[Footnote 72: Plato, Parmenid. pp. 137 C, 142 B.]
[Footnote 73: This part of the argument is the extreme of dialectic subtlety, p. 139 C-D-E.]
[Side-note: First demonstration ends in an assemblage of negative conclusions. _Reductio ad Absurdum_, of the assumption--Unum non Multa.]
All these are impossibilities (concludes Plato). We must therefore go back upon the fundamental principle from which we took our departure, in order to see whether we shall not obtain, on a second trial, any different result.[74]
[Footnote 74: Plato, Parmenid. p. 142 A.]
Here then is a piece of dialectic, put together with ingenuity, showing that everything can be denied, and that nothing can be affirmed of the subject--Unum. All this follows, if you concede the first step, that Unum is not Multa. If Unum be said to have any other attribute except that of being Unum, it would become at once Multa. It cannot even be declared to be either the same with itself, or different from any thing else; because Idem and Diversum are distinct natures from Unum, and if added to it would convert it into Multa.[75] Nay it cannot even be affirmed to be itself: it cannot be named or enunciated: if all predicates are denied, the subject is denied along with them: the subject is nothing but the sum total of its predicates--and when they are all withdrawn, no subject remains. As far as I can understand the bearing of this self-contradictory demonstration, it appears a _reductio ad absurdum_ of the proposition--_Unum is not Multa_. Now _Unum which is not Multa_ designates the [Greek: Au)to\-E(\n] or Unum Ideale; which Plato himself affirmed, and which Aristotle impugned.[76] If this be what is meant, the dialogue Parmenides would present here, as in other places, a statement of difficulties understood by Plato as attaching to his own doctrines.
[Footnote 75: This is the main point of Demonstration 1, and is stated pp. 139 D, 140 A, compared with p. 137 C.]
[Footnote 76: Aristot. Metaph. A. 987, b. 20; A. 992, a. 8; B. 1001, a. 27; I. 1053, b. 18. Some ancient expositors thought that the purpose of Plato in the Parmenides was to demonstrate this [Greek: Au)to\-E(\n]; see Schol. ad Aristot. Metaph. p. 786, a. 10, Brandis.