The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
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...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2019.
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| Έκδοση: | 1st ed. 2019. |
| Σειρά: | 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 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
