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Ptolemy in Philosophical Context: a Study of the Relationships Between Physics, Mathematics, and Theology

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Ptolemy in Philosophical Context: a Study of the Relationships Between Physics, Mathematics, and Theology Ptolemy in Philosophical Context: A Study of the Relationships Between Physics, Mathematics, and Theology by Jacqueline Feke A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Jacqueline Feke, 2009 Abstract Ptolemy in Philosophical Context: A Study of the Relationships Between Physics, Mathematics, and Theology Jacqueline Feke, Doctor of Philosophy, 2009 Institute for the History and Philosophy of Science and Technology University of Toronto This study situates Ptolemy’s philosophy within the second-century milieu of Middle Platonism and the nascent Aristotelian commentary tradition. It focuses on Ptolemy’s adaptation and application of Aristotle’s tripartite division of theoretical philosophy into the physical, mathematical, and theological. In Almagest 1.1, Ptolemy defines these three sciences, describes their relations and objects of study, and addresses their epistemic success. According to Ptolemy, physics and theology are conjectural, and mathematics alone yields knowledge. This claim is unprecedented in the history of ancient Greek philosophy. Ptolemy substantiates this claim by constructing and employing a scientific method consistent with it. In Almagest 1.1, after defining the theoretical sciences, Ptolemy adds that, while theology and physics are conjectural, mathematics can make a good guess at the nature of theological objects and contribute significantly to the study of physics. He puts this claim into practice in the remainder of his corpus by applying mathematics to theology and physics in order to produce results in these fields. After the introductory chapter, I present Ptolemy’s philosophy and practice of the three theoretical sciences. In Chapter 2, I examine how and why Ptolemy defines the sciences in ii Almagest 1.1. In Chapter 3, I further analyze how Ptolemy defines mathematical objects, how he describes the relationships between the tools and branches of mathematics, and whether he demonstrates in the Harmonics and Almagest that he believed mathematics yields sure and incontrovertible knowledge, as he claims in Almagest 1.1. In Chapter 4, I present Ptolemy’s natural philosophy. While in Chapter 2 I discuss his element theory, in Chapter 4 I focus on his physics of composite bodies: astrology, psychology, and cosmology as conveyed in the Tetrabiblos, On the Kritêrion, Harmonics, and Planetary Hypotheses. I do not devote a chapter to theology, as Ptolemy refers to this science only once in his corpus. Therefore, I limit my analysis of his definition and practice of theology to Chapter 2. In the concluding chapter, I discuss Ptolemy’s ethical motivation for studying mathematics. What emerges from this dissertation is a portrait of Ptolemy’s philosophy of science and the scientific method he employs consistently in his texts. iii Acknowledgements It is with much emotion and kind regards that I thank my colleagues, friends, and family who supported me during the writing of this dissertation. First, I would like to thank my supervisor, Prof. Alexander Jones, for teaching me how to be a historian. I benefited from his generosity, patience, and encouragement. I must also thank my two committee members: Prof. Brad Inwood, for his expansive knowledge of ancient Greek philosophy and, above all, his willingness to tell it like it is, and Prof. Craig Fraser, for his interest in my work as well as his assistance in tacking the mathematical aspects of my research. Prof. Marga Vicedo, a voting member for my defense, offered perspective, good humor, and enthusiasm. Prof. Stephan Heilen, my external examiner, generously provided me with extensive comments and suggestions that will no doubt be instrumental in transforming this dissertation into a book. I must thank all of the faculty and staff at the Institute for the History and Philosophy of Science and Technology as well as the Department of Classics, the former for giving me an educational home, the latter for offering me several teaching appointments, on which my financial stability depended. Denise Horsley, Muna Salloum, Coral Gavrilovic, and Ann-Marie Matti were fundamental in providing me with administrative support. The fellows of Massey College were pivotal in making me feel at home in Toronto. Ulrich Germann assisted me in translating Ptolemy’s Planetary Hypotheses. Prof. Nathan Sidoli acted as a mentor for me and shared invaluable advice on how to succeed in my studies. Prof. Deborah Boedeker served as a constant source of inspiration and encouragement. She provided me with the direction to study the iv history of ancient science, and Prof. David Pingree advised me to attend the University of Toronto. The loyalty and support of my friends have guided me through every obstacle, and I am thankful that they never let life get too serious. I would like to single out Elizabeth Burns, who has been like family to me. I am so glad that we share a