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Mathematics and philosophy /
This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cub...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London : Hoboken, NJ :
ISTE Ltd ; John Wiley & Sons, Inc.,
2018.
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| Colección: | Mathematics and statistics series (ISTE)
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Table of Contents; Introduction; PART: 1 The Contribution of Mathematician-Philosophers; Introduction to Part 1; 1 Irrational Quantities; 1.1. The appearance of irrationals or the end of the Pythagorean dream; 1.2. The first philosophical impact; 1.3. Consequences of the discovery of irrationals; 1.4. Possible solutions; 1.5. A famous example: the golden number; 1.6. Plato and the dichotomic processes; 1.7. The Platonic generalization of ancient Pythagoreanism; 1.8. Epistemological consequences: the evolution of reason; 2 All About the Doubling of the Cube.
- 6 Complexes, Logarithms and Exponentials6.1. The road to complex numbers; 6.2. Logarithms and exponentials; 6.3. De Moivre's and Euler's formulas; 6.4. Consequences on Hegelian philosophy; 6.5. Euler's formula; 6.6. Euler, Diderot and the existence of God; 6.7. The approximation of functions; 6.8. Wronski's philosophy and mathematics; 6.9. Historical positivism and spiritual metaphysics; 6.10. The physical interest of complex numbers; 6.11. Consequences on Bergsonian philosophy; PART: 3 Significant Advances; Introduction to Part 3; 7 Chance, Probability and Metaphysics.
- 7.1. Calculating probability: a brief history7.2. Pascal's "wager"; 7.3. Social applications, from Condorcet to Musil; 7.4. Chance, coincidences and omniscience; 8 The Geometric Revolution; 8.1. The limits of the Euclidean demonstrative ideal; 8.2. Contesting Euclidean geometry; 8.3. Bolyai's and Lobatchevsky geometries; 8.4. Riemann's elliptical geometry; 8.5. Bachelard and the philosophy of "non"; 8.6. The unification of Geometry by Beltrami and Klein; 8.7. Hilbert's axiomatization; 8.8. The reception of non-Euclidean geometries; 8.9. A distant impact: Finsler's philosophy.