It will be noted how much clearer the historical position of Zeno becomes if we follow Plato in assigning him to a somewhat later date than is usual. We have first Parmenides, then the pluralists, and then the criticism of Zeno. This, at any rate, seems to have been the view which Aristotle took of the historical development.[[878]]

What is the unit?

159. The polemic of Zeno is clearly directed in the first instance against a certain view of the unit. Eudemos, in his Physics,[[879]] quoted from him the saying that “if any one could tell him what the one was, he would be able to say what things are.” The commentary of Alexander on this, preserved by Simplicius,[[880]] is quite satisfactory. “As Eudemos relates,” he says, “Zeno the disciple of Parmenides tried to show that it was impossible that things could be a many, seeing that there was no unit in things, whereas ‘many’ means a number of units.” Here we have a clear reference to the Pythagorean view that everything may be reduced to a sum of units, which is what Zeno denied.[[881]]

The Fragments.

160. The fragments of Zeno himself also show that this was his line of argument. I give them according to the arrangement of Diels.

(1)

If the one had no magnitude, it would not even be.... But, if it is, each one must have a certain magnitude and a certain thickness, and must be at a certain distance from another, and the same may be said of what is in front of it; for it, too, will have magnitude, and something will be in front of it.[[882]] It is all the same to say this once and to say it always; for no such part of it will be the last, nor will one thing not be compared with another.[[883]] So, if things are a many, they must be both small and great, so small as not to have any magnitude at all, and so great as to be infinite. R. P. 134.

(2)

For if it were added to any other thing it would not make it any larger; for nothing can gain in magnitude by the addition of what has no magnitude, and thus it follows at once that what was added was nothing.[[884]] But if, when this is taken away from another thing, that thing is no less; and again, if, when it is added to another thing, that does not increase, it is plain that what was added was nothing, and what was taken away was nothing. R. P. 132.

(3)