  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.
