This study comprises a translation and commentary of Book I of the Planetary Hypotheses by the second century A.D. Greco-Roman astronomer, Claudius Ptolemy. It closely examines the Planetary Hypotheses on its own and in relation to Ptolemy’s other writings. Where necessary I rely on astronomical, philosophical, and technological works by other writers in order to better situate Ptolemy’s ideas into the context of Greco-Roman science. The dissertation is organized into three sections. Section I consists of an extended introduction to the Planetary Hypotheses. I offer a synopsis of the Planetary Hypotheses and a history of the text in Sections I.1 and I.2. Section I.3 consists of a brief introduction to notation and sexagesimal numbers while Section I.4 analyzes the aim and function of Ptolemy’s planetary models. Section II is a translation of the existing Greek text of the Planetary Hypotheses, namely Book I Part A, and a précis of Book I, Part B. The translation is made from J.L. Heiberg’s edited Greek text and the précis relies on the English translation by Bernard Goldstein, the French translation by Regis Morelon, and the Arabic Manuscripts found in the British Library (Arabic-A) and the Library at the University of Leiden (Arabic-B). The footnotes include variant readings from the different Greek and Arabic Manuscripts. A list of all existing manuscripts of the Planetary Hypotheses can be found in Section I.2 Section III is a commentary of the entirety of Book I (Parts A and B). This section is arranged so that it loosely follows the order of topics found in the Planetary Hypotheses. Section III.1 examines the Planetary Hypotheses in terms of instrument-making. Section III.2 discusses the geometric models that Ptolemy presents along with a discussion of the changes that he makes. I give an overview of the period relations and mean motions presented in the Planetary Hypotheses in Section III.3 and III.4 and the new frame of reference in Section III.5. Section III.6 briefly examines Book II of the Planetary Hypotheses and Section III.7 addresses the relationship of Book I and Book II and contextualizes this work in the history of Greco-Roman science. Finally, Section III.8 examines the role the Planetary Hypotheses played in developments within Medieval Islamic astronomy. While I focus on the changes that Ptolemy made to the models in the Planetary Hypotheses from his theories in the Canobic Inscription, Handy Tables, and the Almagest, this work aims to explore the motivations behind these changes. Additionally, I contextualize the Planetary Hypotheses within Greco-Roman and Islamic astronomy and technology. What emerges from this dissertation is a consideration of Ptolemy’s ideas about the practice of science and an analysis of how he modeled astronomical observations.

This study comprises a translation and commentary of Book I of the Planetary Hypotheses by the second century A.D. Greco-Roman astronomer, Claudius Ptolemy. It closely examines the Planetary Hypotheses on its own and in relation to Ptolemy’s other writings. Where necessary I rely on astronomical, philosophical, and technological works by other writers in order to better situate Ptolemy’s ideas into the context of Greco-Roman science. The dissertation is organized into three sections. Section I consists of an extended introduction to the Planetary Hypotheses. I offer a synopsis of the Planetary Hypotheses and a history of the text in Sections I.1 and I.2. Section I.3 consists of a brief introduction to notation and sexagesimal numbers while Section I.4 analyzes the aim and function of Ptolemy’s planetary models. Section II is a translation of the existing Greek text of the Planetary Hypotheses, namely Book I Part A, and a précis of Book I, Part B. The translation is made from J.L. Heiberg’s edited Greek text and the précis relies on the English translation by Bernard Goldstein, the French translation by Regis Morelon, and the Arabic Manuscripts found in the British Library (Arabic-A) and the Library at the University of Leiden (Arabic-B). The footnotes include variant readings from the different Greek and Arabic Manuscripts. A list of all existing manuscripts of the Planetary Hypotheses can be found in Section I.2 Section III is a commentary of the entirety of Book I (Parts A and B). This section is arranged so that it loosely follows the order of topics found in the Planetary Hypotheses. Section III.1 examines the Planetary Hypotheses in terms of instrument-making. Section III.2 discusses the geometric models that Ptolemy presents along with a discussion of the changes that he makes. I give an overview of the period relations and mean motions presented in the Planetary Hypotheses in Section III.3 and III.4 and the new frame of reference in Section III.5. Section III.6 briefly examines Book II of the Planetary Hypotheses and Section III.7 addresses the relationship of Book I and Book II and contextualizes this work in the history of Greco-Roman science. Finally, Section III.8 examines the role the Planetary Hypotheses played in developments within Medieval Islamic astronomy. While I focus on the changes that Ptolemy made to the models in the Planetary Hypotheses from his theories in the Canobic Inscription, Handy Tables, and the Almagest, this work aims to explore the motivations behind these changes. Additionally, I contextualize the Planetary Hypotheses within Greco-Roman and Islamic astronomy and technology. What emerges from this dissertation is a consideration of Ptolemy’s ideas about the practice of science and an analysis of how he modeled astronomical observations.

