ABSTRACT
Plato's second account of the eide is best characterized as "arithmological" rather than "arithmetical", in recognition of the non-mathematical nature of the units that are united as an "arithmos" in an eidetic number. Plato's arithmological account of the eide therefore replaces the Socratic account's metaphorical logos of participation with the Stranger and Theaetetus account's arithmological logos. The Sophist's discussion of the five greatest kinds is informed by the strange status of the "common thing" (koinon) exhibited by the mathematical numbers that are among intelligible objects in comparison with the "common thing" exhibited by non-mathematical intelligible objects. The manner in which the eide of justice and health are shared by more than one thing and are thus common to each of the things that share in them contrasts sharply with the way the things that share in the common thing of a mathematical number are related to what (number) they have in common.
