 201 Rieke, Richard 292 Risse, Wilhelm 280 Roberts, Victor 154 Rose, Paul Lawrence 143, 312, 314 Rosen, Edward xxvi, 5, 8–9, 18, 24, 49, 127, 137, 145, 150, 172–75, 184–197, 200, 202, 211, 215–216, 219, 222–223, 227–229, 234–238, 243–252, 256, 264–270, 276–278, 282, 294, 296–297, 311, 314, 318, 321, 325, 327, 330, 340–341, 345–346, 348, 355, 358, 361, 364, 371–372, 375, 378, 381–382, 389–390, 394–403, 409, 412 Rosenberg, Bernhard-Maria 200–201, 210 Rosińska, Grażyna 15, 25, 89, 144–146, 151–153, 156, 161, 227, 381, 484 Rospond, Stanisław 9 Ross, W. D. 86, 322 Rossmann, F. 244 Rouse, Richard xiii Rupprich, Hans 141, 160 Ryan, Paul 228

534

index of names

Sabra, A. I. 476–478 Saliba, George xix, 154, 262–265 Sarnowsky, Jürgen xvi, 102, 104, 112, 132, 158, 338 Savage-Smith, Emilie 485 Schmauch, Hans 5, 7–9, 11–12, 19, 208 Schmeidler, Felix 172, 189, 191, 215–216, 230, 236, 243–244, 248, 269, 327, 349, 362, 365, 385, 395, 397–399, 402 Schmitt, Charles 90 Schofield, Christine 254 Schupp, Franz 52, 62, 80 Schwinges, Rainer 17 Segel, Harold 139, 141, 194 Segonds, Alain 390 Seńko, Władisław 36, 38, 89, 95, 111, 142 Serene, Eileen 58, 280 Shank, Michael 139, 158, 187, 295 Sharples, R. W. 93 Sikorski, Jerzy 21, 436 Simon, Peter 285 Siorvanes, Lucas 92 Slomkowski, Paul 52, 62, 296 Smith, A. Mark 372 Smith, Pamela 476 Smith, Robin 51, 54–55 Solmsen, Friedrich 89, 338 Sorbelli, Albano 179, 193 Speca, Anthony 52 Spitz, Lewis 141 Spruyt, Joke 26, 63, 68, 72, 280, 292 Steneck, Nicholas 127, 159 Stephenson, Bruce 429, 433 Stocks, J. L. 392 Stravinsky, Igor xvii Strzelecka, Bożena 47 Stump, Eleonore 51–52, 55–56, 59–65, 288 Swerdlow, Noel xiii, xxvi, 6, 151, 154–155, 190, 194, 215–217, 219, 221, 242–245, 248–249, 253–254, 257, 260, 262, 264, 267, 269, 295, 302, 325–326, 328–330, 333, 360, 365, 371–372, 374, 377, 381–382, 384–385, 492 Szczeciniarz, Jean-Jacques 332–333, 355 Szczucki, Lech 244, 404 Szelińska, Wacława 36, 38, 40–42, 44–46, 139–141 Szujski, Józef 73 Świeżawski, Stefan 36, 89, 103, 105, 166, 241

Tarnowska, Irena 40 Tatarkiewicz, Władysław 403 Tessicini, Dario 143, 187, 239–240, 294–295 Thijssen, Hans (also Johannes) xiv, 90 Thimm, W. 21 Thoren, Victor 254, 433 Thorndike, Lynn 375 Tomkowicz, Stanisław 27 Toomer, Gerald xxvi, 143, 147, 158, 217–218 Toulmin, Stephen 280, 292–293 Trifogli, Cecilia 89, 103 Troupe, Bonnie xvi Turnbull, Robert 228 Ueberweg, Friedrich 159 Ulewicz, Tadeusz 137 Usowicz, Aleksander 36 Valentin, H. 191 Van Eemeren, Frans 292 Van Luchene, Stephen 93 Varzi, Achille 285 Vasoli, Cesare 174, 230 Verdet, Jean-Pierre 369, 371, 390 Vermij, Rienk 404 Vickers, Brian 194 Visconti, Alessandro 204 Voelkel, James 424, 430 Voullième, E. 461 Wagner, David 42 Walde, O. 213 Wallace, William 58, 319 Warrington, John 87 Wasiutyński, Jeremi 151 Waters, C. Kenneth 277 Wattenberg, Diedrich 219–220 Weijers, Olga 52 Weisheipl, James 89, 93, 101, 115 Westman, Robert S. xiii, 179, 186, 191, 254, 293, 295, 317, 372, 375, 380, 388, 403, 405–406, 410–411, 421–422, 424–426, 428, 432–433, 436 White, Lynn Jr. xiii Wieacker, Franz 180 Williams, Joseph 292 Windakiewicz, Stanisław 23 Wisłocki, Władisław 80, 461 Wiszniewski, Michał 37 Wittgenstein, Ludwig 90 Włodarczyck, Jarosław 152–153

index of names Włodek, Zofia 35, 37–39, 41–42, 46, 80, 89, 107, 373 Wörner, Marcus xvi Wolff, Michael 333, 338–341, 347–348 Wróblewski, Andrzey 137 Wündisch, Veronika 436

535

Zajdel, Dariusz 436 Zarębski, Ignacy 140 Zathey, Jerzy 41, 43, 161 Zekl, Hans 244–245, 264 Zinner, Ernst 25, 137, 159, 172, 189, 216, 217, 219–220, 230, 403 Zwiercan, Marian xiv, 26–27, 35–39, 48–49, 79, 89

