The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics

• Main Author: Bell, John L. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: The Western Ontario Series in Philosophy of Science, A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields, 82
• Subjects: Mathematics-Philosophy.; Philosophy.; Mathematical logic.; Mathematical analysis.; Analysis (Mathematics).; Differential geometry.; Mathematics.; History.; Philosophy of Mathematics.; History of Philosophy.; Mathematical Logic and Formal Languages.; Analysis.; Differential Geometry.; History of Mathematical Sciences.

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, t...

Table of Contents:

• Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought
• Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages
• Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus
• Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity
• Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries
• Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries
• Part II: Continuity and Infinitesimals in Today's Mathematics
• Chapter 6. Topology
• Chapter 7. Category/Topos Theory
• Chapter 8. Nonstandard Analysis
• Chapter 9. The Constructive and Intuitionistic Continua
• Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry.