PARMENIDES by Plato, Part 10
How do you mean?
If anything were a part of many, being itself one of them, it will surely be a part of itself, which is impossible, and it will be a part of each one of the other parts, if of all; for if not a part of some one, it will be a part of all the others but this one, and thus will not be a part of each one; and if not a part of each, one it will not be a part of anyone of the many; and not being a part of any one, it cannot be a part or anything else of all those things of none of which it is anything.
Then the part is not a part of the many, nor of all, but is of a certain single form, which we call a whole, being one perfect unity framed out of all-of this the part will be a part.
If, then, the others have parts, they will participate in the whole and in the one.
Then the others than the one must be one perfect whole, having parts.
And the same argument holds of each part, for the part must participate in the one; for if each of the parts is a part, this means, I suppose, that it is one separate from the rest and self-related; otherwise it is not each.
But when we speak of the part participating in the one, it must clearly be other than one; for if not, it would merely have participated, but would have been one; whereas only the itself can be one.
Both the whole and the part must participate in the one; for the whole will be one whole, of which the parts will be parts; and each part will be one part of the whole which is the whole of the part.
And will not the things which participate in the one, be other than it?
And the things which are other than the one will be many; for if the things which are other than the one were neither one nor more than one, they would be nothing.
But, seeing that the things which participate in the one as a part, and in the one as a whole, are more than one, must not those very things which participate in the one be infinite in number?
Let us look at the matter thus:-Is it not a fact that in partaking of the one they are not one, and do not partake of the one at the very time. when they are partaking of it?
They do so then as multitudes in which the one is not present?
And if we were to abstract from them in idea the very smallest fraction, must not that least fraction, if it does not partake of the one, be a multitude and not one?
And if we continue to look at the other side of their nature, regarded simply, and in itself, will not they, as far as we see them, be unlimited in number?
And yet, when each several part becomes a part, then the parts have a limit in relation to the whole and to each other, and the whole in relation to the parts.
The result to the others than the one is that of themselves and the one appears to create a new element in them which gives to them limitation in relation to one another; whereas in their own nature they have no limit.
That is clear.
Then the others than the one, both as whole and parts, are infinite, and also partake of limit.
Then they are both like and unlike one another and themselves.
How is that?
Inasmuch as they are unlimited in their own nature, they are all affected in the same way.
And inasmuch as they all partake of limit, they are all affected in the same way.
But inasmuch as their state is both limited and unlimited, they are affected in opposite ways.
And opposites are the most unlike of things.
Considered, then, in regard to either one of their affections, they will be like themselves and one another; considered in reference to both of them together, most opposed and most unlike.
That appears to be true.
Then the others are both like and unlike themselves and one another?
And they are the same and also different from one another, and in motion and at rest, and experience every sort of opposite affection, as may be proved without difficulty of them, since they have been shown to have experienced the affections aforesaid?
Suppose, now, that we leave the further discussion of these matters as evident, and consider again upon the hypothesis that the one is, whether opposite of all this is or is not equally true of the others.
By all means.
Then let us begin again, and ask, If one is, what must be the affections of the others?
Let us ask that question.
Must not the one be distinct from the others, and the others from the one?
Why, because there is nothing else beside them which is distinct from both of them; for the expression "one and the others" includes all things.
Yes, all things.
Then we cannot suppose that there is anything different from them in which both the one and the others might exist?
There is nothing.
Then the one and the others are never in the same?
Then they are separated from each other?
And we surely cannot say that what is truly one has parts?
Then the one will not be in the others as a whole, nor as part, if it be separated from the others, and has no parts?
Then there is no way in which the others can partake of the one, if they do not partake either in whole or in part?
It would seem not.
Then there is no way in which the others are one, or have in themselves any unity?
There is not.
Nor are the others many; for if they were many, each part of them would be a part of the whole; but now the others, not partaking in any way of the one, are neither one nor many, nor whole, nor part.
Then the others neither are nor contain two or three, if entirely deprived of the one?
Then the others are neither like nor unlike the one, nor is likeness and unlikeness in them; for if they were like and unlike, or had in them likeness and unlikeness, they would have two natures in them opposite to one another.
That is clear.
But for that which partakes of nothing to partake of two things was held by us to be impossible?
Then the others are neither like nor unlike nor both, for if they were like or unlike they would partake of one of those two natures, which would be one thing, and if they were both they would partake of opposites which would be two things, and this has been shown to be impossible.
Therefore they are neither the same, nor other, nor in motion, nor at rest, nor in a state of becoming, nor of being destroyed, nor greater, nor less, nor equal, nor have they experienced anything else of the sort; for, if they are capable of experiencing any such affection, they will participate in one and two and three, and odd and even, and in these, as has been proved, they do not participate, seeing that they are altogether and in every way devoid of the one.
Therefore if one is, the one is all things, and also nothing, both in relation to itself and to other things.
Well, and ought we not to consider next what will be the consequence if the one is not?
Yes; we ought.
What is the meaning of the hypothesis-If the one is not; is there any difference between this and the hypothesis-If the not one is not?
There is a difference, certainly.
Is there a difference only, or rather are not the two expressions-if the one is not, and if the not one is not, entirely opposed?
They are entirely opposed.
And suppose a person to say:-If greatness is not, if smallness is not, or anything of that sort, does he not mean, whenever he uses such an expression, that "what is not" is other than other things?
To be sure.
And so when he says "If one is not" he clearly means, that what "is not" is other than all others; we know what he means-do we not?
Yes, we do.
When he says "one," he says something which is known; and secondly something which is other than all other things; it makes no difference whether he predicate of one being or not being, for that which is said "not to be" is known to be something all the same, and is distinguished from other things.
Then I will begin again, and ask: If one is not, what are the consequences? In the first place, as would appear, there is a knowledge of it, or the very meaning of the words, "if one is not," would not be known.