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Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus

David Rabouin & Richard T. W. Arthur

Archive for History of Exact Sciences 74 (5):401-443 (2020)

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Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work.Oscar M. Esquisabel & Federico Raffo Quintana - 2021 - Archive for History of Exact Sciences 75 (6):613-647.details This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to (...) Download Export citation Bookmark 1 citation
Leibniz on Bodies and Infinities: Rerum Natura and Mathematical Fictions.Mikhail G. Katz, Karl Kuhlemann, David Sherry & Monica Ugaglia - 2024 - Review of Symbolic Logic 17 (1):36-66.details The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility innature, rather than inmathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in (...) Download Export citation Bookmark
Sets, Set Sizes, and Infinity in Badiou's Being and Event.Tzuchien Tho - 2020 - Filozofski Vestnik 41 (2).details This paper argues that Cantorian transfinite cardinality is not a necessary assumption for the ontological claims in Badiou’s L’Être et l’Événement (Vol. 1). The necessary structure for Badiou’s mathematical ontology in this work was only the ordinality of sets. The method for reckoning the sizes of sets was only assumed to follow the standard Cantorian measure. In the face of different and compelling forms of measuring non-finite sets (following Benci and Di Nasso, and Mancosu), it is argued that Badiou’s project (...) Download Export citation Bookmark
Introduction.Valérie Debuiche & David Rabouin - 2021 - Philosophia Scientiae 25:5-20.details « Les Mathematiciens ont autant besoin d’estre philosophes que les philosophes d’estre Mathematiciens » [Leibniz à Nicolas Malebranche, 13/23 mars 1699 ]. Cette déclaration que fait Leibniz à Malebranche en 1699 n’est pas de façade et il la met lui-même en action à de multiples occasions. Ainsi, présentant en 1677 une des notions centrales de sa « caractéristique géométrique », il commente : Il n’est pas si aisé qu’on pense, de donner des veritables demonstrations en metaphysique.... Download Export citation Bookmark
Leibniz y la aplicación de la matemática a la física.Federico Raffo Quintana - 2025 - Anales Del Seminario de Historia de la Filosofía 42 (1):67-75.details En este trabajo analizaremos la concepción de Leibniz acerca de la aplicación de la matemática a la física entre los años 1677 y 1690. Reconstruiremos esta concepción fundamentalmente a partir de algunos conceptos relacionados, como son los de “atributos” o “cualidades acompañantes”. Veremos que, por aplicación de la matemática a la física, Leibniz entendió específicamente la posibilidad de dar explicaciones mecánicas que dan cuenta de la causa inmediata e inteligible por la cual tienen lugar las cualidades confusas, en un sentido (...) Download Export citation Bookmark

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