论文标题
柏拉图（Plato
Theodorus' lesson in Plato's Theaetetus (147d1-d6) Revisited-A New Perspective
论文作者
论文摘要
本文是柏拉图剧院（147d-148b）所谓的“数学部分”研究的第一部分。这个“数学部分”的主题是非理性的，这是早期希腊数学中最重要的主题之一。由于数学家，数学史学家以及哲学的浓厚兴趣，对此进行了大量研究。在我们的工作中，我们重新审视了这个问题，因为我们认为缺少某些东西：同时从这三个观点来看，对柏拉图的文本进行了全球分析：历史，数学和哲学。这是我们通过新的翻译进行的，这是对数学课程的新解释，以及从这三个角度来看对整个段落的新颖解释。我们的指南是认真考虑柏拉图的著作，而不是一些有趣的作品。这个简单的规则确实是令人惊讶的限制，但是它使我们能够在欧国人前数学前的罕见直接浏览，这与数学史以及哲学史上的“主要标准解释”相矛盾。出于社论原因，这项研究分为两个部分。在本文中，我们提出了对“数学部分”的第一部分，Theodorus的课程的分析。在第二篇文章（Brisson-Ofman（出现））中，我们介绍了整个对话框架内的“数学部分”的续集以及对“数学部分”的哲学解释。这两篇文章构成了整体。它们都是针对没有任何特定数学背景的观众的，并且仅需要基本的数学知识，本质上是高中级的。然而，附录中仍在开发一些更精致的观点。
This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As of huge interest for mathematicians, historians of mathematics as well as of philosophy, there had been an avalanche of studies about it. In our work, we revisit this question, for we think something is missing: a global analysis of Plato's text, from these three points of view simultaneously: history, mathematics and philosophy. It is what we have undertook through a new translation, a new interpretation of the mathematical lesson about irrational magnitudes and a novel interpretation of the whole passage from these three points of view. Our guideline is considering Plato's writings seriously, not as some playful work. This simple rule is indeed surprisingly constraining, but it allows us to get a rare direct glance inside pre-Euclidean mathematics, in contradiction with the 'Main Standard Interpretation' prevailing in history of mathematics as well as in history of philosophy. This study had been divided in two parts for editorial reasons. In the present article, we propose an analysis of the first part of this 'mathematical part', Theodorus' lesson. In the second article (Brisson-Ofman (to appear)), we present the sequel of the lesson and a philosophical interpretation of the 'mathematical part' within the framework of the entire dialogue. Both articles form a whole. They are both aimed to an audience without any particular mathematical background, and require only elementary mathematical knowledge, essentially of high school-level. Some more delicate points are nevertheless developed in the Appendices.
