Parmenides (136-140)

Quite right,

but if you wish to get better training, you must do something more than that; you must consider not only what happens if a particular hypothesis is true, but also what happens if it is not true.

What do you mean?

Take, for instance,

that hypothesis of Zeno’s if the many exist, you should inquire what will happen to the many themselves in relation to themselves and to the one, and to the one in relation to itself and to the many, and also what will happen to the one and the many in relation to themselves and to each other, if the many do not exist. And likewise if you suppose the existence or non-existence of likeness, what will happen to the things supposed and to other things in relation to themselves and to each other under each of the two hypotheses. The same applies to unlikeness and to motion and rest, creation and destruction, and even to being and not being. In brief, whatever the subject of your hypothesis, if you suppose that it is or is not, or that it experiences any other affection, you must consider what happens to it and to any other particular things you may choose, and to a greater number and to all in the same way; and you must consider other things in relation to themselves and to anything else you may choose in any instance, whether you suppose that the subject of your hypothesis exists or does not exist, if you are to train yourself completely to see the truth perfectly.

Parmenides,

it is a stupendous amount of study which you propose, and I do not understand very well. Why do you not yourself frame an hypothesis and discuss it, to make me understand better?

That is a great task, Socrates,

to impose upon a man of my age.

But you, Zeno,

why do not you do it for us?

Let us ask it of Parmenides himself, Socrates; for there is a great deal in what he says, and perhaps you do not see how heavy a task you are imposing upon him. If there were more of us, it would not be fair to ask it of him; for it is not suitable for him to speak on such subjects before many, especially at his age; for the many do not know that except by this devious passage through all things the mind cannot attain to the truth. So I, Parmenides, join Socrates in his request, that I myself may hear the method, which I have not heard for a long time.

I must perforce do as you ask.

And yet I feel very much like the horse in the poem of Ibycus [*]—an old race-horse who was entered for a chariot race and was trembling with fear of what was before him, because he knew it by experience. Ibycus says he is compelled to fall in love against his will in his old age, and compares himself to the horse. So I am filled with terror when I remember through what a fearful ocean of words I must swim, old man that I am. However, I will do it, for I must be obliging, especially since we are, as Zeno says, alone. Well, how shall we begin? What shall be our first hypothesis? Or, since you are determined that I must engage in a laborious pastime, shall I begin with myself, taking my own hypothesis and discussing the consequences of the supposition that the one exists or that it does not exist?

By all means,

Who then,

to answer my questions? Shall we say the youngest? He would be least likely to be over-curious and most likely to say what he thinks and moreover his replies would give me a chance to rest.

I am ready, Parmenides, to do that,

for I am the youngest, so you mean me. Ask your questions and I will answer.

Well then,

if the one exists, the one cannot be many, can it?

No, of course not.

Then there can be no parts of it, nor can it be a whole.

How is that?

The part surely is part of a whole.

Yes.

And what is the whole? Is not a whole that of which no part is wanting?

Certainly.

Then in both cases the one would consist of parts, being a whole and having parts.

Inevitably.

Then in both cases the one would be many, not one.

True.

Yet it must be not many, but one.

Yes.

Then the one, if it is to be one, will not be a whole and will not have parts.

No.

And if it has no parts, it can have no beginning, or middle, or end, for those would be parts of it?

Quite right.

Beginning and end are, however, the limits of everything.

Of course.

Then the one, if it has neither beginning nor end, is unlimited.

Yes, it is unlimited.

And it is without form, for it partakes neither of the round nor of the straight.

How so?

The round, of course, is that of which the extremes are everywhere equally distant from the center.

Yes.

And the straight, again, is that of which the middle is in the nearest line between the two extremes.

It is.

Then the one would have parts and would be many, whether it partook of straight or of round form.

Certainly.

Then it is neither straight nor round, since it has no parts.

Right.

Moreover, being of such a nature, it cannot be anywhere, for it could not be either in anything else or in itself.

How is that?

If it were in something else, it would be encircled by that in which it would be and would be touched in many places by many parts of it; but that which is one and without parts and does not partake of the circular nature cannot be touched by a circle in many places.

No, it cannot.

But, furthermore, being in itself it would also be surrounding with itself naught other than itself, if it were in itself; for nothing can be in anything which does not surround it.

No, it cannot.

Then that which surrounds would be other than that which is surrounded; for a whole cannot be both active and passive in the same action; and thus one would be no longer one, but two.

True.

Then the one is not anywhere, neither in itself nor in something else.

No, it is not.

This being the case, see whether it can be either at rest or in motion.

Why not?

Because if in motion it would be either moving in place or changing; for those are the only kinds of motion.

Yes.

But the one, if changing to something other than itself, cannot any longer be one.

It cannot.

Then it is not in motion by the method of change.

Apparently not.

But by moving in place?

Perhaps.

But if the one moved in place, it would either revolve in the same spot or pass from one place to another.

