Sur la conception des objets et des méthodes mathématiques dans les textes philosophiques de d'Alembert |
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Institution: | 1. Section of Medical and Forensic Anthropology, Faculty of Health Sciences, Montigny-Le-Bretonneux 78180, France;2. National Museum of Natural History, Department of Anthropology, Paris, France;3. Visual Forensic, Parc Audiovisual de Catalunya, Barcelona, Spain;4. Department of Otolaryngology—Head and Neck Surgery, Rouen University Hospital, Rouen, France;5. John Adams Institute, Amsterdam, Netherlands;6. Department of Radiology, University Hospital Pitié-Salpétrière, Paris, France |
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Abstract: | This paper is devoted to the conception of mathematical objects and methods according to d'Alembert. We first recall his vision of the place of mathematics in the knowledge of nature, then the internal hierarchy of the various fields of this science, based on their degree of abstraction from sensations (41 and 2). Then we come to the ideas of definitions, primitive ideas, simple ideas, and their generation as well as their generalization (43 and 4). Then, having looked at what he means by quantities, numbers, quantities, as well as his conception of the objects and rules of algebra as abstract ideas by generalization (45), we approach the question of the reality of mathematical objects with the example of the irrational (46). The following paragraphs of the text are devoted to the difficulties encountered in various fields and the way d'Alembert tries to solve them: algebra and negative quantities (47); principles of geometry (48); the notion of limit as the basis of infinitesimal calculus (49). His reflections, even if unfinished, were not without posterity (410). |
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Keywords: | d'Alembert Mathematical philosophy Mathematical epistemology 18th century mathematics Foundations of mathematics |
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