PARMENIDES by Plato, Part 07
Again, the like is opposed to the unlike?
And the other to the same?
And the one was also shown to be the same with the others?
And to be, the same with the others is the opposite of being other than the others?
And in that it was other it was shown to be like?
But in that it was the same it will be unlike by virtue of the opposite affection to that which made it and this was the affection of otherness.
The same then will make it unlike; otherwise it will not be the opposite of the other.
Then the one will be both like and unlike the others; like in so far as it is other, and unlike in so far as it is the same.
Yes, that argument may be used.
And there is another argument.
In so far as it is affected in the same way it is not affected otherwise, and not being affected otherwise is not unlike, and not being unlike, is like; but in so far as it is affected by other it is otherwise, and being otherwise affected is unlike.
Then because the one is the same with the others and other than the others, on either of these two grounds, or on both of them, it will be both like and unlike the others?
And in the same way as being other than itself, and the same with itself on either of these two grounds and on both of them, it will be like and unlike itself.
Again, how far can the one touch or not touch itself and others?-Consider.
I am considering.
The one was shown to be in itself which was a whole?
And also in other things?
In so far as it is in other things it would touch other things, but in so far as it is in itself it would be debarred from touching them, and would touch itself only.
Then the inference is that it would touch both?
But what do you say to a new point of view? Must not that which is to touch another be next to that which it is to touch, and occupy the place nearest to that in which what it touches is situated?
Then the one, if it is to touch itself, ought to be situated next to itself, and occupy the place next to that in which itself is?
And that would require that the one should be two, and be in two places at once, and this, while it is one, will never happen.
Then the one cannot touch itself any more than it can be two?
Neither can it touch others.
The reason is, that whatever is to touch another must be in separation from, and next to, that which it is to touch, and no third thing can be between them.
Two things, then, at the least ate necessary to make contact possible?
And if to the two a third be added in due order, the number of terms will be three, and the contacts two?
And every additional term makes one additional contact, whence it follows that the contacts are one less in number than the terms; the first two terms exceeded the number of contacts by one, and the whole number of terms exceeds the whole number of contacts by one in like manner; and for every one which is afterwards added to the number of terms, one contact is added to the contacts.
Whatever is the whole number of things, the contacts will be always one less.
But if there be only one, and not two, there will be no contact?
How can there be?
And do we not say that the others being other than the one are not one and have no part in the one?
Then they have no number, if they have no one in them?
Of course not.
Then the others are neither one nor two, nor are they called by the name of any number?
One, then, alone is one, and two do not exist?
And if there are not two, there is no contact?
There is not.
Then neither does the one touch the others, nor the others the one, if there is no contact?
For all which reasons the one touches and does not touch itself and the others?
Further-is the one equal and unequal to itself and others?
How do you mean?
If the one were greater or less than the others, or the others greater or less than the one, they would not be greater or less than each other in virtue of their being the one and the others; but, if in addition to their being what they are they had equality, they would be equal to one another, or if the one had smallness and the others greatness, or the one had greatness and the others smallness-whichever kind had greatness would be greater, and whichever had smallness would be smaller?
Then there are two such ideas as greatness and smallness; for if they were not they could not be opposed to each other and be present in that which is.
How could they?
If, then, smallness is present in the one it will be present either in the whole or in a part of the whole?
Suppose the first; it will be either co-equal and co-extensive with the whole one, or will contain the one?
If it be co-extensive with the one it will be coequal with the one, or if containing the one it will be greater than the one?
But can smallness be equal to anything or greater than anything, and have the functions of greatness and equality and not its own functions?
Then smallness cannot be in the whole of one, but, if at all, in a part only?
And surely not in all of a part, for then the difficulty of the whole will recur; it will be equal to or greater than any part in which it is.
Then smallness will not be in anything, whether in a whole or in a part; nor will there be anything small but actual smallness.
Neither will greatness be in the one, for if greatness be in anything there will be something greater other and besides greatness itself, namely, that in which greatness is; and this too when the small itself is not there, which the one, if it is great, must exceed; this, however, is impossible, seeing that smallness is wholly absent.
But absolute greatness is only greater than absolute smallness, and smallness is only smaller than absolute greatness.
Then other things not greater or less than the one, if they have neither greatness nor smallness; nor have greatness or smallness any power of exceeding or being exceeded in relation to the one, but only in relation to one another; nor will the one be greater or less than them or others, if it has neither greatness nor smallness.
Then if the one is neither greater nor less than the others, it cannot either exceed or be exceeded by them?
And that which neither exceeds nor is exceeded, must be on an equality; and being on an equality, must be equal.
And this will be true also of the relation of the one to itself; having neither greatness nor smallness in itself, it will neither exceed nor be exceeded by itself, but will be on an equality with and equal to itself.