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The Relationship between Hypotheses and Images in the Mathematical Subsection of the Divided Line of Plato's Republic

Published online by Cambridge University Press:  13 April 2010

Moon-Heum Yang
Moon-Heum Yang
Affiliation:
Dongguk University, Korea
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Abstract

In explaining the relationship between hypotheses and images in the Line of Plato's Republic VI, I first focus on Plato's elucidation of the nature of mathematics as the mathematician himself understands it. I go on to criticize traditional interpretations of the relationship above based on the doubtful assumption that mathematics concerns Platonic Forms. To formulate my view of that relationship I exploit the notion of “structure.” I show how “hypotheses” as principles of proof can determine the structures of “images” by which the corresponding intelligible ones of mathematical objects become known.

Résumé

En expliquant la relation entre hypothèses et images dans l'analogie de la ligne du livre Vl de la République de Platon, je m'attarde d'abordsur l'élucidation platonicienne de la nature des mathématiques telle que la conçoit le mathématicien lui-même. Je poursuis avec une critique des interprétations traditionnelles de cette relation, qui partent de l'assomption douteuse que les mathématiques s'occupent des Formes platoniciennes. Pour formuler mon point de vue sur cette relation, j'exploite la notion de «structure». Je montre comment les «hypothèses» comme principes de preuve peuvent déterminer les structures des «images» par lesquelles les structures intelligibles correspondantes des objets mathématiques en viennent à être connues.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 44 , Issue 2 , Spring 2005 , pp. 285 - 312
Copyright
Copyright © Canadian Philosophical Association 2005

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