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Mathematical Generality, Letter-Labels, and All That

In: Phronesis
Author:
F. Acerbi CNRS, UMR 8167 Orient et Méditerranée Paris

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Abstract

This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, and the ontological commitments underlying the stylistic practice.

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