INDEX OF PLACES Baltic 7 Baltic Sea 5, 207 Basel 138, 411 Berkidy 5 Black Sea 7, 222 Bohemia 216, 428 Bologna xxiii, 11–14, 18–19, 22–24, 107, 138, 140, 152, 162, 167, 173–188, 192–193, 195–197, 199, 201, 203–205, 211, 216, 238, 275, 278, 282, 284, 322–323, 370, 388 Bourges 178 Braniewo (Braunsberg) 3, 6, 187, 207, 213

Lidzbark-Warmiński (Heilsberg) 2–3, 187, 200, 204, 207–208, 211–215, 226, 229, 235–236, 269–271, 341 Lublin 89

Chełmno (Kulm) 2–3 Cologne 11, 16, 19, 42, 72–73, 81–82, 93, 96, 282–283, 322 Constance 138 Constantinople 221 Cracow (Kraków) xiii–xiv, xxi–xxvi, Chapters 1–5, 171–172, 179, 184–186, 191–194, 202, 207–208, 211, 214, 216, 219–220, 225, 237–238, 241, 245, 262, 267, 269–271, 275, 277–278, 281, 283, 285, 298, 322–323, 332, 334, 336, 338, 357–358, 361, 327–374, 388, 398, 419, 424, 437, 484 Crete 222

Olmütz 216 Olsztyn (Allenstein) 2–3, 9, 200, 207 Oxford 14, 16

Elbląg (Elbing) 2–3, 6 Erfurt 282–283 Ferrara 171, 173–174, 176, 178, 180, 198–199, 203–204 Florence 141, 224, 414 Frombork (Frauenburg) 2–3, 6, 134, 177, 187, 207–209, 211–215, 226, 229–230, 235–237, 269–271, 293, 321, 341, 436–437 Gdańsk (Danzig) 411 Geismar 9 Hesse 9

2–3, 5–6, 137, 210,

Mantua 238 Mierzeja Wiślana (Vistulan Sandbar) 3, 207 Milan 162, 196, 218 Naples 138, 199 Nicaea 221 Nogat River 3, 207 Nürnberg 172, 207

Padua xxiii, 14, 22, 155, 162, 171, 173, 184, 191, 196, 198–201, 203–204, 268, 278 Paris 13–16, 39, 73, 93, 142, 149, 177, 420, 424 Pieniężno (Mehlsack) 3, 200 Poland xi, xix, 1–2, 5–9, 15, 43–44, 47, 74, 94–95, 138–140, 142, 169, 178, 183, 188, 192, 194–196, 198, 204, 207, 214, 216, 235, 261, 361, 437 Pomerania xi, 3, 5–6, 207 Prague 14–15, 56 Rome 139, 171, 173, 175–177, 180, 197, 205, 411 Royal Prussia 5–9 Stockholm 214 Sweden 208, 212–213, 226, 341 Toruń (Thorn) xxi, 2–3, 5–9, 11–13, 17–19, 43, 137–138, 172, 207–208, 436–437 Trapezunt 222 Ukraine 7 Uppsala 134, 146, 150, 191, 195–196, 202, 208–209, 211–214, 216, 222, 226,

index of places 228–229, 235, 238, 249, 258–259, 321–322, 400, 436, 471 Varmia (Warmia, Ermland) xi, xxiv, 3, 6–7, 9, 11, 19–22, 134, 172, 175, 178, 187, 196–197, 200, 205, 207–208, 210–213, 226, 270–271, 361 Venice 201, 422 Vienna 12, 35, 139, 141, 143, 159, 221

Vistula River (Wiśła, Weichsel) 2–3, 5–6, 11, 207, 437

537 xxi,

Warsaw 2, 5 Wieliczka 139 Wittenberg 405, 422 Wocławik (Leslau) 12 Wrocław 43, 47, 141, 150 Zalew Wiślany (Vistula Lagoon) 207

INDEX OF SUBJECTS Albertism 42, 89, 96 Alfonsine Tables 35, 146, 149–150, 154, 211, 221, 418 Aristotelianism xv, xxii, xxiv–xxv, 90, 93, 95, 99, 134, 172, 225, 325–326, 330, 387 Copernican 171, 401, 403–404, 408, 435 Paduan 58, 198–199, 203, 268–269 Scholastic xxv, 86, 89, 91–93, 98, 110, 127–128, 133–135, 142, 171–172, 181, 184, 209, 230–231, 236, 238, 276, 283, 330–331, 340, 344, 347–353, 359, 372, 387–401, 408, 412, 474 Tradition xxi–xxii, 36, 89–93, 97, 179 astronomy, astronomical xxi–xxiii, xxvii, 9–16, 23–29, 33, 35–41, 43, 45–50, 53, 58, 68, 72, 88–89, 93–94, 96, 105, 107, 114, 120, 123, 134–135, 137–167, 171–174, 180, 182–184, 190, 192–197, 203–205, 208–209, 215, 219, 239–242, 270–271, 275, 278–279, 284, 291, 293–296, 299, 301–306, 311, 317, 320, 322–327, 330–337, 358–359, 369–371, 374, 383, 387–388, 390, 401, 404, 407, 410–424, 427–428, 431–432, 435, 437, 477, 484–485 anomaly 158, 221, 249, 379, 429 astrology 10, 15, 29, 32, 35, 38–41, 45–46, 48, 137, 145–146, 149, 160–161, 186, 190–191, 202–203, 370, 411 bounded elongation 125, 133, 241, 246, 249, 253, 257, 312–314, 329, 358, 386, 489 calendar 25–26, 30, 35, 41, 144–145, 149, 160–161, 295, 299, 436 concentric, homocentric 123, 128–129, 134–135, 143, 145, 148, 155–156, 158–159, 161, 163–164, 184, 239–240, 242, 244–245, 248–251, 264, 267, 294–296, 328, 364, 371, 375, 377, 401, 408, 477–478, 484 cosmos, kósmos 91–92, 94, 99, 101, 115–116, 118, 126, 135, 143,