love for Ptolemy. In addition, Susanna Ciotti, Jessica Jones, and Ruth Kramer have always been there for me, night and day. More than anyone else, my parents, Gilbert and Carol Feke, deserve thanks. They have given me unconditional love and support, and it is to them that I dedicate this dissertation. v Table of Contents 1 Introduction 1 2 Ptolemy on the Definitions of Physics, Mathematics, and Theology 17 2.1 Aristotle’s Division of Knowledge 18 2.2 Ptolemy’s Definitions of Physics, Mathematics, and Theology 23 2.3 Knowledge and Conjecture: The Epistemic Value of Physics, Mathematics, and Theology 39 2.4 The Contribution of Astronomy to the Study of Theology 64 2.5 Conclusion 66 3 Ptolemy’s Epistemology and Ontology of Mathematics 68 3.1 Harmonia 69 3.2 Mathematical Objects as Beautiful 91 3.3 Harmonic Ratios in the Human Soul 97 3.4 Harmonic Ratios in the Heavens 103 3.5 The Relationship between Harmonics and Astronomy 112 3.6 Observation as a Criterion and Mathematics’ Contribution to Physics 148 4 Ptolemy’s Epistemology and Ontology of Physics 152 4.1 Astrology 153 4.2 The Nature of the Human Soul 173 4.3 The Three Faculties of the Human Soul in On the Kritêrion and Hêgemonikon 178 4.4 The Models of the Human Soul in the Harmonics 185 4.5 Celestial Souls and Bodies in Planetary Hypotheses 2 201 4.6 Conclusion 219 5 Conclusion 221 Bibliography 229 vi Chapter 1 Introduction Klaudios Ptolemaios, or Ptolemy, is known today mainly for his scientific contributions. Living in the second century C.E. in or around Alexandria, he developed astronomical models that served as the western world’s paradigm in astronomy for approximately 1400 years, up to the time of the Scientific Revolution. He composed an astrological work, the Tetrabiblos, which modern astrologers still hold in high regard,1 and he wrote treatises on harmonics, optics, and geography, which influenced the practice of these sciences from antiquity to the renaissance. In the Greco-Roman world, the study and practice of the sciences was generally a philosophical endeavor. What we translate as science was epistême, knowledge or a field of intellectual activity. Aristotle distinguishes theoretical, productive, and practical knowledge in the Metaphysics, and this categorization became paradigmatic in ancient Greek philosophy. As a student and practitioner of the theoretical sciences, Ptolemy identifies himself as a genuine philosopher in the introduction to the Almagest. 1 For instance, James R. Lewis, a professional astrologer and author of The Astrology Encyclopedia, calls Ptolemy “the father of Western astrology” and “the most influential single astrologer in Western history.” See James R. Lewis, The Astrology Encyclopedia (Detroit: Visible Ink Press, 1994), 442. 1 2 The Almagest, originally called the Mathematical Composition (mathêmatikê syntaxis), is Ptolemy’s longest and arguably most influential text.2 In it, he presents a series of astronomical models, which aim to account for the movements of the stars and planets, including the sun and moon. The models are both demonstrative and predictive, since by using the tables, an astrologer would have been able to determine the perceptible location of any celestial body on any given date. The first chapter, Almagest 1.1, serves as a philosophical introduction to the text. Ptolemy sets the philosophical groundwork for his astronomical hypotheseis and provides one of his few citations of a philosophical predecessor, Aristotle. This citation is especially significant, because we have no direct evidence of Ptolemy’s education. The very little of Ptolemy’s life that we know derives mainly from his extant texts, and in them he neither affiliates himself with a specific school nor proclaims himself an eclectic, as did his contemporary Galen. Nevertheless, the citation of Aristotle establishes Ptolemy’s familiarity with the Aristotelian tradition. Moreover, after he cites Aristotle, Ptolemy affirms that philosophers are correct in distinguishing theoretical from practical philosophy, as Aristotle does in the Metaphysics, and he appropriates Aristotle’s trichotomy of the three theoretical sciences: physics, mathematics, and theology. Ptolemy’s definitions of the three theoretical sciences, as well as his descriptions of their relations, their objects of study, and their epistemic success, are the focus of this dissertation. Liba Taub recognizes the significance of Almagest 1.1 as a statement of Ptolemy’s philosophy in her book Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy.3 Taub discusses both the Almagest and the Planetary Hypotheses, but she dedicates the bulk of Ptolemy’s Universe to Book 1 of the Almagest. Her contribution 2 J.L. Heiberg, Claudii Ptolemaei: Syntaxis Mathematica, vol. 1, Claudii Ptolemaei: Opera Quae Exstant Omnia (Leipzig: Teubner, 1898); G.J. Toomer, Ptolemy’s Almagest (London: Duckworth, 1984). 3 Chicago: Open Court, 1993. 3 mainly consists in her arguments for the following two points: (1) Much of Ptolemy’s language and many of his ideas are not Aristotle’s, and (2) Ptolemy’s portrayal of the ethical benefits of studying astronomy is Platonic.
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