Aristotle and the Just Proportion in Communities of Exchange
The Mathematical Reading
Abstract
This paper analyses the Aristotelian notion of τὸ ἀντιπεπονθός, traditionally understood as reciprocity, and presents a strictly mathematical interpretation of the kind of justice established for commercial exchanges in Nicomachean Ethics V 5. Justice understood as equality and, in turn, as a mean, allows Aristotle to present an alternative mathematical conception to the Pythagorean one. The few occurrences of the term ἀντιπεπονθός and derivatives appear in Euclid’s Elements and they are relevant to understanding this notion. Some definitions in Book six and several propositions allow to establish with some certainty the correspondence between the Aristotelian scheme and the straight line divided in extreme and mean ratio, also known as the golden ratio.
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References
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