Part 26

Clearly.

Then the inference is that it would touch both?

It would.

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?

True.

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?

It ought.

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.

No.

Then the one cannot touch itself any more than it can be two?

It cannot.

Neither can it touch others.

Why not?

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.

True.

Two things, then, at the least are necessary to make contact possible?

They are.

And if to the two a third be added in due order, the number of terms will be three, and the contacts two?

Yes.

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.

True.

Whatever is the whole number of things, the contacts will be always one less.

True.

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?

True.

Then they have no number, if they have no one in them?