Sophia A. Stone

The paper analyzes the final proof with Greek mathematics and the possibility of intermediates in the Phaedo. The final proof in Plato’s Phaedo depends on a claim at 105c6, that μονάς, ‘unit’, generates περιττός ‘odd’ in number. So, ψυχή ‘soul’ generates ζωή ‘life’ in a body, at 105c10-11. Yet commentators disagree how to understand these mathematical terms and their relation to the soul in Plato’s arguments. The Greek mathematicians understood odd numbers in one of two ways: either that which is not divisible into two equal parts, or that which differs from an even number by a unit. Plato uses the second way in the final proof. This paper argues that a proper understanding of these mathematical terms within Greek mathematics shows that the argument for the final proof is better than previously thought. Such an interpretation of the final proof lends credence to Platonic intermediates.

Using an interdisciplinary approach to reading Plato's Apology of Socrates, I argue that the counter penalty offered by Socrates, what is commonly translated as maintenance in the Prytaneion, was a literary addition from Plato, resembling comic topoi from Aristophanes. I begin with the accounts we have from Plato and Xenophon, then analyze the culture and context of the Prytaneion. Given the evidence, I provide arguments for why the historical Socrates wouldn't respond with sitēsis in the Prytaneion. I suggest that Plato borrows the grammatical phrase from Aristophanes' Knights.