Concluding words of the Parmenides — Declaration that he has demonstrated the Both and the Neither of many different propositions.
Here we find ourselves at the close of the Parmenides. Plato announces his purpose to be, to elicit contradictory conclusions, by different trains of reasoning, out of the same fundamental assumption.[109] He declares, in the concluding words, that — on the hypothesis of Unum est, as well as on that of Unum non est — he has succeeded in demonstrating the Both and the Neither of many distinct propositions, respecting Unum and respecting Cætera.
[109] Compare, with the passage cited in the last note, another passage, p. 159 B, at the beginning of Demonstration 5.
Οὐκοῦν ταῦτα μὲν ἤδη ἐῶμεν ὡς φανερά, ἐπισκοπῶμεν δὲ πάλιν, ἓν εἰ ἔστιν, ἆρα καὶ οὐχ οὕτως ἔχει τἄλλα τοῦ ἑνὸς ἢ οὕτω μόνον;
Here the purpose to prove οὐχ οὕτως, immediately on the heels of οὕτως, is plainly enunciated.
Comparison of the conclusion of the Parmenides to an enigma of the Republic. Difference. The constructor of the enigma adapted its conditions to a foreknown solution. Plato did not.
The close of the Parmenides, as it stands here, may be fairly compared to the enigma announced by Plato in his Republic — “A man and no man, struck and did not strike, with a stone and no stone, a bird and no bird, sitting upon wood and no wood”.[110] This is an enigma, propounded for youthful auditors to guess: stimulating their curiosity, and tasking their intelligence to find it out. As far as I can see, the puzzling antinomies in the Parmenides have no other purpose. They drag back the forward and youthful Sokrates from affirmative dogmatism to negative doubt and embarrassment. There is however this difference between the enigma in the Republic, and the Antinomies in the Parmenides. The constructor of the enigma had certainly a preconceived solution to which he adapted the conditions of his problem: whereas we have no sufficient ground for asserting that the author of the Antinomies had any such solution present or operative in his mind. How much of truth Plato may himself have recognised, or may have wished others to recognise, in them, we have no means of determining. We find in them many equivocal propositions and unwarranted inferences — much blending of truth with error, intentionally or unintentionally. The veteran Parmenides imposes the severance of the two, as a lesson, upon his youthful hearers Sokrates and Aristoteles.
[110] Plato, Republ. v. 479 C. The allusion was to an eunuch knocking down a bat seated upon a reed. Αἰνός τις ἔστιν ὡς ἀνήρ τε κοὐκ ἀνήρ, Ὄρνιθά τε κοὐκ ὄρνιθ’ ἰδών τε κοὐκ ἰδών, Ἐπὶ ξύλου τε κοὐ ξύλου καθημένην Λίθῳ τε κοὐ λίθῳ βάλοι τε κοὐ βάλοι.
I read with astonishment the amount of positive philosophy which a commentator like Steinhart extracts from the concluding enigma of the Parmenides, and which he even affirms that no attentive reader of the dialogue can possibly miss (Einleitung zum Parmenides, pp. 302-303).