That which you heard Zeno practising; at the same time, I give you credit for saying to him that you did not care to examine the perplexity in reference to visible things, or to consider the question that way; but only in reference to objects of thought, and to what may be called ideas.
Why, yes, he said, there appears to me to be no difficulty in showing by this method that visible things are like and unlike and may experience anything.
Quite true, said Parmenides; but I think that you should go a step further, and consider not only the consequences which flow from a given hypothesis, but also the consequences which flow from denying the hypothesis; and that will be still better training for you.
What do you mean? he said.
I mean, for example, that in the case of this very hypothesis of Zeno"s about the many, you should inquire not only what will be the consequences to the many in relation to themselves and to the one, and to the one in relation to itself and the many, on the hypothesis of the being of the many, but also what will be the consequences to the one and the many in their relation to themselves and to each other, on the opposite hypothesis. Or, again, if likeness is or is not, what will be the consequences in either of these cases to the subjects of the hypothesis, and to other things, in relation both to themselves and to one another, and so of unlikeness; and the same holds good of motion and rest, of generation and destruction, and even of being and not-being.
In a word, when you suppose anything to be or not to be, or to be in any way affected, you must look at the consequences in relation to the thing itself, and to any other things which you choose,--to each of them singly, to more than one, and to all; and so of other things, you must look at them in relation to themselves and to anything else which you suppose either to be or not to be, if you would train yourself perfectly and see the real truth.
That, Parmenides, is a tremendous business of which you speak, and I do not quite understand you; will you take some hypothesis and go through the steps?--then I shall apprehend you better.
That, Socrates, is a serious task to impose on a man of my years.
Then will you, Zeno? said Socrates.
Zeno answered with a smile:--Let us make our pet.i.tion to Parmenides himself, who is quite right in saying that you are hardly aware of the extent of the task which you are imposing on him; and if there were more of us I should not ask him, for these are not subjects which any one, especially at his age, can well speak of before a large audience; most people are not aware that this roundabout progress through all things is the only way in which the mind can attain truth and wisdom. And therefore, Parmenides, I join in the request of Socrates, that I may hear the process again which I have not heard for a long time.
When Zeno had thus spoken, Pythodorus, according to Antiphon"s report of him, said, that he himself and Aristoteles and the whole company entreated Parmenides to give an example of the process. I cannot refuse, said Parmenides; and yet I feel rather like Ibycus, who, when in his old age, against his will, he fell in love, compared himself to an old racehorse, who was about to run in a chariot race, shaking with fear at the course he knew so well--this was his simile of himself. And I also experience a trembling when I remember through what an ocean of words I have to wade at my time of life. But I must indulge you, as Zeno says that I ought, and we are alone. Where shall I begin? And what shall be our first hypothesis, if I am to attempt this laborious pastime? Shall I begin with myself, and take my own hypothesis the one? and consider the consequences which follow on the supposition either of the being or of the not-being of one?
By all means, said Zeno.
And who will answer me? he said. Shall I propose the youngest? He will not make difficulties and will be the most likely to say what he thinks; and his answers will give me time to breathe.
I am the one whom you mean, Parmenides, said Aristoteles; for I am the youngest and at your service. Ask, and I will answer.
Parmenides proceeded: 1.a. If one is, he said, the one cannot be many?
Impossible.
Then the one cannot have parts, and cannot be a whole?
Why not?
Because every part is part of a whole; is it not?
Yes.
And what is a whole? would not that of which no part is wanting be a whole?
Certainly.
Then, in either case, the one would be made up of parts; both as being a whole, and also as having parts?
To be sure.
And in either case, the one would be many, and not one?
True.
But, surely, it ought to be one and not many?
It ought.
Then, if the one is to remain one, it will not be a whole, and will not have parts?
No.
But if it has no parts, it will have neither beginning, middle, nor end; for these would of course be parts of it.
Right.
But then, again, a beginning and an end are the limits of everything?
Certainly.
Then the one, having neither beginning nor end, is unlimited?
Yes, unlimited.
And therefore formless; for it cannot partake either of round or straight.
But why?
Why, because the round is that of which all the extreme points are equidistant from the centre?
Yes.
And the straight is that of which the centre intercepts the view of the extremes?
True.
Then the one would have parts and would be many, if it partook either of a straight or of a circular form?
a.s.suredly.
But having no parts, it will be neither straight nor round?
Right.
And, being of such a nature, it cannot be in any place, for it cannot be either in another or in itself.
How so?
Because if it were in another, it would be encircled by that in which it was, and would touch it at many places and with many parts; but that which is one and indivisible, and does not partake of a circular nature, cannot be touched all round in many places.
Certainly not.
But if, on the other hand, one were in itself, it would also be contained by nothing else but itself; that is to say, if it were really in itself; for nothing can be in anything which does not contain it.