阿里斯托尔《玻色子的数学实例》,《物理学》3.4,203a10-16

Lorenzo Salerno
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摘要

本文研究了亚里士多德《物理学》中的一个复杂段落,其中通过一个涉及侏儒的数学例子解释了毕达哥拉斯学说。最近,Ugaglia 和 Acerbi 对这段话的传统解释(由 Milhaud 和 Burnet 提出)提出了新的挑战。本文旨在分析他们的解释中存在的困难,并提出一种新的解释。迄今为止,所有解释这段文字的尝试都假定 "gnomons "表示 "奇数"。本文认为,"gnomon "与多边形数有关的用法通常被认为是晚期用法,但至少可以追溯到公元前五/四世纪;特别是,本文解释了亚里士多德这段话中哲学解释与数学解释之间的联系。
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THE MATHEMATICAL EXAMPLE OF GNOMONS IN ARISTOTLE, PHYSICS 3.4, 203a10–16
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.
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PHILOSOPHY IN DIO CHRYSOSTOM, ON ANACHÔRÊSIS (ORATION 20) THE MATHEMATICAL EXAMPLE OF GNOMONS IN ARISTOTLE, PHYSICS 3.4, 203a10–16 HELOTS AT THERMOPYLAE: THE GREEK DEAD AT HERODOTUS 8.25 A SERVILE RIDDLE FROM POMPEII? (CIL 4.1877) JULIUS CAESAR AND THE LARCH: BURNING QUESTIONS AT VITRUVIUS’ DE ARCHITECTVRA 2.9.15–16 – ERRATUM
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