PHILIP THE CHANCELLOR, BONAVENTURE OF BAGNOREGIO, AND THOMAS AQUINAS ON THE ETERNITY OF THE WORLD A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Joseph William Yarbrough, III May 2011 © 2011 Joseph William Yarbrough, III PHILIP THE CHANCELLOR, BONAVENTURE OF BAGNOREGIO, AND THOMAS AQUINAS ON THE ETERNITY OF THE WORLD Joseph William Yarbrough, III, Ph.D. Cornell University 2011 Some philosophers have thought that there are sound arguments proving that past time is necessarily finite in duration. In light of these arguments, I examine the positions taken on past time by Philip the Chancellor, Bonaventure, and Thomas Aquinas. Philip argues that nothing created can be eternal and that everything which is not eternal is finite in past duration; I argue that many of the insights of Philip’s position can be preserved even if the world is infinite in past duration. Bonaventure also believes that a created world must be finite in past duration, but, as I show, he accepts the conceptual possibility of infinite past time in an uncreated world. Despite being more liberal about infinite past time than is often believed, Bonaventure maintains the principle that it is impossible for an infinite number of things to exist simultaneously. I discuss how this principle bears on the eternity of the world discussion in both Bonaventure’s writing and Aquinas’. Aquinas holds this principle for much of his career, albeit with some hesitation, but at the end of his life, he rejects it. I suggest that material from his Physics commentary on immaterial multitudes may give some insight as to why he does so. I also argue that Aquinas offers a successful reply to the argument that infinite past time is conceptually impossible because it entails the completion of an actually infinite series. BIOGRAPHICAL SKETCH Joseph William Yarbrough, III was born on March 27, 1980 in Lansing, Michigan, the first son of Joseph and Diane Yarbrough. He began his education at Maplewood Elementary School in Lansing, but when the family moved to East Lansing, MI, he entered Marble Elementary. In due course, he attended MacDonald Middle School and East Lansing High School where he graduated in 1998. He completed in 2002 his B.A. (magna cum laude) at Valparaiso University (Indiana) in Classics and Philosophy. It was there that Dr. Sandra Visser first kindled in him an interest in analytic philosophy as an academic discipline and as a way to think about the perennial questions of metaphysics and epistemology. In the following academic year, Joseph went up to the University of Oxford, matriculating there during Michaelmas Term 2002. While a member of St. Cross College and living at the Centre for Hebrew and Jewish Studies in Yarnton, he pursued a course of studies in the ancient Hebrew tongue, Jewish history and philosophy. He wrote a thesis concerning Maimonides’ views on the beginning of the world for the degree of Master of Studies under the supervision of Dr. Joanna Weinberg. In the fall of 2003 he entered Cornell University where he completed a doctoral dissertation on the eternity of the world under the supervision of Professor Scott MacDonald. Since 2009 he has lived with his wife and children in Ave Maria, FL, where he teaches classics and philosophy at Ave Maria University. iii In gratitude to my parents, Joseph and Diane, and to my grandparents, Emerson and Marjorie, I dedicate this work. iv ACKNOWLEDGMENTS I would like to thank my dissertation committee – Scott MacDonald, Charles Brittain, and Harold Hodes – for the time and feedback they gave to me over the course of this project. I am also grateful to Ave Maria University, to the academic dean, Michael Dauphinais, and to the chair of the Classics Department, Bradley Ritter, for their patience as I finished this project somewhat later than I had initially hoped. Finally, I will always warmly remember the friends who made graduate school at Cornell that much more fruitful: Jacob Klein, Mark Wyman, Jeffrey Corbeil, Robert Gahl, Stephen Ippolito, Mathew Lu and Rachel Lu (née Smith). v TABLE OF CONTENTS Biographical Sketch iii Dedication iv Acknowledgments v Introduction – The Question of a Beginningless World 1 Chapter 1 – Conceptions of Time and Eternity 7 Chapter 2 – Philip the Chancellor on Time and Eternity 26 Chapter 3 – Bonaventure Reconsidered 69 Chapter 4 – Aquinas and a Beginningless World 105 Conclusion – The Significance of Philip, Bonaventure, and Aquinas 148 Appendix A – Translation: Bonaventure on the Eternity of the World 153 Appendix B – Translation: Bonaventure on Infinity & God’s Power 170 Bibliography 209 vi INTRODUCTION THE QUESTION OF A BEGINNINGLESS WORLD Is it conceptually possible that past time is infinite in duration? That is, irrespective of the physical laws of the actual world, is it possible that some world is