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UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO -THEAETEUS (147d-148b

By Salomon Ofman

Abstract

International audienceThis paper is an updated translation of an article published in French in the Journal Lato Sensu (I, 2014, p. 70-80). We study here the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. The difficulty to understand it lies in the close intertwining of different fields we found in it: philosophy, history and mathematics. But conversely, correctly understood, it gives some evidences both about the question of the origins of the irrationals in Greek mathematics and some points concerning Plato's thought. Taking into account the historical context and the philosophical background generally forgotten in mathematical analyses, we get a new interpretation of this text, which far from being a tribute to some mathematicians, is a radical criticism of their ways of thinking. And the mathematical lesson, far from being a tribute to some future mathematical achievements, is ending on an aporia, in accordance with the whole dialogue. Résumé. Cet article est une traduction anglaise révisée d'un article paru en français dans la revue Lato Sensu (I, 2014, p. 70-80)

Topics: anthyphairesis, apory, Babylonian mathematics, definition, demonstration, irrationals (origin of the), knowledge, learning, mathematics, mathematical truth, philosophy, Plato, Pythagoras’ theorem, science, [SHS.HISPHILSO] Humanities and Social Sciences/History, Philosophy and Sociology of Sciences, [SHS.PHIL] Humanities and Social Sciences/Philosophy
Publisher: Société de philosophie des sciences
Year: 2014
OAI identifier: oai:HAL:hal-01305361v1
Provided by: Hal-Diderot

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