This chapter treats the seemingly opposed or, rather, unrelated endeavors of mathematics and sophistry that Plato juxtaposes in the Theaetetus through the characters of Protagoras and Theodorus. Theodorus is evidence that, while mathematics may lead the soul upward to the realm of intelligible being, this should not obscure the fact that it might just as easily lead the soul downward, with the danger of sophistry lurking as a distinct possibility. The problem is that mathematical knowledge, in and of itself, cannot grasp itself as an expression of logos, or rationality more broadly and correctly construed. Only by coming to know itself, that is, knowing its place as part of a more encompassing intelligible whole, will mathematics realize that its peculiar mode of being is not self-explanatory since it is constituted by the activity of a principle that transcends it. Self-knowledge, therefore, is the ingredient that transmutes the mathematical sciences into dialectic.