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Poincaré, Philosopher of ScienceHenri Poincaré: A Scientist Inspired by His Philosophy

Poincaré, Philosopher of Science: Henri Poincaré: A Scientist Inspired by His Philosophy [This paper attempts to analyze the philosophical connections that PoincaréPoincaré established between the domains of physics and mathematics, both explicitly in his philosophical work, and implicitly in his original solutions in mathematics. Particular emphasis will be placed on the signs of coherence or incoherence between what is explicit and what is implicit, that is, between his thought in general and his scientific practicescientific practice. In Poincaré’s early work on the groupgroup-theoretical approach to differential equationsdifferential equations, we see the beginnings of an original way of connecting geometrygeometry with physics. Similarly, in his attack on the three-body problemthree-body problem in celestial mechanicscelestial mechanics, and his study of the stability of the solar system, we see a geometrical approach replacing the analytical one. His group-theoretic approach to geometry later became the basis for his approach to the “dynamics of the electron” between 1904 and 1906, an important part of the history of relativity theory. These are examples of the ways in which, according to Poincaré, “l’esprit mathématique” leads to the “true, profound analogies,” that is, the deep structural forms, at the foundations of our physical theories. The understanding of these connections in practice will illuminate Poincaré’s philosophical view of the connection between mathematics and physics. But we can say that, on the other hand, Poincaré’s philosophical views also influenced his scientific work.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Poincaré, Philosopher of ScienceHenri Poincaré: A Scientist Inspired by His Philosophy

Part of the The Western Ontario Series in Philosophy of Science Book Series (volume 79)
Editors: de Paz, María; DiSalle, Robert
Serra, Isabel
Poincaré, Philosopher of Science — Mar 12, 2014
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References (21)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media Dordrecht 2014
ISBN
978-94-017-8779-6
Pages
153 –166
DOI
10.1007/978-94-017-8780-2_9
Publisher site
See Chapter on Publisher Site

Abstract

[This paper attempts to analyze the philosophical connections that PoincaréPoincaré established between the domains of physics and mathematics, both explicitly in his philosophical work, and implicitly in his original solutions in mathematics. Particular emphasis will be placed on the signs of coherence or incoherence between what is explicit and what is implicit, that is, between his thought in general and his scientific practicescientific practice. In Poincaré’s early work on the groupgroup-theoretical approach to differential equationsdifferential equations, we see the beginnings of an original way of connecting geometrygeometry with physics. Similarly, in his attack on the three-body problemthree-body problem in celestial mechanicscelestial mechanics, and his study of the stability of the solar system, we see a geometrical approach replacing the analytical one. His group-theoretic approach to geometry later became the basis for his approach to the “dynamics of the electron” between 1904 and 1906, an important part of the history of relativity theory. These are examples of the ways in which, according to Poincaré, “l’esprit mathématique” leads to the “true, profound analogies,” that is, the deep structural forms, at the foundations of our physical theories. The understanding of these connections in practice will illuminate Poincaré’s philosophical view of the connection between mathematics and physics. But we can say that, on the other hand, Poincaré’s philosophical views also influenced his scientific work.]

Published: Mar 12, 2014

Keywords: Lorentz Transformation; Lorentz Group; Group Group; Philosophical Thought; Mathematical Unity

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