Plato and the dice: A reassessment of Theaetetus 154A-155D

Abstract

This paper focuses on the pair of philosophical puzzles, in the first section of Plato's Theaetetus, concerning the comparison between cardinalities and sizes. My initial task is to analyse some difficulties and distractions which affect our understanding of the argumentation that Socrates puts forward on Protagoras' behalf. I then offer a revised interpretation that integrates the puzzles with the rest of the Protagorean/Heraclitean theory. The emerging discussion, far from being a bridging passage or detour, is a unit with its own specific identity. Its goal is to stretch the Protagorean/Heraclitean metaphysics of events to a new limit: the dematerialisation of change. Change may also be the simple effect of quantitative comparisons as such. At the same time, important traces of Plato's indirect move against Protagoras are detected: the conceivability itself of this Protagorean view descends from a common application of mathematics. © The Author(s) 2012. Published by Cambridge University Press.