148–149, 226, 231, 287–288, 290, 298, 328, 337, 347, 355–358, 371, 399, 401–402, 427, 473–474 distances, planetary and stellar, angular and linear 115, 124–126, 130, 144–145, 218, 221, 241, 246, 248, 252–257, 260, 266, 279, 307–308, 311, 314, 318, 321, 329, 355, 364–365, 379–380, 383, 388, 398–399, 401–402, 413, 428, 431, 480, 483, 487–489 ecliptic 118–120, 124–125, 127, 129, 131, 190, 192, 197, 218–219, 264, 267, 311, 399, 477 ephemerides 15, 35, 150, 270 geocentric xxiv, 123, 134–135, 143–145, 147, 158, 174, 242–243, 246–247, 251, 256–257, 272, 315, 321–322, 324, 327, 353, 366, 383, 388, 410, 425 heliocentric xxiv, 16, 24, 44, 93, 173–174, 186, 206–208, 215, 238, 242–243, 249–253, 255, 272, 276, 279, 297, 300, 321, 327–328, 330–331, 339, 353, 358, 362, 381, 388–390, 401, 404, 406, 410, 413–414, 418, 420, 422, 425, 429, 432–433, 437 heliostatic 122, 272, 355, 388, 401, 405 instruments 146, 151–154, 172, 191, 218–219, 241, 271 latitude 25, 151–152, 163, 188–189, 219, 248–250, 254, 264, 266–267, 269, 313, 329, 365–366, 379, 407–408, 429–430, 434, 478 longitude 150, 152, 158, 163, 249–250, 266–267, 269, 365–366, 428, 430, 432, 435, 485 mathematical 15, 16, 26, 38, 40, 45–46, 58, 88, 107, 134–135, 142, 145–149, 154, 157–158, 162, 164, 174, 179, 190, 193–195, 199, 206, 219, 225, 229, 240, 242–243, 246–247, 249–251, 256, 262, 267, 270, 272, 276, 279, 300, 305, 308–309, 314–320, 323, 327, 329, 333, 337, 353, 359–361, 364–368,

index of subjects 378, 384, 386, 388, 398, 401, 404–405, 407–408, 418–419, 421, 425, 476–477, 481, 492–493 observations 23, 40, 45, 144, 146–147, 152–153, 160, 163–164, 166, 172, 184, 188–192, 207, 217, 219, 228, 237, 241–242, 244, 246–247, 269–271, 276, 279, 295, 297–300, 305, 308, 310, 313–314, 318, 327, 334, 345, 379, 393, 398–399, 407, 412, 414, 418–419, 421, 425, 476–477, 481, 492–493 period 124–125, 230, 314, 430–431, 492 sidereal 125, 233, 235, 238, 246–247, 252–253, 255, 257, 260–261, 291, 315, 329 synodic 255, 257, 261 zodiacal 125, 130, 233, 253, 257 physical 147–148, 157, 219–220, 246, 262, 305, 309–310, 319, 326–327, 337, 362, 369, 374, 378, 398, 401, 406, 408, 411–412, 415–416, 420, 425–427, 432–433, 435, 477–478, 481 Planetary Hypotheses 156, 253, 492 Ptolemaic 49, 53, 92, 123, 126, 131, 134, 143–144, 146, 150, 154–159, 163, 172, 174, 183, 191, 215, 219, 221, 228, 238, 241–242, 246, 257, 262, 268, 270, 291, 294, 296, 300–302, 322, 325–327, 358, 382, 386, 389, 408, 411, 413, 421–424, 434, 473, 477–478, 484 retrograde motion 124, 133, 241, 246, 248–249, 253–255, 257, 311, 313–314, 316, 329, 358, 368, 379, 383, 386, 388, 407, 479, 488–489 stellar parallax 246, 314, 355–356, 398, 407 tables 10, 15, 35, 45, 143, 146, 149–154, 160–162, 172, 189–190, 211, 214, 221, 270, 418, 437, 484 Tabula directionum 146, 150, 161–162, 211, 216, 259 Tabula eclipsium 151, 160 Tabulae resolutae 46, 146, 150–151, 160 Theorica 147, 253 trepidation 144, 478 Tychonic 191 year sidereal 125, 192, 233, 248, 251, 261

