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Mathematics and philosophy

Author: Daniel Parrochia
Publisher: London : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., 2018.
Series: Mathematics and statistics series (ISTE)
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 cube, trisection of the angle ...). Subsequently, mathematicians freed themselves from philosophy (with Analysis,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Parrochia, Daniel, 1951-
Mathematics and philosophy.
London : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., 2018
(OCoLC)1011012502
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Daniel Parrochia
ISBN: 9781119527794 1119527791 9781119426813 1119426812 9781119528074 1119528070
OCLC Number: 1037946124
Description: 1 online resource.
Contents: 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.
Series Title: Mathematics and statistics series (ISTE)
Responsibility: Daniel Parrochia.

Abstract:

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 cube, trisection of the angle ...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to inspire philosophers (Descartes, Leibniz, Hegel, Husserl, etc.). However, from a certain level of complexity, the mathematicians themselves became philosophers (a movement that begins with Wronsky and Clifford, and continues until Grothendieck).

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