Or will each equal thing, if possessing some small portion of equality less than absolute equality, be equal to some other thing by virtue of that portion only?

Impossible.

Or suppose one of us to have a portion of smallness; this is but a part of the small, and therefore the absolutely small is greater; if the absolutely small be greater, that to which the part of the small is added will be smaller and not greater than before.

How absurd!

Then in what way, Socrates, will all things participate in the ideas, if they are unable to participate in them either as parts or wholes?

Indeed, he said, you have asked a question which is not easily answered.

Well, said Parmenides, and what do you say of another question?

What question?

I imagine that the way in which you are led to assume one idea of each kind is as follows:—You see a number of great objects, and when you look at them there seems to you to be one and the same idea (or nature) in them all; hence you conceive of greatness as one.

Very true, said Socrates.

And if you go on and allow your mind in like manner to embrace in one view the idea of greatness and of great things which are not the idea, and to compare them, will not another greatness arise, which will appear to be the source of all these?

It would seem so.

Then another idea of greatness now comes into view over and above absolute greatness, and the individuals which partake of it; and then another, over and above all these, by virtue of which they will all be great, and so each idea instead of being one will be infinitely multiplied.

But may not the ideas, asked Socrates, be thoughts only, and have no proper existence except in our minds, Parmenides? For in that case each idea may still be one, and not experience this infinite multiplication.

And can there be individual thoughts which are thoughts of nothing?

Impossible, he said.

The thought must be of something?

Yes.

Of something which is or which is not?

Of something which is.

Must it not be of a single something, which the thought recognizes as attaching to all, being a single form or nature?

Yes.

And will not the something which is apprehended as one and the same in all, be an idea?

From that, again, there is no escape.

Then, said Parmenides, if you say that everything else participates in the ideas, must you not say either that everything is made up of thoughts, and that all things think; or that they are thoughts but have no thought?

The latter view, Parmenides, is no more rational than the previous one. In my opinion, the ideas are, as it were, patterns fixed in nature, and other things are like them, and resemblances of them—what is meant by the participation of other things in the ideas, is really assimilation to them.

But if, said he, the individual is like the idea, must not the idea also be like the individual, in so far as the individual is a resemblance of the idea? That which is like, cannot be conceived of as other than the like of like.

Impossible.

And when two things are alike, must they not partake of the same idea?

They must.

And will not that of which the two partake, and which makes them alike, be the idea itself?

Certainly.

Then the idea cannot be like the individual, or the individual like the idea; for if they are alike, some further idea of likeness will always be coming to light, and if that be like anything else, another; and new ideas will be always arising, if the idea resembles that which partakes of it?

Quite true.

The theory, then, that other things participate in the ideas by resemblance, has to be given up, and some other mode of participation devised?

It would seem so.

Do you see then, Socrates, how great is the difficulty of affirming the ideas to be absolute?

Yes, indeed.

And, further, let me say that as yet you only understand a small part of the difficulty which is involved if you make of each thing a single idea, parting it off from other things.

What difficulty? he said.

There are many, but the greatest of all is this:—If an opponent argues that these ideas, being such as we say they ought to be, must remain unknown, no one can prove to him that he is wrong, unless he who denies their existence be a man of great ability and knowledge, and is willing to follow a long and laborious demonstration; he will remain unconvinced, and still insist that they cannot be known.

What do you mean, Parmenides? said Socrates.

In the first place, I think, Socrates, that you, or any one who maintains the existence of absolute essences, will admit that they cannot exist in us.

No, said Socrates; for then they would be no longer absolute.

True, he said; and therefore when ideas are what they are in relation to one another, their essence is determined by a relation among themselves, and has nothing to do with the resemblances, or whatever they are to be termed, which are in our sphere, and from which we receive this or that name when we partake of them. And the things which are within our sphere and have the same names with them, are likewise only relative to one another, and not to the ideas which have the same names with them, but belong to themselves and not to them.

What do you mean? said Socrates.

I may illustrate my meaning in this way, said Parmenides:—A master has a slave; now there is nothing absolute in the relation between them, which is simply a relation of one man to another. But there is also an idea of mastership in the abstract, which is relative to the idea of slavery in the abstract. These natures have nothing to do with us, nor we with them; they are concerned with themselves only, and we with ourselves. Do you see my meaning?

Yes, said Socrates, I quite see your meaning.

And will not knowledge—I mean absolute knowledge—answer to absolute truth?

Certainly.