Truth and Knowledge: the Incorrect Definition of `Powers' by Theaetetus-A New Interpretation of Theaetetus (147d7-148b2)

TL;DR

This paper offers a new interpretation of a key passage in Plato's Theaetetus, linking mathematical, historical, and philosophical perspectives to shed light on Plato's views on knowledge and powers.

Contribution

It provides a novel analysis of a crucial passage, challenging standard interpretations and connecting Plato's philosophy with the history of mathematics and Euclidean propositions.

Findings

Reinterprets the passage as essential for understanding Plato's philosophy.

Links the mathematical discussion to Euclid's Elements and incommensurability.

Challenges the 'Modern Standard Interpretation' of the passage.

Abstract

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 well as its philosophical interpretation in connection with the whole dialogue. As in the previous article, we analyze it simultaneously from the mathematical, the historical and the philosophical points of view, a necessity to understand it. Our strategy is once again to take seriously Plato's text, not as the dream of a poet. Our analysis casts a new light on this passage, as an essential testimony for both Plato's philosophy and for history of mathematics. Plato's relation to Theodorus and Theaetetus is more complex than usually claimed; the search for a definition of knowledge conducted in a large part of the dialogue and even in some other dialogues is rooted in the mathematical passage; it needs a reevaluation of its connection to Euclid's Elements, in particular the proposition X.9, as well as a supposed Euclid's 'catastrophic' mistake (to quote Jean Itard) on incommensurability. In a nutshell, the passage has to be understood differently than in the usual interpretations gathered together under the collective so-called name 'Modern Standard Interpretation' (or MSI). 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 complex points are developed in an Appendix at the end of the article.