Yes, it must do so.

And that which revolves must rest upon a center and have other parts which turn about the center; but what possible way is there for that which has no center and no parts to revolve upon a center?

There is none.

But does it change its place by coming into one place at one time and another at another, and move in that way?

Yes, if it moves at all.

Did we not find that it could not be in anything?

Yes.

And is it not still more impossible for it to come into anything?

I do not understand why.

If anything comes into anything, it must be not yet in it, while it is still coming in, nor still entirely outside of it, if it is already coming in, must it not?

It must.

Now if anything goes through this process, it can be only that which has parts; for a part of it could be already in the other, and the rest outside; but that which has no parts cannot by any possibility be entirely neither inside nor outside of anything at the same time.

True.

But is it not still more impossible for that which has no parts and is not a whole to come into anything, since it comes in neither in parts nor as a whole?

Clearly.

Then it does not change its place by going anywhere or into anything, nor does it revolve in a circle, nor change.

Apparently not.

Then the one is without any kind of motion.

It is motionless.

Furthermore, we say that it cannot be in anything.

We do.

Then it is never in the same.

Why is that?

Because it would then be in that with which the same is identical.

Certainly.

But we saw that it cannot be either in itself or in anything else.

No, it cannot.

Then the one is never in the same.

Apparently not.

But that which is never in the same is neither motionless nor at rest.

No, it cannot be so.

The one, then, it appears, is neither in motion nor at rest.

No, apparently not.

Neither, surely, can it be the same with another or with itself; nor again other than itself or another.

Why not?

If it were other than itself, it would be other than one and would not be one.

True.

And, surely, if it were the same with another, it would be that other, and would not be itself; therefore in this case also it would not be that which it is, namely one, but other than one.

Quite so.

Then it will not be the same as another, nor other than itself.

No.

But it will not be other than another, so long as it is one. For one cannot be other than anything; only other, and nothing else, can be other than another.

Right.

Then it will not be other by reason of being one, will it?

Certainly not.

And if not for this reason, not by reason of itself; and if not by reason of itself, not itself; but since itself is not other at all, it will not be other than anything.

Right.

And yet one will not be the same with itself.

Why not?

The nature of one is surely not the same as that of the same.

Why?

Because when a thing becomes the same as anything, it does not thereby become one.

But why not?

That which becomes the same as many, becomes necessarily many, not one.

True.

But if the one and the same were identical, whenever anything became the same it would always become one, and when it became one, the same.

Certainly.

Then if the one is the same with itself, it will not be one with itself; and thus, being one, it will not be one; this, however, is impossible; it is therefore impossible for one to be either the other of other or the same with itself.

Impossible.

Thus the one cannot be either other or the same to itself or another.

No, it cannot.

And again it will not be like or unlike anything, either itself or another.

Why not?

Because the like is that which is affected in the same way.

Yes.

But we saw that the same was of a nature distinct from that of the one.

Yes, so we did.

But if the one were affected in any way apart from being one, it would be so affected as to be more than one, and that is impossible.

Yes.

Then the one cannot possibly be affected in the same way as another or as itself.

Evidently not.

Then it cannot be like another or itself.

No, so it appears.

Nor can the one be so affected as to be other; for in that case it would be so affected as to be more than one.

Yes, it would be more.

But that which is affected in a way other than itself or other, would be unlike itself or other, if that which is affected in the same way is like.

Right.

But the one, as it appears, being never affected in a way other than itself or other, is never unlike either itself or other.

Evidently not.

Then the one will be neither like nor unlike either other or itself.

So it seems.

Since, then, it is of such a nature, it can be neither equal nor unequal to itself or other.

Why not?

If it is equal, it is of the same measures as that to which it is equal.

Yes.

And if it is greater or less than things with which it is commensurate, it will have more measures than the things which are less and less measures than the things which are greater.

Yes.

And in the case of things with which it is not commensurate, it will have smaller measures than some and greater measures than others.

Of course.

Is it not impossible for that which does not participate in sameness to have either the same measures or anything else the same?

Impossible.

Then not having the same measures, it cannot be equal either to itself or to anything else.

No, apparently not.

But whether it have more measures or less, it will have as many parts as measures and thus one will be no longer one, but will be as many as are its measures.

Right.

But if it were of one measure, it would be equal to the measure; but we have seen that it cannot be equal to anything.

Yes, so we have.

Then it will partake neither of one measure, nor of many, nor of few; nor will it partake at all of the same, nor will it ever, apparently, be equal to itself or to anything else; nor will it be greater or less than itself or another.

Perfectly true.

Well, does anyone believe that the one can be older or younger or of the same age?

Why not?

Because if it has the same age as itself or as anything else, it will partake of equality and likeness of time, and we said the one had no part in likeness or equality.

Yes, we said that.

And we said also that it does not partake of unlikeness or inequality.

Certainly.