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The Infinite

By: A. W. Moore | Book details

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Page vii
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Contents
Preface to the Second Edition xi
Preface xx
Introduction: Paradoxes of the Infinite 1
1 Paradoxes of the infinitely small 3
2 Paradoxes of the infinitely big 5
3 Paradoxes of the one and the many 9
4 Paradoxes of thought about the infinite 11
PART ONE:THE HISTORY
1 Early Greek Thought 17
1 Anaximander and to apeiron17
2 The Pythagoreans 19
3 The Eleatics 23
4 Plato 26
5 Early Greek mathematics 28
2 Aristotle 34
1 Preliminaries 34
2 The problem 36
3 The solution: the potential infinite and the actual infinite 39
4 Application of the solution 40
5 A remaining difficulty 44
3 Medieval and Renaissance Thought 45
1 The Greek legacy: reactions and developments 45
2 Aquinas 48
3 Later developments: the mathematically infinite 50
4 Nicholas of Cusa. The end of the Renaissance 55
4 The Calculus 57
1 The fundamental principles of the calculus 57

-vii-

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