Note 89 — Chapter XXVII · PARMENIDES.
Reading edition
Prantl (in his Geschichte der Logik, vol. i. s. 3, pp. 70-71-73) maintains, if I rightly understand him, not only that Plato did not adopt the principium identitatis et contradictionis as the basis of his reasonings, but that one of Plato’s express objects was to demonstrate the contrary of it, partly in the Philêbus, but especially in the Parmenides:—
“Eine arge Täuschung ist es, zu glauben, dass das principium identitatis et contradictionis oberstes logisches Princip des Plato sei … Es ist gerade eine Hauptaufgabe, welche sich Plato stellen musste, die Coexistenz der Gegensätze nachzuweisen, wie diess bekanntlich im Philebus und besonders im Parmenides geschieht.”
According to this view, the Antinomies in the Parmenides are all of them good proofs, and the conclusions of all of them, summed up as they are in the final sentence of the dialogue, constitute an addition to the positive knowledge of Sokrates. I confess that this to me is unintelligible. I understand these Antinomies as ἀπορίαι to be cleared up, but in no other character.
Prantl speaks (p. 73) of “die antinomische Begründung der Ideenlehre im Parmenides,” &c. This is the same language as that used by Zeller, upon which I have already remarked.