539

solar 144, 197, 241, 248 tropical 192, 247–248, 252, 422 zodiacal 125, 130, 233, 252, 257 Averroism xxv, 184 Paduan 295 Baltic Research Center 436 Bible, Sacred Scripture 12, 20, 295, 299, 406, 409–410, 413–415, 421 Brethren of the Common Life 11–13 Collegio Romano 58 Council of Trent 178, 406 Earth 94, 97, 109–110, 114, 117–120, 125–133, 143–145, 148–149, 153, 157, 186, 188–192, 218, 220–221, 226, 230–235, 238, 246, 260, 287–288, 290, 305–306, 321, 346, 375–377, 473–475, 477, 479 motion of 230, 234, 246–249, 252–257, 259, 268, 279, 288, 291, 297–299, 307–313, 315–317, 321, 327–342, 345, 347–348, 350–351, 353–359, 362, 368, 370–372, 374, 379–402, 405–409, 413–418, 422–424, 426–427, 435, 488–489, 493 education 1, 5, 8, 11–14, 16–18, 20, 22–24, 31, 33, 37–38, 44, 49, 51, 64, 75, 85, 96, 99, 138–140, 147, 162, 169, 171–174, 177–180, 183, 188, 193, 198, 200, 203, 206, 215, 271, 275, 278–282, 387, 389, 437 astronomy xxi, Chapter 5 curriculum xxii, 8, 15–16, 24–28, 49, 52, 62, 64, 74, 89, 93, 114, 140, 142, 145–154, 173, 175, 198–199, 205 early, elementary 5, 7–8, 12–13, 196 liberal arts (see liberal arts) mathematics 10–11, 15, 18, 23, 25, 28, 40, 46, 48–49, 143, 145, 159, 171, 193, 198, 201, 223–224, 301, 304–305 music 10–13, 26, 28, 32–33, 41, 160 quadrivium (also quadrivium) 12, 26, 32 School of St. John 8–9, 11, 13 teachers xxii, 12–13, 16, 23–25, 28–30, 32–33, 75, 93–95, 99, 101, 114, 124, 131, 133, 140, 151, 159–166, 184, 199, 205, 275, 284, 322, 325, 484 trivium 26

540

index of subjects

elements xxvi, 92, 97, 101–102, 115, 117, 119–121, 127, 132, 150, 184, 223, 230, 232, 235, 255, 287, 325, 332, 336–338, 345, 347–348, 354, 374, 376, 380, 392–393, 402–403, 415, 435, 473 aether (also ether) 116–117, 120, 126, 232–233, 288, 345–346, 348, 354, 375, 377 atom, atomism 122, 345 earth 118, 125, 231, 288, 342–343, 345–346, 350–351, 370–373, 396, 417, 474 fire 233, 345, 395 fictionalism (see hypotheses and instrumentalism) saving the hypotheses 321 saving the phenomena 163, 327 Florentine Academy 142, 224 geocentrism 54, 116, 252, 291, 315, 317, 320, 326, 330–332, 337, 353, 358, 367, 408, 410, 416, 473 geography 9, 35, 43, 47, 120, 142, 212, 238, 306 navigation 149 heliocentrism xv, xxvii, 202, 242–243, 291, 320, 329, 331, 336, 360, 381, 386, 396, 403, 408, 411, 421 humanism xxii, 39, 43–44, 49, 99, Chapter 5, 137–167, 178–179, 182, 194, 199–201 hypotheses xxv, 11, 28, 53, 67, 72, 75, 85, 88, 90, 129, 131, 171, 209–210, 212, 215, 228, 237, 242, 256, 272, 276–280, 291, 296, 299–300, 302, 305, 314–318, 320–324, 328, 360–369, 385–391, 404–405, 408, 410, 412, 414, 416–427, 430–432, 476, 485, 487, 492–493 fictitious, imaginary 147, 157–158, 315, 366, 369, 378, 477 assumption 57, 115, 145, 242–243, 246–247, 250–251, 254, 256, 271–272, 278, 280, 284–286, 305, 312, 315, 320, 324, 326, 330, 354, 359, 361–363, 367–369, 383, 385–386, 391, 404, 412–413, 415, 421, 477 axiom 37, 131, 147, 165, 217, 243, 253, 277, 316, 327, 342, 362, 367–368, 377, 383, 396, 401, 407, 421, 429–430, 477, 493

postulate 228, 240, 243, 245–246, 250–253, 256, 291, 307, 375, 382–383, 419 principle 55, 58–61, 73, 85–86, 92–95, 101–102, 107–108, 110, 113, 117–118, 124, 128, 130–131, 133, 135, 145, 151, 171–172, 176–177, 180–181, 183, 212, 215, 223–224, 229–230, 240, 243–245, 250–255, 257, 275, 277–278, 291–293, 296, 305, 307–308, 310–317, 321–322, 324–328, 330–332, 334–335, 337, 339–340, 344, 348, 351, 353, 357–358, 360, 362–363, 367–370, 374, 376–378, 380–382, 385–388, 390–396, 398–399, 401–402, 405, 408, 413, 415, 417–418, 421, 427, 430, 433, 435, 437, 474, 487–489, 493 instrumentalism xxv Islamic astronomy 145, 476–485 Jagiellonian Library 35, 40, 95–96, 107, 128, 139, 142, 151, 225 languages German xxi, 5, 7, 9, 13–14, 17, 139 Greek xxiii, 43–44, 59, 140, 171, 173, 180, 184–185, 193–197, 204–205, 211, 219, 221, 229, 234–236, 244, 415 Latin xxi, 8–9, 13, 43, 146, 193–196, 210–211, 235, 296, 415 Polish xxi, 5, 7, 9 law xxiii, 10–11, 14–15, 18–24, 42, 45–46, 49, 138, 140, 166–167, 171, 173–183, 192, 198, 203–205, 214, 275, 278, 282, 285, 370, 389 liberal arts xxi–xxii, 8, 11, 18, 23–24, 27, 33, 35–36, 38, 142, 177, 193, 195, 279, 304, 317, 404, 410, 435 logic, logical xxi–xxii, xxiv, 9, 11–13, 16, 24–33, 35–42, 45–49, Chapter 3, Chapter 8, 387–391, 397, 404–405, 415–416, 422, 425–427, 429, 431–432, 437, 477, 484–485 antecedent/consequent 61–62, 68–72, 75–86, 88, 106, 183, 247, 277, 290, 387, 391, 422, 450–451, 453, 455, 478–479, 487 argumentation xxiv–xxv, 53–57, 60, 65, 73, 180, 299, 301, 336, 354, 356–357, 370, 385, 390, 401, 433, 437, 474

