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Poincaré, Philosopher of SciencePoincaré and the Principles of the Calculus

Poincaré, Philosopher of Science: Poincaré and the Principles of the Calculus [PoincaréPoincaré wrote several papers and sections of books on geometry and space, less on the continuumcontinuum, but very little on the basic notions of the infinitesimalinfinitesimal calculus. The 1905 paper “CournotCournot et les Principes du Calcul Infinitesimal” is one of the very few places where Poincaré expounds his own views on the subject, although by way of comment of Cournot’s Traité élémentaire des fonctions … (1841) and Traité de l’enchaînement des idées … (1861), which he cites profusely, and whose ideas in this subject were otherwise neglected by both contemporaries and modern commentators. In this paper we analyze Poincaré’s paper with two aims: to characterize briefly his ideas regarding the calculus and, in particular, the use of actual infinitesimals, and the relation between these findings and his concept of the continuum. It would seem that Poincaré endorses most if not all of what Cournot has to say about infinitesimals.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Poincaré, Philosopher of SciencePoincaré and the Principles of the Calculus

Part of the The Western Ontario Series in Philosophy of Science Book Series (volume 79)
Editors: de Paz, María; DiSalle, Robert
de Oliveira, Augusto J. Franco
Poincaré, Philosopher of Science — Mar 12, 2014
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References (5)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media Dordrecht 2014
ISBN
978-94-017-8779-6
Pages
101 –111
DOI
10.1007/978-94-017-8780-2_6
Publisher site
See Chapter on Publisher Site

Abstract

[PoincaréPoincaré wrote several papers and sections of books on geometry and space, less on the continuumcontinuum, but very little on the basic notions of the infinitesimalinfinitesimal calculus. The 1905 paper “CournotCournot et les Principes du Calcul Infinitesimal” is one of the very few places where Poincaré expounds his own views on the subject, although by way of comment of Cournot’s Traité élémentaire des fonctions … (1841) and Traité de l’enchaînement des idées … (1861), which he cites profusely, and whose ideas in this subject were otherwise neglected by both contemporaries and modern commentators. In this paper we analyze Poincaré’s paper with two aims: to characterize briefly his ideas regarding the calculus and, in particular, the use of actual infinitesimals, and the relation between these findings and his concept of the continuum. It would seem that Poincaré endorses most if not all of what Cournot has to say about infinitesimals.]

Published: Mar 12, 2014

Keywords: Rational Order; Nonstandard Analysis; Psychological Constitution; Actual Infinite; Mathematical Continuum

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