[33] Ueberweg. Hist. of Philos., Vol. I, § 29, p. 77.
SEC. 25. The reasoning in the Platonic Dialogues is very frequently not above suspicion; but it is not easy to find anywhere such a nest of paralogisms as we have in the Parmenides. How far Plato was in earnest in all this quibbling, and what was his aim, I will not pretend to say. He has, however, very well illustrated the possibilities of equivocation in juggling with samenesses, and I shall quote a bit of the argument concerning the one and the many to show how readily this is done. Almost any part of the dialogue would do, but I choose the first bout between Parmenides and Aristoteles. I take Professor Jowett's version:[34]
[34] The Dialogues of Plato. N. Y., 1878. Vol. III, p. 255.
Parmenides proceeded: If one is, he said, the one cannot be many?
Then the one cannot have parts, and cannot be a whole?
Why, the part would surely be the part of a whole?
And that of which no part is wanting, would be a whole?
Then, in either case, one would be made up of parts; both as being a whole, and also as having parts?
And in either case, the one would be many, and not one?
But, surely, one ought to be not many, but one?
Then, if one is to remain one, it will not be a whole, and will not have parts?
And if one has no parts, it will have neither beginning, middle, nor end; for these would be parts of one?
But then, again, a beginning and an end are the limits of everything?
Then the one, neither having beginning nor end, is unlimited?
And therefore formless, as not being able to partake either of round or straight.
Why, the round is that of which all the extreme points are equidistant from the centre?
And the straight is that of which the middle intercepts the extremes?
Then the one would have parts, and would be many, whether it partook of a straight or of a round form?
But having no parts, one will be neither straight nor round?
Then, being of such a nature, one cannot be in any place, for it cannot be either in another or in itself.
Because, if one be in another, it will be encircled in that other in which it is contained, and will touch it in many places; but that which is one and indivisible, and does not partake of a circular nature, cannot be touched by a circle in many places.