index of subjects conditional 52, 61, 68, 71, 76, 80, 183, 275, 334–335 connexivist 69 consequences xv, 26, 51–53, 56–57, 60, 62, 64, 68–69, 72–73, 75–84, 88, 108, 123, 183, 228, 277–278, 281–282, 285–286, 289, 315, 317–318, 324, 404, 423 convertibility 412 demonstration 54–60, 64–65, 72–74, 85, 131, 135, 185, 199, 203, 242, 244, 246, 249, 251, 262, 267, 279–281, 283, 315, 318, 322, 335, 366–369, 378, 390, 405–416, 421–423, 454, 484 dialectic 55–58, 60, 64, 72–88, 93, 119, 127–128, 173–178, 180–184, 205, 214, 218, 220, 230, 242, 275, 278, 290, 295, 323, 329, 336, 338, 359, 387, 389 dialectical method 59, 251–256, 276, 291, 301, 314, 321–326, 330, 389 dialectical topics 52–57, 62, 100, 108, 113–114, 171, 179, 181–182, 203, 279–286, 292–314, 322, 387, 390, 413, 426–427, 435 authority 56–57, 157, 181–182, 284–285, 297–298, 305, 308, 409, 412, 416, 441, 443 extrinsic 64–65, 67, 69, 83, 182, 283–284, 297, 442–443 intermediate 61, 64–65, 67, 69, 283–284, 443–444 intrinsic 64–65, 67, 69, 83–84, 182, 283–284, 441–442 part/whole (see mereology) enthymemes 60, 63–64, 181, 283, 292, 303, 323 example 63, 181 habitudo 80–81, 83 hypothetico-deductive system 59, 277, 323–324 induction 63, 86, 181, 277 inference 51, 56, 58, 60, 63, 65, 68–69, 71, 73, 78, 183, 185, 247, 278, 282, 288–289, 296, 307, 427 metábasis 107, 156, 318 necessary propositions 56, 58, 62, 68–69, 73, 76, 183, 277, 280–281, 315, 367, 422, 424, 431 omission 387, 389 paradoxes xv, 51–53, 57, 62, 72–73, 99, 182, 203, 218, 278, 280, 291–292, 354, 358, 387, 390, 404, 412, 415, 424, 436

541

probable propositions 56–57, 59, 64–65, 72–73, 99, 182, 203, 218, 278, 280, 291–292, 354, 358, 387, 390, 404 regressus 412, 415, 424, 436 relevance 56–57, 62, 66, 68–69, 71–72, 75–76, 81, 84–85, 88, 108, 171, 228, 251, 275, 277–278, 280, 285, 296, 299, 315, 321–322, 324, 367, 369, 387, 389–390, 432, 487 rhetoric 23, 25–30, 33, 44–45, 48, 53–57, 70, 93, 178, 184, 214, 222, 279–282, 286, 293, 295, 297, 299–301, 303–305, 323, 327, 330, 345, 355, 388, 396, 451 semantics 56, 60, 62 simplicity 301, 313, 334, 354, 426, 437, 488 syllogism 30, 51–52, 60–61, 63–65, 73–75, 86–87, 181, 185, 217–218, 220, 281, 283, 286, 293, 296, 323 syncategorematic terms 26, 62, 64, 68, 82 terminism 63, 72 typology 362, 369, 404, 420, 425 validity 60–62, 65, 69, 73, 81, 275, 277–278, 281–282, 285, 323–324, 387 warrants 62–63, 75, 280, 282, 284, 292–293, 296–297, 299, 304–311, 317, 323, 425–426, 488 Lutheranism 13, 44, 177, 405–406, 410 matter (see metaphysics under natural philosophy) medicine 14–15, 20–23, 49, 171, 173–174, 176, 178, 185, 190, 198–204, 230, 416 Melanchthon Circle 405, 411, 421, 425 mereology 83, 285–291 part/whole 66–67, 81, 83, 113–119, 127, 163, 183, 238, 278, 283, 285–291, 296–300, 307–308, 310–312, 314, 317, 343–344, 348, 350–351, 359, 369, 380, 385, 392, 396, 413, 417–418, 426–427, 441–442, 459–460, 462, 472–474, 487–488 models 23, 88, 92, 123, 126, 129–130, 133–135, 143–149, 154–158, 161, 163–164, 166, 174, 191–192, 206, 218–221, 223, 229, 239–242, 244–246, 248, 250–252, 255–256, 261, 268, 270, 272, 294, 302, 313–316, 320, 327–329, 333, 353, 355, 358–369, 371, 377–378, 380, 383, 385, 388, 402, 404–405,

