Note 79 — Chapter XXVII · PARMENIDES.

Plato, Parmenid. pp. 142-143. This is exactly what Sokrates in the early part of the dialogue (p. 129 B-D) had pronounced to be utterly inadmissible, viz.: That ὃ ἔστιν ἓν should be πολλὰ — that ὃ ἔστιν ὅμοιον should be ἀνόμοιον. The essential characteristic of the Platonic Ideas is here denied. However, it appears to me that Plato here reasons upon two contradictory assumptions; first, that Unum Ens is a total composed of two parts separately assignable — Unum and Ens; next, that Unum is not assignable separately from Ens, nor Ens from Unum. Proceeding upon the first, he declares that the division must be carried on ad infinitum, because you can never reach either the separate Ens or the separate Unum. But these two assumptions cannot be admitted both together. Plato must make his election; either he takes the first, in which case the total Unum Ens is divisible, and its two factors, Unum and Ens, can be assigned separately; or he takes the second, in which case Unum and Ens cannot be assigned separately — are not distinguishable factors, — so that Unum Ens instead of being infinitely divisible, is not divisible at all.

The reasoning as it now stands is, in my judgment, fallacious.