Dialectically imageless investigation of eidē : Plato's “unwritten teachings”

The dialogues' second account of the eidē is neither readily apparent nor Socratic. In place of the dramatic figures of the philosopher Socrates and various non-philosophers, the figure of the unnamed philosopher from Elea (the “Stranger”) and the accomplished mathematician Theaetetus pursue to its end – to be sure in the presence of and at the initiative of Socrates – the “right use” of the technē proper to counting and calculation for redirecting the whole soul to the source of being and truth. In other words, they complete in deed what is merely prescriptive in the Socratic account of the eidē. Their dialectically imageless investigation of the eidē, and, more precisely, of the “greatest” (most original) “kinds” (genē), is presented in a manner in which the inexactness of the images belonging to Socratic myth is superseded by the exactness of number and the one. (In the Cratylus, Socrates calls attention to the crucial difference in exactness between an image and a number by pointing out that an image necessarily lacks attributes of its original, because otherwise it would not be an image but another original, while a number necessarily cannot be missing any part and remain what it is.) Because of their greatest originality, each of these five genē, “itself by itself” (auto kath' auto), is shown as the necessary presuppositions for the “intelligibility” of any eidos.