Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Clarendon Paperbacks)

The Pythagorean idea that number is the key to understanding reality inspired philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics using mathematical models. These theories were to become influential in medieval and early modern philosophy, yet until now, they have not received the serious attention they deserve. This book marks a breakthrough in our understanding of the subject by examining two themes in conjunction for the first time: the figure of Pythagoras as interpreted by the Neoplatonist philosophers of the period, and the use of mathematical ideas in physics and metaphysics. Table of Contents......Page 10 Introduction......Page 14 Part I: The Revival Of Pythagoreanism In the Neoplatonic School......Page 20 1. Varieties of Pythagoreanism in the Second and Third Centuries AD......Page 22 1. Numenius of Apamea......Page 23 2. Nicomachus of Gerasa......Page 27 3. Anatolius......Page 36 4. Porphyry......Page 38 2. Iamblichus' Work On Pythagoreanism: Title, Plan, the First Four Books......Page 43 1. The Title and Overall Plan......Page 45 2. Pythagoras (Book I: On the Pythagorean Life)......Page 48 3. Pythagorean Philosophy (Book II: the Protreptic)......Page 53 4. Pythagorean Mathematical Science (Book III: On General Mathematical Science)......Page 57 5. Arithmetic (Book IV: On Nicomachus' Arithmetical Introduction)......Page 64 1. Michael Psellus, Philosophical Excerptor......Page 66 2. Psellus' Excerpts from On Pythagoreanism V–VII......Page 70 3. On Pythagoreanism V......Page 73 4. On Pythagoreanism VI......Page 83 5. On Pythagoreanism VII......Page 89 4. Iamblichus' Work On Pythagoreanism: General Conclusions......Page 99 1. On Pythagoreanism: A Brief Review......Page 100 2. The Relation of On Pythagoreanism to Iamblichus' Other Works and Interests......Page 104 3. Iamblichean Pythagoreanism and its Predecessors......Page 114 Part II: Iamblichean Pythagoreanism In the Athenian School......Page 120 5. Hierocles......Page 122 1. The Introduction of Iamblichean Philosophy at Athens in the Fourth Century......Page 123 2. Hierocles on the History of Philosophy......Page 124 3. Pythagoreanism in Hierocles' Commentary on the Golden Verses......Page 127 4. Conclusion......Page 131 1. The History of Philosophy in Syrianus......Page 132 2. Philosophy as Revelation in Hermias' Commentary on the Phaedrus......Page 137 3. Mathematics and Philosophy in Syrianus' Commentary on the Metaphysics......Page 141 7. Proclus: Some Preliminary Issues......Page 155 1. The Rivalry with the Mathematician Domninus of Larissa......Page 156 2. Plato and Pythagoras......Page 158 3. The Theory of Superior Souls......Page 162 4. Learning, Discovery, and Revelation......Page 165 8. Proclus on Mathematics......Page 169 1. General Mathematics......Page 170 2. Arithmetic and (or?) Geometry......Page 179 3. Geometry......Page 183 4. Conclusions......Page 188 1. Aristotle's Physics Geometricized......Page 190 2. Plato's Timaeus as ‘Pythagorean’ Physics......Page 192 3. The Geometrical Method of Plato's Physics......Page 194 4. Is Physics a Science?......Page 195 5. The Application of Mathematical Truths in Physics......Page 198 6. Concluding Comment......Page 205 10. Mathematics and Metaphysics in Proclus......Page 208 1. The Elements of Theology: A Geometrical Metaphysics?......Page 209 2. The Science of Dialectic......Page 211 3. Mathematical Theology and Dialectic......Page 217 4. Concluding Comment......Page 221 Conclusion......Page 223 I. The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes......Page 230 II. The Arabic Commentaries on the Golden Verses attributed to Iamblichus and Proclus......Page 243 1. Ancient Authors......Page 246 2. Modern Authors......Page 249 D......Page 260 J......Page 261 P......Page 262 S......Page 263 Z......Page 264 Table of Contents 10 Introduction 14 Part I: The Revival Of Pythagoreanism In the Neoplatonic School 20 1. Varieties of Pythagoreanism in the Second and Third Centuries AD 22 1. Numenius of Apamea 23 2. Nicomachus of Gerasa 27 3. Anatolius 36 4. Porphyry 38 2. Iamblichus' Work On Pythagoreanism: Title, Plan, the First Four Books 43 1. The Title and Overall Plan 45 2. Pythagoras (Book I: On the Pythagorean Life) 48 3. Pythagorean Philosophy (Book II: the Protreptic) 53 4. Pythagorean Mathematical Science (Book III: On General Mathematical Science) 57 5. Arithmetic (Book IV: On Nicomachus' Arithmetical Introduction) 64 3. On Pythagoreanism V–VII: The Excerpts in Michael Psellus 66 1. Michael Psellus, Philosophical Excerptor 66 2. Psellus' Excerpts from On Pythagoreanism V–VII 70 3. On Pythagoreanism V 73 4. On Pythagoreanism VI 83 5. On Pythagoreanism VII 89 4. Iamblichus' Work On Pythagoreanism: General Conclusions 99 1. On Pythagoreanism: A Brief Review 100 2. The Relation of On Pythagoreanism to Iamblichus' Other Works and Interests 104 3. Iamblichean Pythagoreanism and its Predecessors 114 Part II: Iamblichean Pythagoreanism In the Athenian School 120 5. Hierocles 122 1. The Introduction of Iamblichean Philosophy at Athens in the Fourth Century 123 2. Hierocles on the History of Philosophy 124 3. Pythagoreanism in Hierocles' Commentary on the Golden Verses 127 4. Conclusion 131 6. Syrianus 132 1. The History of Philosophy in Syrianus 132 2. Philosophy as Revelation in Hermias' Commentary on the Phaedrus 137 3. Mathematics and Philosophy in Syrianus' Commentary on the Metaphysics 141 7. Proclus: Some Preliminary Issues 155 1. The Rivalry with the Mathematician Domninus of Larissa 156 2. Plato and Pythagoras 158 3. The Theory of Superior Souls 162 4. Learning, Discovery, and Revelation 165 8. Proclus on Mathematics 169 1. General Mathematics 170 2. Arithmetic and (or?) Geometry 179 3. Geometry 183 4. Conclusions 188 9. Mathematics and Physics in Proclus 190 1. Aristotle's Physics Geometricized 190 2. Plato's Timaeus as ‘Pythagorean’ Physics 192 3. The Geometrical Method of Plato's Physics 194 4. Is Physics a Science? 195 5. The Application of Mathematical Truths in Physics 198 6. Concluding Comment 205 10. Mathematics and Metaphysics in Proclus 208 1. The Elements of Theology: A Geometrical Metaphysics? 209 2. The Science of Dialectic 211 3. Mathematical Theology and Dialectic 217 4. Concluding Comment 221 Conclusion 223 Appendices 230 I. The Excerpts from Iamblichus' On Pythagoreanism V–VII in Psellus: Text, Translation, and Notes 230 II. The Arabic Commentaries on the Golden Verses attributed to Iamblichus and Proclus 243 Bibliography 246 1. Ancient Authors 246 2. Modern Authors 249 Index 260 A 260 B 260 C 260 D 260 E 261 F 261 G 261 H 261 I 261 J 261 K 262 L 262 M 262 N 262 O 262 P 262 R 263 S 263 T 264 U 264 V 264 W 264 X 264 Z 264