542

index of subjects

407–408, 413–414, 418–420, 423, 425, 476–486, 492–493 Apollonius’s theorem 249 Capellan 159, 254–255, 257, 313, 381–383, 385 crank mechanism 158 device, mechanism 131, 155–158, 262–269, 315, 365–369, 378, 381, 384–386, 401, 477–485, 492 oscillatory, reciprocation, rolling 155, 165, 248–250, 252, 261–262, 264, 266–269, 365, 477–485 double-epicycle 165–166, 248–251, 363–364, 378, 381, 408, 484 eccentreccentric 313, 341, 364, 408 eccentric and epicycle-deferent 85, 123–124, 126, 128–130, 133–135, 143, 145, 147–150, 155–158, 161, 164–166, 221, 239–241, 245–246, 248–255, 257, 259–268, 291, 308, 312–316, 328–329, 341, 355, 363–365, 367–368, 371–372, 376–382, 384, 388, 407–408, 419, 422, 428–429, 431–435, 463, 477–485, 488, 492 Egyptian 159 equant xxvi, 130–131, 133, 135, 145, 149, 154, 156–158, 161, 165, 245, 251, 253, 262, 264, 268–269, 291, 316, 321, 329, 368, 371, 377, 380–386, 407, 429, 431, 434, 477–478, 492–493 Eudoxan, Eudoxian 155–156, 477–478 libration 264, 363, 366 Maragha 154–156, 261, 476, 478, 484–485 oval 158, 232, 313 radius 165, 260, 262, 364, 480, 482 orbital 259 three-orb system 130, 148, 375 Tusi couple/device 155, 157, 248, 261–267, 476–477, 480–481, 485 Tychonic 381–382 Moon 10, 107, 110, 117, 119, 121, 125, 128, 132, 144, 148, 155–158, 165, 193, 217–218, 230, 232–235, 248, 252, 254–255, 260, 262, 291, 311–312, 316, 334, 348, 353, 359, 363–364, 370–372, 376–378, 380, 383, 388, 398, 400, 406–408, 427, 473–475, 479, 484 motion 91, 94, 98, 101–103, 107–108, 111–112, 127, 131, 149–150, 195, 216,

230, 235, Chapter 9, 411, 413–417, 428–431, 435 acceleration 58, 103, 119–122, 129, 343, 393–394 circular xv, 37, 105, 114–118, 120, 122–125, 130, 135, 147, 163–165, 215–218, 232–233, 238–240, 242, 251–253, 255, 266, 268–269, 290, 306–307, 309–311, 315–320, 365, 367–374, 379–380, 395–399, 401–402, 407, 435, 473, 477–485, 487–489, 493 compound 255, 306, 310, 393, 397 cone-shaped 232 conical 372 directionality 126, 290, 348, 474, 490 force, virtus, vis 92, 102, 111–113, 118–119, 132, 135, 158, 240, 306, 372–374, 393–395, 411, 413, 424, 433, 445–446, 455–459, 465, 492–493 gyrational/spiral 240 impetus 48, 89, 92, 98–100, 110–112, 129, 132, 373–374, 393–395, 457–458, 471 inclination 58, 101–102, 113, 132, 271, 376, 396, 399, 456, 473, 490–491 inertia 98, 338, 473 mechanics 58, 90, 97, 338, 360, 381, 492 natural 91, 94, 105, 109, 116, 118, 122–123, 129, 132–133, 255, 286–288, 309, 325, 331, 334, 336–338, 340–344, 351–352, 356, 358–359, 393–394, 416–417, 437, 473 non-uniform 156, 164, 248, 251–252, 255, 262, 287, 306–307, 311, 339, 364, 367–369, 375, 379–380, 383, 385–386, 479, 481, 492 periodic mean 492 planetary 45, 129, 133, 143, 145–146, 158, 163–164, 186–192, 219–220, 230, 244, 246–249, 253–254, 256, 279, 291, 297–300, 313, 316–317, 362–364, 370–373, 380, 391, 404–405, 408, 412, 421–423, 437, 476, 489, 493 projectile, violent 91–92, 110–111, 129, 132–133, 231, 325, 335, 341, 351, 400 rectilinear 115, 117, 123, 131, 155, 165, 217, 252, 255, 262, 266–267,