infinite in past duration? This question has been a point of philosophical dispute from ancient times. The discussion over this question was most heated during the 13th century at the University of Paris, but it has not wanted for partisans even at the present day. Yet why would anyone think that the infinite duration of past time is a conceptual impossibility? Let us look at the following putative problems in regard to past time and infinity. Supposing time were infinite in past duration, every negative integer would correspond to a moment of elapsed time. On the timeline below, 0 is the present moment, the negative integers mark discrete moments of past time equal in duration, and the positive integers do the same for future moments of time. ∞ …-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 … This illustration suggests that, on the condition that past time is infinite in duration, the entire series of negative integers has been exhausted!1 That is, a moment ago, the very last of the negative integers was used in counting down the moments of past time. Yet how could all of the negative integers have been used up? Since there is no greatest integer, how could the supply ever run out? Another puzzle appears on the assumption of infinite past time: if I had to count all of the integers (whether positive or negative), I would never reach the end of my task, even if I had an unending amount of time to work with. Yet somehow, out of the misty past, shrouded 1 “Simple as it is, this may well be the most formidable and intriguing argument ever offered against the possibility of a beginningless world. If its attractiveness for the audacious party in the medieval debate isn’t immediately obvious, just think about correlating each negative integer with one past day and counting all the negative integers, ending with -3, -2, -1” (Kretzmann 1998, 177-178). 1 in the obscurity of infinity, time has run through all of the negative integers and has reached 0, the present moment. One side of the debate denies that something like this is possible; the other side makes the opposite claim. Unlike some other philosophical questions which spawn various schools of thought and many nuanced solutions, there can be only two camps in regard to the conceptual possibility of past time’s infinite duration: either it is possible or it is not. Should not some decisive account have laid the matter to rest long ago? Or are there certain characteristics which have made this debate one for the ages? I think that we can identify certain conflicting intuitions about the concept of infinity which lead to the disagreement over past time and which remain unreconciled even after the mathematics of infinity has reached a high level of clarity. The nature of infinity has held a prominent place in this discussion since Aristotle, but this aspect of the debate became all the more important after the work of Georg Cantor during the 19th century in transfinite mathematics. Set theory, which posits infinite sets, supported the intuition in the minds of some that past time is possibly infinite. Other mathematicians, while they grudgingly acknowledged a place for the actually infinite in mathematics, thought that actually infinite sequences existed nowhere but in the mathematical realm and, thus, that analogies could not be drawn between such mathematical quantities and quantities of non-mathematical objects. I devote Chapter 1 to examining these puzzles about infinity at greater length while also providing an introduction to the technical terminology which regularly occurs in the discussion of infinite past time. Chapters 2-4 are the heart of the dissertation in which I evaluate the contributions of Philip the Chancellor (1160? – 1236), Bonaventure of Bagnoregio (1221-1274), and Thomas Aquinas (1225-1274). But why am I writing about these three figures in particular? In Chapter 2, I look at Philip the Chancellor, who taught in Paris at the beginning of the 13th century when 2 Aristotle’s writings, which greatly influenced the medieval discussion of the eternity of the world, were entering the Latin West.2 Philip is thus important because he stands at the head of a tradition of Catholic thinkers reading and interpreting Aristotle. The Philosopher, as he was often known, had burst onto the philosophical scene, eclipsing in his writings on natural philosophy the earlier tradition in which Plato and the Timaeus had figured prominently. Because of the power of his thought, Aristotle posed a challenge to the Catholic Church, which, unlike Aristotle, taught that the world had begun a finite number of years ago. Thus, Philip’s reading of Aristotle which attempts to reconcile the Catholic belief in the finitude of past time with Aristotle’s arguments for beginningless past time is of particular interest.