Comprendre Les Mathématiques Pour Comprendre Platon - Théétète (147d-148b)

Ofman, Salomon

doi:10.20416/lsrsps.v1i1.53

Cited by 3 publications

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“…33-39), and states that the proofs Theodorus provided were based on the Pythagorean arithmetic of the even and the odd, and that with this kind of oddeven argument one cannot prove that √ 17 is irrational. This justification has been backed by W. R. Knorr, who devotes the main part of Knorr (1979) to present a detailed version of this theory, in McCabe (1976), Caveing (1996), in Ofman (2010), and in Ofman (2014).…”

Section: Other Axiom Systems For the Arithmetic Of The Even And The Oddmentioning

confidence: 99%

The Arithmetic of the Even and the Odd

Pambuccian

2016

The Review of Symbolic Logic

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Section: Other Axiom Systems For the Arithmetic Of The Even And The Oddmentioning

confidence: 99%

The Arithmetic of the Even and the Odd

Pambuccian

2016

The Review of Symbolic Logic

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“…Probablemente, la prevención de Platón hacia determinadas representaciones auxiliares esté motivada por la falta de rigor de algunos matemáticos. A través del análisis de Teeteto 147d-148b, en que se estudian las potencias inconmensurables con uno, Ofman (2014) ha mostrado cómo, en ausencia de métodos deductivos precisos, la utilización incorrecta de imágenes visuales podía conducir a errores y falsas demostraciones. La importancia de los sistemas técnicos de notación para el conocimiento humano en general es por lo demás innegable.…”

Section: Introductionunclassified

Sugerencias sobre el modo de combinar las formas platónicas para superar las dificultades interpretativas del Diálogo Parménides. La distinción entre la participación inmediata y la participación relacional

Cubillo¹

2019

Endoxa (Madr.)

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Este trabajo pretende ser una referencia útil para los estudiosos de la filosofía de Platón. Aporta un enfoque original a la investigación de los procesos lógicos que condicionan que unas formas participen de otras. Con la introducción del concepto de participación relacional, abre una posible vía de solución a las distintas versiones del argumento del «tercer hombre». Puede resultar de interés asimismo el método de generación de los números a partir de lo par y lo impar, propuesto en la interpretación de Parménides 143e-144a. El escrito tiene continuidad en un segundo artículo acerca del ser y la verdad en Platón.

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A Trivial Source of Wonder: Some Mathematical Examples in Plato’s Dialogues

Marongiu

2023

Archiv Für Geschichte Der Philosophie

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The purpose of this paper is to reassess some mathematical examples in Plato’s dialogues which at a first glance may appear to be nothing more than trivial puzzles. In order to provide the necessary background for this analysis, I shall begin by sketching a brief overview of Plato’s mathematical passages and discuss the criteria for aptly selecting them. Second, I shall explain what I mean by ‘mathematical examples,’ and reflect on their function in light of the discussion on παραδείγματα outlined in the Sophist and the Statesman. Against this framework, I shall move to a close examination of specific examples drawn from the Theaetetus (154c–55d), the Republic (523c–24d), and the Phaedo (96d–97b, 100e–101d). By placing these examples in the broader context of pre-Euclidean mathematics, I shall show that their mathematical content is often less elementary than might appear at first sight. Moreover, by placing emphasis on the specific philosophical concerns that motivated their introduction, I shall argue that the examples are not merely nonsensical jokes. Even if their illustrative purpose is not always immediately clear, and even if they can sound playful and bizarre, they in fact fulfil an important function: by virtue of their power to generate wonder or confusion, they serve as exercises and act as a trigger with respect to the difficult philosophical issues they are intended to clarify.

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Comprendre Les Mathématiques Pour Comprendre Platon - Théétète (147d-148b)

Cited by 3 publications

References 0 publications

The Arithmetic of the Even and the Odd

The Arithmetic of the Even and the Odd

Sugerencias sobre el modo de combinar las formas platónicas para superar las dificultades interpretativas del Diálogo Parménides. La distinción entre la participación inmediata y la participación relacional

A Trivial Source of Wonder: Some Mathematical Examples in Plato’s Dialogues

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