This article examines a complex passage of Aristotle’s Physics in which a Pythagorean doctrine is explained by means of a mathematical example involving gnomons. The traditional interpretation of this passage (proposed by Milhaud and Burnet) has recently been challenged by Ugaglia and Acerbi, who have proposed a new one. The aim of this article is to analyse difficulties in their account and to advance a new interpretation. All attempts at interpreting the passage so far have assumed that ‘gnomons’ should indicate ‘odd numbers’. In this article it is argued that the usage of ‘gnomon’ related to polygonal numbers, which is normally considered late, could be backdated to at least the fifth/fourth centuries B.C.; in particular, it explains the link between the philosophical explanandum and the mathematical explanans in Aristotle’s passage.

The mathematical example of gnomons in Physics 3.4, 203a10-16

Salerno, Lorenzo
Writing – Original Draft Preparation
2024

Abstract

This article examines a complex passage of Aristotle’s Physics in which a Pythagorean doctrine is explained by means of a mathematical example involving gnomons. The traditional interpretation of this passage (proposed by Milhaud and Burnet) has recently been challenged by Ugaglia and Acerbi, who have proposed a new one. The aim of this article is to analyse difficulties in their account and to advance a new interpretation. All attempts at interpreting the passage so far have assumed that ‘gnomons’ should indicate ‘odd numbers’. In this article it is argued that the usage of ‘gnomon’ related to polygonal numbers, which is normally considered late, could be backdated to at least the fifth/fourth centuries B.C.; in particular, it explains the link between the philosophical explanandum and the mathematical explanans in Aristotle’s passage.
2024
Settore M-FIL/07 - Storia della Filosofia Antica
Settore L-FIL-LET/05 - Filologia Classica
gnomon; polygonal numbers; Aristotle’s Physics; Pythagorean mathematics; even and odd; Philolaus
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/142363
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