Abstract

This chapter examines Plato's recurrent response to the “Growing Argument” in the dialogue that exhibits Plato's most extensive evaluation of the concept of “number,” Phaedo. There, Plato illustrates mathematical Pythagorean argumentative techniques in the figures of Socrates's interlocutors Simmias and Cebes, and critiques them according to whether or not they exhibit a proper methodological rigor. The proposition of Forms and teleological causation generates new ways of thinking about number. When Socrates finally develops the most complete analysis of number that can be found in Plato's oeuvre, in the final argument, he does so chiefly in order to lay the groundwork for a proof of the soul's immortality. The Phaedo thus illustrates Plato's most circumspect appropriation of mathematical Pythagorean concepts.