index of subjects 309–310, 319, 340, 342–344, 349, 351–352, 354, 391, 393–398, 427, 478–481 relativity of 393 resistance 119, 129, 334–335, 342, 344, 391, 393 simple 94, 102, 110, 115–116, 122–123, 126, 157, 163, 165, 287–288, 290, 309–310, 325, 332, 336, 339–340, 343–345, 347–348, 358–359, 371, 378–379, 391–393, 396, 462–463 teleological 238, 287, 347–348 uniform xv, 98, 129, 147, 155–156, 244–246, 251–253, 255, 296, 320, 368, 378, 382–389, 395, 400, 435, 492–493 void 91, 97–100, 104, 110–112, 117, 123, 135, 145, 165, 218, 230–232, 262, 356–358, 375, 377, 397 natural philosophy xxi–xxiii, xxvii, 15–16, 24, 26, 28, 30–33, 35–36, 38, 40–41, 48–49, 53, 75, Chapter 4, 147–149, 163, 171–172, 174, 176, 198, 201, 212, 214–216, 225, 236, 240, 247, 256, 276, 279, 284, 292–293, 299, 307–308, 317–320, 323, Chapter 9, 362–363, 367–369, 373, 385, 387, 389, 391–392, 399, 403–405, 408, 410, 412–415, 418, 421, 427, 435, 437, 477 according to nature 91, 115, 123, 310, 333–334, 341–342, 350–352, 393 body 58, 97–98, 101, 103–104, 107, 109, 111–112, 115–117, 122–123, 126, 129–132, 135, 155, 157–158, 163–164, 218, 231–232, 235, 255, 287–288, 306, 308–310, 313, 325, 333–337, 339–341, 343–345, 348, 350–352, 358, 375, 378–380, 393–396, 429, 473–474, 478–480, 488–489, 492 heavy 103, 109, 111, 114, 116–119, 122, 124, 126, 131, 217, 231–232, 309–310, 325, 343–344, 346, 348, 356, 359, 393, 395, 446, 464, 473–474 light 111, 116, 118–119, 122, 126, 217, 231–233, 310, 312, 342–343, 346, 348, 393, 395–396, 474 shape 108, 110, 118–119, 122, 126, 132, 158, 189, 216–217, 230–232, 305–307, 333, 354, 398

543

cosmology xv, xxiii–xxiv, 53, 88, 93, 96, 134–135, 208, 253, 323, 326, 330–331, 339, 344–345, 353, 358, 360, Chapter 10 architectonic 313, 317, 369, 389, 435 axiom (see hypotheses) commensurability 296, 300–301, 329, 363 cornerstone (primarius lapis) 362–363 enclosed/enclosing 307–308, 310, 331, 488 eternity 91, 116, 223, 230, 239, 290, 310, 332, 378, 394–395, 401, 480 harmony 252, 301–302, 311, 329, 411–412 intelligence, vital force 98, 101, 112, 129–130, 135, 156, 158, 163, 239–240, 290, 335, 340, 385, 479, 481, 491–493 prime mobile, mover 124–125, 224, 340, 400–401, 477 symmetry 128, 301, 403 system, systema 118, 122–123, 129, 148, 173, 245–246, 252–253, 255, 257, 259, 262, 268, 277, 291, 297, 302, 314, 316, 321–322, 325, 328–331, 335, 353–358, 363, 366, 368–369, 372–373, 375, 377, 391, 413, 418, 429–431, 484, 492 gravity 129, 131, 235, 238, 246, 252, 298, 306, 311, 335, 343, 347–348, 353, 376, 393, 396, 427, 435 inclination, appetite, desire 101–102, 113, 129, 132, 238, 325, 340, 343–344, 348, 350, 352, 380, 393, 396, 399, 427, 456, 473 metaphysics, metaphysical principles Chapter 10 accident 55, 59, 66–67, 83, 103, 113, 129, 239, 283, 343, 350, 352, 357, 374, 391, 442, 451, 455, 457, 459–460, 466–468 actuality/potentiality 103, 119–121, 247, 332, 374, 400–401 cause/effect 65–68, 71, 77–78, 81, 84, 88, 91, 98, 101–102, 108, 111–114, 117–133, 158, 185, 230, 242, 246–249, 256, 276, 283–284, 290, 297, 305–309, 318, 321–322, 332–346, 350, 370, 379–380, 385,

544

index of subjects

390, 393–395, 402, 404–405, 412–413, 419–423, 431–433, 442, 458, 464, 470, 487–488, 492 dignity 78, 293, 308, 310, 336, 421 empyrean 357, 397 essence 54, 233, 350, 391, 412 form/matter xxvi, 54, 91–92, 97, 100–103, 105–109, 114–117, 119, 123, 216–217, 223, 230, 238–239, 290, 305–306, 311, 325–333, 337, 339, 342–345, 351, 353–354, 360, 370–374, 378, 380, 385, 388, 395, 426–427, 434, 445, 447, 449–452, 454–455, 458, 464–465, 468, 470, 487 perfection 103, 130, 132, 208, 223, 295, 336, 351, 361, 446 power 101–102, 111, 186, 341, 350, 356, 373, 379, 433 principle, see hypotheses quality 111, 132, 311, 340, 395–396 substance 65–66, 108, 112, 115, 120–121, 125, 283, 287, 289–290, 325, 372, 388, 433, 441 physics 325–326, 337, 342, 353, 377, 383, 418, 433 place 66, 98–105, 113, 116–119, 123–124, 131–132, 216, 218, 230–231, 288, 310, 325, 333, 337–338, 343–351, 357–358, 376, 393–395, 398–400, 473 Neoplatonism xxiv–xxv, 43, 92, 94, 97, 141–142, 172, 220, 222, 224, 229, 275, 288, 318, 327, 349, 389, 394, 473 planets 45, 106–107, 117, 119, 127–133, 143–146, 148–152, 154, 156, 158–159, 162–165, 186, 191–193, 197, 202, 230, 244–245, 250, 252, 256, 262, 264, 291, 298, 300, 308, 310–311, 318, 321, 325, 328, 332, 348, 353–356, 358–359, 369–381, 383–384, 386, 397–400, 404–405, 407, 412, 419, 422, 429–431, 433–435, 453, 462–463, 474, 476–483, 488–489, 492 Mars 125–126, 128, 189, 218, 221, 232–235, 247–248, 253–255, 257, 259–260, 312–313, 382, 388, 408, 413, 427–428, 434, 489 Mercury 125, 128, 130, 133, 144, 159, 161, 165, 172, 186, 207, 217–219, 221, 227, 232–235, 238, 241, 246, 249, 253–255, 257,

