The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics 1st edition by John 3030187071 9783030187071

The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics 1st edition by John Bell – Ebook Instant Download/Delivery ISBN(s): 3030187071, 9783030187071

Product details:

• ISBN 10: 3030187071
• ISBN 13: 9783030187071
• Author: John Bell

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy.  Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’  reviews the work of Plato, Aristotle, Epicurus, and other  Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme.

Table of contents:

Part I. The Continuous, the Discrete, and the Infinitesimal in the History of Thought

1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages

2. The Sixteenth and Seventeenth Centuries. The Founding of the Infinitesimal Calculus

3. The Eighteenth and Early Nineteenth Centuries: The Age of Continuity

4. The Reduction of the Continuous to the Discrete in the Nineteenth and Early Twentieth Centuries

5. Dissenting Voices: Divergent Conceptions of the Continuum in the Nineteenth and Early Twentieth Centuries

Part II. Continuity and Infinitesimals in Today’s Mathematics

6. Topology

7. Category/Topos Theory

8. Nonstandard Analysis

9. The Continuum in Constructive and Intuitionistic Mathematics

10. Smooth Infinitesimal Analysis/Synthetic Differential Geometry

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