The Pythagorean idea that numbers are the key to understanding reality inspired philosophers in late Antiquity (4th and 5th centuries A.D.) to develop theories in physics and metaphysics based on mathematical models. This book draws on some newly discovered evidence, including fragments of Iamblichus's On Pythagoreanism, to examine these early theories and trace their influence on later Neoplatonists (particularly Proclus and Syrianus) and on medieval and early modern philosophy.

The Pythagorean idea that number is the key to understanding reality inspired Neoplatonist philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics based on mathematical models. The theories produced by this revived interest in Pythagoreanism were to become influential in medieval and early modern philosophy, and this book makes use of some newly-discovered evidence to examine for the first time the development of those theories. This title examines the Pythagorean idea that number is the key to understanding reality, describing first the Pythagorean interests of Platonists in the second and third centuries and then Iamblichus's programme to Pythagoreanize Platonism in the fourth century in his work 'On Pythagoreanism' The Pythagorean idea that number is the key to understanding reality inspired philosophers in the 4th and 5th centuries AD to develop theories in physics and metaphysics based on mathematical models. This book examines their theories in the light of newly discovered evidence. Pythagorean theory inspired philosophers in the 4th and 5th centuries AD to develop theories in physics and metaphysics based on mathematical models. This book uses newly discovered evidence to examine these theories. Dominic J. O'meara. Includes Index. Bibliography: P. [233]-246.