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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 |
|---|---|
| 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 |
MARC
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| 100 | 1 | |a Parrochia, Daniel, |d 1951- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJbxJdt64QcydD83TpR7pP | |
| 245 | 1 | 0 | |a Mathematics and philosophy / |c Daniel Parrochia. |
| 264 | 1 | |a London : |b ISTE Ltd ; |a Hoboken, NJ : |b John Wiley & Sons, Inc., |c 2018. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and statistics series | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed May 30, 2018). | |
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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). | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Reference. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast | |
| 758 | |i has work: |a Mathematics and philosophy (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGPMTc7YrVyXWWfDDd87VC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Parrochia, Daniel, 1951- |t Mathematics and philosophy. |d London : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., 2018 |z 1786302098 |z 9781786302090 |w (OCoLC)1011012502 |
| 830 | 0 | |a Mathematics and statistics series (ISTE) | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5401173 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 3.6. What came next and the conclusion to the history of πPART: 2 Mathematics Becomes More Powerful; Introduction to Part 2; 4 Exploring Mathesis in the 17th Century; 4.1. The innovations of Cartesian mathematics; 4.2. The "plan" for Descartes' Geometry; 4.3. Studying the classification of curves; 4.4. Legitimate constructions; 4.5. Scientific consequences of Cartesian definitions; 4.6. Metaphysical consequences of Cartesian mathematics; 5 The Question of Infinitesimals; 5.1. Antiquity -- the prehistory of the infinite; 5.2. The birth of the infinitesimal calculus. | |
| 880 | 8 | |6 505-01/(S |a 2.1. History of the question of doubling a cube2.2. The non-rationality of the solution; 2.3. The theory proposed by Hippocrates of Chios; 2.4. A philosophical application: platonic cosmology; 2.5. The problem and its solutions; 2.6. The trisection of an angle; 2.7. Impossible problems and badly formulated problems; 2.8. The modern demonstration; 3 Quadratures, Trigonometry and Transcendance; 3.1. π -- the mysterious number; 3.2. The error of the "squarers"; 3.3. The explicit computation of π; 3.4. Trigonometric considerations; 3.5. The paradoxical philosophy of Nicholas of Cusa. | |
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