相关论文: The Anthyphairetic Revolutions of the Platonic Ide…

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…

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…

In the celebrated Theaetetus 147d3-e1 passage Theodorus is giving a lesson to Theaetetus and his companion, proving certain quadratic incommensurabilities. The dominant view on this passage, expressed independently by H. Cherniss and M.…

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 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…

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, 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 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 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…

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…

In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract…

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and…

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 offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability and syncategorematicity, and the closely related…

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…

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…

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 -…

This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…

In his Ph.D. thesis, Michal Szabados conjectured that for a not fully periodic configuration with a minimal periodic decomposition the nonexpansive lines are exactly the lines that contain a period for some periodic configuration in such…