Related papers: On Theodorus' lesson in the Theaetetus 147d-e

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…

In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…

In the present chapter, we obtain the reconstruction of Theaetetus' theory of ratios of magnitudes based, according to Aristotle's Topics 158b, on the definition of proportion in terms of equal anthyphairesis. Our reconstruction is built on…

In a first article (referred here as B-O), we studied the first part of the so-called 'mathematical part' of Plato's Theaetetus, i.e. Theodorus' lesson. In the present one, we consider the sequel and the end of the passage (147d7-148b2), as…

In the present work it is shown, by an examination of the Platonic dialogues Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the philosophic analogue of a pair of lines incommensurable in length only, (b) the…

Even though Plato's philosophy in ancient times was always closely associated with mathematics, modern Platonic scholarship, during the last five centuries, has moved steadily toward de-mathematization. The present work aims to outline a…

Both lectures focus on the first part of the so-called 'mathematical part' of Plato's Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into…

To account for the first proof of existence of an irrational magnitude, historians of science as well as commentators of Aristotle refer to the texts on the incommensurability of the diagonal in Prior Analytics, since they are the most…

Unquestionably the greatest discovery of the Pythagoreans is the existence of incommensurable magnitudes, most probably the incommensurability of the diameter to the side of a square, but there is no agreement among historians of Greek…

In this paper the claim that Zeno's paradoxes have been solved is contested. Although no one has ever touched Zeno without refuting him (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not…

The aim of this paper is to show that Plato's theory of knowledge of Forms (intelligible Beings, Ideas) in the Sophistes, obtained by Division and Collection, is a close philosophic analogue of the geometric theory of periodic…

This paper examines the incommensurability thesis - one of the most important and controversial ideas to emerge from the simultaneous work of Kuhn and Feyerabend. In the first half, I discuss three aspects of incommensurability -…

In the present work, we aim to restore Book X of the $\it{Elements}$ to its original Theaetetean, pre-Eudoxean form in two separate ways. First, we restore the considerable mathematical content of Book X, by correlating Book X with Plato's…

The main aim of this article is to defend the thesis that Plato apprehended the structure of incommensurable magnitudes in a way that these magnitudes correspond in a unique and well defined manner to the modern concept of the "Dedekind…

After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns a quantization of the principle of relative simultaneity. This leads me to a distinction between time and…

In two articles ([Brisson-Ofman1, 2]), we have analyzed the so-called 'mathematical passage' of Plato's Theaetetus, the first dialogue of a trilogy including the Sophist and the Statesman. In the present article, we study an important point…

We investigate field theories on the non-commutative torus upon varying theta, the parameter of non-commutativity. We argue that one should think of Morita equivalence as a symmetry of algebras describing the same space rather than of…

We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target…

In a previous article, we discussed a paradox in Timaeus' cosmology: that there is no void inside the universe, even though it is entirely filled with polyhedra-a mathematical impossibility (Brisson-Ofman 2025). In the present article, we…

In his 2008 thesis, Tateno claimed a counterexample to the Bonato-Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno's unpublished ideas to provide a rigorous exposition, constructing…