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Article

French

ID: <

10670/1.q3171f

>

Where these data come from
“The Academy and Geometers: Uses and limits of Platon Geometry in Carneade”

Abstract

International audience This paper traces the intellectual continuity existing in the analysis of geometry from Plato to the end of the Academy. It is first argued that, in books 6-7 of the Republic, Plato does not advocate a reform of contemporary geometrical practices, but specifies the inescapable constraints of geometrical reasoning (constructions, hypotheses), which constitute and limit its objectivity. This analysis is then shown to be the framework of later Academic thoughts about geometry. Speusippus adopts and develops Plato's thoughts on geometrical construction, which are applied (from Speusippus to Crantor) to cosmology and the theory of first principles, in order to explain how they can grasp eternal objects in a indirect manner, starting from the world of becoming. The paper then locates the criticism of mathematics offered by the New Academy of Arcesilaus and Carneades in the broader context of hellenistic philosophical debates about the uses of mathematics, and interprets it as a reminder of the limits of mathematical objectivity against the dogmatic uses of geometry as a universal model of reasoning.

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