Parmenides

Plato

Plato in Twelve Volumes, Vol. 4 translated by Harold North Fowler; Introduction by W.R.M. Lamb. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1926.

Ceph.Then there would be even times even, odd times odd, odd times even, and even times odd.Yes.Then if that is true, do you believe any number is left out, which does not necessarily exist?By no means.Then if one exists, number must also exist.It must.But if number exists, there must be many, indeed an infinite multitude, of existences; or is not number infinite in multitude and participant of existence?Certainly it is.Then if all number partakes of existence, every part of number will partake of it?Yes.Existence, then, is distributed over all things, which are many, and is not wanting in any existing thing from the greatest to the smallest? Indeed, is it not absurd even to ask that question? For how can existence be wanting in any existing thing?It cannot by any means.Then it is split up into the smallest and greatest and all kinds of existences nothing else is so much divided, and in short the parts of existence are infinite.That is true.Its parts are the most numerous of all.Yes, they are the most numerous.Well, is there any one of them which is a part of existence, but is no part?How could that be?But if there is, it must, I imagine, so long as it is, be some one thing; it cannot be nothing.That is inevitable.Then unity is an attribute of every part of existence and is not wanting to a smaller or larger or any other part.True.Can the one be in many places at once and still be a whole? Consider that question.I am considering and I see that it is impossible.Then it is divided into parts, if it is not a whole; for it cannot be attached to all the parts of existence at once unless it is divided.I agree.And that which is divided into parts must certainly be as numerous as its parts.It must.Then what we said just now—that existence was divided into the greatest number of parts—was not true for it is not divided, you see, into any more parts than one, but, as it seems, into the same number as one for existence is not wanting to the one, nor the one to existence, but being two they are equal throughout.That is perfectly clear.The one, then, split up by existence, is many and infinite in number.Clearly.Then not only the existent one is many, but the absolute one divided by existence, must be many.Certainly.