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 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.

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 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.

Thesis (Ph. D. in Religion)--Vanderbilt University, Dec. 2007. / Title from title screen. Includes bibliographical references.

My dissertation advances a solution to what I have called the problem of opposites in Heraclitus. The problem is this: Heraclitus often juxtaposes pairs of opposites, but the opposites he cites seem to be of many different kinds. How are we to explain this feature of the fragments? The default method of solution for interpreters has been to find a single thesis under which to subsume all the divergent examples of opposites. Some such theses are as follows: opposites are identical (Aristotle, Barnes), opposites are essentially connected (Kirk), opposites are transformationally equivalent (Graham), identical things can have opposite significances in different situations (Osborne). The main problem all these solutions face is that each is only able to make sense of some of the examples of opposition in Heraclitus, while ignoring or downplaying the significance of others. In order to solve this problem, I offer an interpretation on which Heraclitus was advancing multiple opposites theses, each of which contains interesting, philosophical content. The theses are as follows: The Transformation Thesis: the world contains opposing stuffs which transform into one another in such a way that they are transformationally equivalent, and therefore unified. The Dependence Thesis: objects are ontologically dependent for their existence (i.e. that they exist) and their identity (i.e. their ‘nature’ or φύσις) on opposing, yet essential properties which are necessarily inherent in them. The Value Thesis: it is possible for one and the same object to have opposing values (i.e. to be both objectively good and objectively bad). But why would Heraclitus promote multiple opposites theses? On my interpretation Heraclitus was responding to his Ionian predecessors who treated opposites as explanatory principles. Heraclitus seems to be saying that opposites are not explanatory principles since opposites themselves need to be explained. Hence the opposites are explananda, for Heraclitus, and the three theses are his explanantia. / Dissertation / Doctor of Philosophy (PhD) / In this dissertation I offer a new interpretation of an ancient Greek philosopher named Heraclitus who stands at the beginning of the timeline of Western philosophy (around 500BC). It has often been thought that Heraclitus had something interesting to say about opposites (e.g. hot and cold, up and down). Most scholars think that Heraclitus intended to say that opposites are connected; that is, hot is connected to cold since we cannot think of hot without its opposite, cold. I argue in this dissertation that this interpretation and other, alternative interpretations, fail to make good sense of what Heraclitus said about opposites. Rather, I argue that Heraclitus was treating opposites (e.g. hot and cold, up and down) as philosophical problems that need to be explained in order to be solved.

The purpose of the present study is to assess the explanatory value of the concept of the World Soul in the cosmological account of Plato&rsquo / s Timaeus. The World Soul plays a crucial role in the account of the world of Becoming in the Timaeus and in Plato&rsquo / s philosophy of science. The World Soul explains why there is motion at all in the universe and sustains the regularity and uniformity of the motion of the celestial objects. Its constitution and the way it is generated by the Demiurge endow it an intermediary status between the world of Being and the world of Becoming. Through this status the World Soul facilitates the applicability of the items of the former world (Forms and Numbers) in the explanation of the latter, hence makes natural science possible. The appreciation of the place of the World Soul in the natural philosophy of Plato leads us to a better place to view Plato&rsquo / s contribution to ancient natural philosophy and science.

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