REASON, RELIGION, AND PLATO: ORPHISM AND THE MATHEMATICAL MEDIATION BETWEEN BEING AND BECOMING A thesis submitted in fulfilment of the requirements for the Degree of Doctor of Philosophy in Philosophy in the University of Canterbury by Stephen Peter McNicholl University of Canterbury 2003 iii TABLE OF CONTENTS TABLE O.F CONTENTS .................................................................................................. iii TABLE OF FIGURES ..................................................................................................... vi ABSTRACT ..................................................................................................................... vii ACKNO WLEDGEMENTS ............................................................................................. ix NOTE REGARDING TRANSLATIONS ..................................................................... xi Chapter One: Introduction ............................................................................................... 1 1.1 Statement of Purpose ................................................................................................. 2 1.2 Summary of Content. ................................................................................................. 7 PART ONE: LITERACY, AND THE RISE OF THE ORPmC PmLOSOPHER ..... 13 Chapter Two: The Advent of Literacy ......................................................................... 15 2.1 Overview: From Orality to Literacy ....................................................................... 17 2.2 Myth-making, Mnemonics, and Mimesis ...................................... ;....................... 19 2.2.1 Myth ............................................................................................................................ 19 2.2.2 Mnemonics ................................................................................................................. 21 2.2.3 Mimesis ...................................................................................................................... .22 2.3 The Advent and Adoption of the Alphabet.. ..........................................................24 2.4 The Ascent to Abstraction via the Alphabet .......................................................... 27 2.4.1 Redundancy of the Scribe Literacy in Education ................................................. 27 2.4.2 Alphabetic Attack upon the Art of Memory .............................................................. 29 2.4.3 Abstraction .................................................................................................................. 30 2.4.4 The Transformation of Truth Toward Timelessness ................................................. 33 2.4.5 The Theoretical Attitude of Thought ........................................................................ .40 2.5 Making of a New Morality ...................................................................................... 41 2.6 The Pre-Socratic Philosophers as Precursors to the Platonic Paradigm ............... 45 2.6.1 The Presocratics as Philosophic Pioneers .................................................................. .45 2.6.2 The Milesians (fl. c. 585 - 545 Be) .......................................................................... .46 2.6.3 Xenophanes (c. 570 475 Be) ..................................................................................48 2.6.4 Heraclitus (b. c. 540 Be) ............................................................................................50 2.6.5 Pannenides (c. 515 445 Be) ...................................................................................52 2.6.6 Empedocles (c. 495 435 Be) ..................................................................................55 2.6.7 Literacy Among the Presocratics ............................................................................... 56 2.6.8 The Presocratic Achievement. .................................................................................... 57 2.7 Plato the Champion of a new Cultural Form.................................................... 58 1 9 MAR 1,004 iv Chapter Three: The Advent of Orphism...................................................................... 68 3.1 The Religious Setting .............................................................................................. 70 3.2 The Orphic Movement in Ancient Greek Culture ................................................. 71 3.3 The Apollonian - Dionysian Dual Religious Impulses ......................................... 71 3.3.1 The Apollo - Dionysus Duality as an Interpretive Framework ................................ 71 3.3.2 Dionysus ..................................................................................................................... 74 3.3.3 Apollo .........................................................................................................................76 3.4 The Apollonian - Dionysian Synthesis in the Advent of the Orphic Movement ............................................................. 78 3.5 The Orphic Shift in Anthropology .......................................................................... 83 3.5.1 The New Myth of Mankind ........................................................................................ 83 3.5.2 The Holism of Homeric Man ..................................................................................... 84 3.5.3 Orphic Body-Soul Dualism ........................................................................................ 92 3.5.4 The Immortality of the Soul .................................................................................... 102 3.6 The Cultural Importance of Orphism .................................................................. 103 Chapter Four: The Orphic Philosopher .................................................................... 105 4.1 The Orphic Bard Turns Philosopher .................................................................... 107 4.2 Presocratic Orphism ............................................................................................. 108 4.3 Pythagorean Orphism ........................................................................................... 116 4.3.1 The Orphic-Pythagorean Philosophical Synthesis ................................................. 116 4.3.2 Interpreting the Early Pythagoreans ........................................................................ 116 4.3.3 Pythagoras as an Orphic Philosopher...................................................................... 119 4.3.4 Tonal Transposition: From Orphic Mousike to Pythagorean Harmonic Theory ... 124 4.3.5 The Pythagorean Mathematical World-Order ........................................................ 128 4.4 Platonic Orphism .................................................................................................. 130 4.4.1 Plato as an Orphic Philosopher ............................................................................... 130 4.4.2 Explicit References to Orphism in Plato ................................................................. 131 4.4.3 Plato as the Champion of Orphic-Pythagoreanism ................................................. 134 4.5 Philosophical Anthropology: The Orphic Soul becomes RationaL .................. 137 4.5.1 The Priority of the Rational in Man for the Presocratics ........................................ 137 4.5.2 The Pythagorean Rational Soul. .............................................................................. 138 4.5.3 Reason as the Highest and Immortal part of the Soul in Plato ............................... 139 4.5.4 The Way of Philosophy as the Purification of the Soul in Plato ............................ 142 Chapter Five: Mathematics in the Making ............................................................... 144 5.1 Mathematical Practice among the Ancient Babylonian and Egyptian Cultures .................................................... 146 5.1.1 Ambiguity of Mathematics ...................................................................................... 146 5.1.2 Egypt and Babylon as Precursors to Greece ........................................................... 147 5.1.3 Egyptian Mathematics ............................................................................................. 148 5.1.4 Babylonian Mathematics ......................................................................................... 149 5.2 The Shift Towards the Mathematical Practice of a Philosophical Culture ....... 153 5.2.1 Mathematical Abstraction among the Presocratics ................................................ 153 5.2.2 The Contrast with Euclid ......................................................................................... 158 5.2.3 Effect of the Literacy Shift upon Mathematics ....................................................... 160 5.2.4 Effect of the Anthropological Shift upon Mathematics ......................................... 162 5.3 Classical Greek Mathematics: Toward a Deductive Geometry ......................... 165 v PART Two: PLATO AS ORPHIC MATHEMATICIAN .................................. 167 Chapter Six: The Mathematical World of Plato ...................................................... 169 6.1 Mathematics as the Medium of the Cosmos ....................................................... 171 6.2 Platonic Cosmogony ............................................................................................. 172 6.2.1 Cosmo