259–261, 266–267, 269, 312–314, 316, 329, 363–366, 368, 382, 408, 477, 484, 489 Jupiter 125–126, 128, 218, 232–233, 253, 257, 259–260, 269, 312–313, 382, 407, 434, 489 Saturn 125–126, 128, 133, 218, 232–234, 248, 253, 257, 259–260, 264, 269, 312–313, 355, 382, 399, 434, 489 Venus 125–126, 128, 130, 133, 144, 159, 161, 165, 186, 218–219, 221, 227, 232–234, 238, 241, 246, 249, 252–255, 257, 259–261, 264, 312–314, 329, 363–364, 366, 382, 388, 408, 422, 477, 484, 489 Platonic Academy 224, 473–474 Platonism xxiv, 43, 92, 97–98, 101, 107, 118, 132, 135, 141, 159, 172, 198, 220–221, 223–225, 230, 253, 255, 275, 318–319, 326, 328, 338, 347, 357, 394, 456, 473–474, 477 “Platonic axiom,” uniformity and circularity 147, 396 Pythagoreanism 107, 118, 211, 221–223, 232–234, 247, 395, 402, 415, 417 realism, realist xxv, 74–75, 149, 158, 229, 327, 361, 369, 385, 404, 493 Santa Maria Novella 414 Scotism 39, 42, 142 Sodalitas litteraria Vistulana 43–44, 141 space 11, 91, 98, 104, 135, 145, 217–218, 221, 230, 249, 254–255, 308, 310, 312–314, 353, 355–358, 372, 377, 388, 397, 433 sphere xxvi, 37, 97–98, 100, 103–107, 112, 114, 117–118, 120, 122–135, 143–144, 147–150, 153–159, 161, 163–165, 188, 208, 215, 217–219, 230, 232–233, 242, 244–256, 259, 264, 269, 287–288, 290–291, 297–298, 305–308, 311, 313, 325, 331–336, 338–341, 345, 348–358, Chapter 10, 388, 395, 397–402, 407–409, 413, 423, 426–427, 433, 435, 437, 477–480, 487–488, 492 orb 112, 123–126, 128–131, 133, 143–144, 148, 157–158, 163–165, 224, 234, 239–241, 245, 248–250, 256, 264, 333–334, 339, 349, 365, 371, 375–381, 385, 413, 422–423, 426, 429, 432, 434, 444, 452, 464, 490, 492

index of subjects Stobner chair 15, 41, 152–153 Stoicism xxiv–xxv, 51–52, 56, 94, 97, 102, 229–233, 345, 347, 357–358, 374, 398, 473–474 Suda (also Suidae lexicon) 195–197, 214, 235, 344, 348–349, 351, 353, 392, 490–491 Sun 10, 107, 117, 119–121, 125, 127–130, 132–133, 144–145, 148–149, 155–156, 158–159, 163–165, 186, 219, 221, 227, 230, 232–234, 238, 240–241, 246–247, 252–257, 260, 279, 287, 291, 308, 311–313, 315, 317, 320, 328–329, 333, 338, 345, 348, 353, 355–359, 362, 364, 366, 370–373, 375–383, 386, 388, 395, 397–400, 402, 404–408, 413, 422, 427–429, 431, 433–435, 437, 479, 488–489, 493 as king 219, 240 as visible god 400 Teutonic Knights xvii, 7, 175, 177–178, 201, 271, 361 Thomism 42, 96, 100 universe 91, 99, 103, 113, 115, 117–120, 123–124, 129, 136, 164, 218, 223, 230–232, 234, 246–247, 250, 252, 255–256, 286, 290, 296, 298–299, 302, 305, 308–311, 318, 331, 338, 348, 350, 363, 371, 373, 378–379, 393, 400, 402, 410, 415, 426, 435 finite/infinite xxvi, 115, 136, 202, 237–238, 241, 302, 310, 332, 345,

545

355–358, 370, 392, 396–397, 401, 407, 474 structure 91–92, 250–262 university 8, 13 Bologna 11–14, 18–19, 22–24, 138, 140, 152, 162, 167, 173–193, 195–197, 199, 201, 203–205, 211, 215–216, 238, 275, 278, 282, 284, 322–323, 370, 388 German Nation 173, 196 Bourges 178 Cologne 11, 16, 19, 42, 72–73, 81–82, 93, 96, 282–283, 322 Erfurt 282–283 Ferrara 171, 173–174, 176, 178, 180, 198–199, 203–204 Jagiellonian of Cracow 11, 13–33, Chapters 3–5, 179, 244, 279, 281, 357, 372, 374, 387, 389, 437 Oxford 14, 16 Padua 14, 22, 155, 162, 171, 173, 184, 191, 198–203 Paris 13–16, 39, 73, 93, 142, 177 Prague 14–15, 56 Tübingen 283 Vienna 35, 141, 159 Wittenberg Interpretation 405 world 91, 95, 106–107, 115–117, 131, 136, 163–164, 212, 217–223, 225, 231–233, 238–239, 277, 287–288, 297, 322, 402, 424, 429, 431 world machine (machina mundi) 223, 297, 322, 423–424

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