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.
Author(s): Dominic J. O'Meara
Year: 1991
Language: English
Pages: 264
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
