The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry
✍ Scribed by Giorgio Israel; Marta Menghini
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 297 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0315-0860
No coin nor oath required. For personal study only.
✦ Synopsis
An analysis of the different philosophic and scientific visions of Henri Poincare ´and Federigo Enriques relative to qualitative analysis provides us with a complex and interesting image of the ''essential tension'' between ''tradition'' and ''innovation'' within the history of science. In accordance with his scientific paradigm, Poincare ´viewed qualitative analysis as a means for preserving the nucleus of the classical reductionist program, even though it meant ''bending the rules'' somewhat. To Enriques's mind, qualitative analysis represented the affirmation of a synthetic, geometrical vision that would supplant the analytical/quantitative conception characteristic of 19th-century mathematics and mathematical physics. Here, we examine the two different answers given at the turn of the century to the question of the relationship between geometry and analysis and between mathematics, on the one hand, and mechanics and physics, on the other.