The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective

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Overview


This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The Aristotelian model is presented as an application of the ancient, geometrically orthodox conception of extension to the physical world. The other two models, which represent departures from mathematical orthodoxy, are a "quantum" model of spatial magnitude, and a Stoic model, according to which limit entities such as points, edges, and surfaces do not exist in (physical) reality. The book is unique in its discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments.
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Editorial Reviews

From the Publisher

"An unusually productive approach to the history of philosophy, one that combines historical reconstruction through detailed technical analysis from within the perspective of the ancient theories."--Bryn Mawr Classical Review

"Scholarly, provocative, and persuasive....Highly recommended for concentrated collections in classics and in the philosophy of science."--Choice

"Though White's detailed analyses are thoughtful and original, the great virtue of the work lies in its raising new questions concerning the metaphysical underpinnings of the various ways both ancient and contemporary theoreticians have conceptualized continuity. The work will surely be a central reference for future treatments of these problems."--Ancient Philosophy

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Product Details

  • ISBN-13: 9780198239529
  • Publisher: Oxford University Press, USA
  • Publication date: 6/28/1992
  • Pages: 368
  • Product dimensions: 5.69 (w) x 8.75 (h) x 1.11 (d)

Meet the Author

Arizona State University, Tempe
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Table of Contents

List of Figures
Pt.: I Spatial Magnitude, Time, and Motion: An Aristotelian Model
Introduction to Part I 3
1 Aristotle: The Formal Analysis of Spatial Magnitude and Locomotion 7
Spatial Magnitude 7
Locomotion 32
Three Kinematic Mistakes: An Analysis 53
2 Aristotle on Time and Locomotion: Physics and Metaphysics 73
Time 74
The Metaphysics of Kineseis 96
3 Aristotelian Kinematics and Non-Locomotive Kineseis 116
Rotary Motion 116
Non-Kinetic Change 120
Qualitative Kineseis 126
Afterword 130
4 Aristotle and the Mathematicians, Ancient and Modern 133
Aristotle and Ancient Mathematics 134
Aristotle and Modern Mathematics 174
Pt. II Spatial Magnitude, Time, and Motion: Alternatives to Aristotelianism
Introduction to Part II 191
5 The Quantum Model: Spatial Magnitude 193
Arguments for Quanta 198
Geometry and the Quantum Model 230
6 The Quantum Model: Time and Locomotion 252
Aristotle on the Relations among Kinds of Quantum 252
Cinematographic Motion: Diodorus Cronus' View? 259
Epicurean Quantum-Motion: The Micro-Level 269
The Epicurean Conception of Speed: Micro-Level and Macro-Level 273
Overview 280
7 The Stoic Model 284
The Removal of Limit Entities from the Physical World 285
Locomotion: The Doctrine of Motion Athroos 314
Conclusion 324
Peroration 327
Select Bibliography 331
Index 339
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