Fig. 2
A.●●●●
B.●●●●
C.●●●●

Therefore the time which it takes to pass C is twice as long as the time it takes to pass A. But the time which B and C take to reach the position of A is the same. Therefore double the time is equal to the half.[[895]]

According to Aristotle, the paralogism here depends upon the assumption that an equal magnitude moving with equal velocity must move for an equal time, whether the magnitude with which it is equal is at rest or in motion. That is certainly so, but we are not to suppose that this assumption is Zeno’s own. The fourth argument is, in fact, related to the third just as the second is to the first. The Achilles adds a second moving point to the single moving point of the first argument; this argument adds a second moving line to the single moving line of the arrow in flight. The lines, however, are represented as a series of units, which is just how the Pythagoreans represented them; and it is quite true that, if lines are a sum of discrete units, and time is similarly a series of discrete moments, there is no other measure of motion possible than the number of units which each unit passes.

This argument, like the others, is intended to bring out the absurd conclusions which follow from the assumption that all quantity is discrete, and what Zeno has really done is to establish the conception of continuous quantity by a reductio ad absurdum of the other hypothesis. If we remember that Parmenides had asserted the one to be continuous (fr. [8], 25), we shall see how accurate is the account of Zeno’s method which Plato puts into the mouth of Sokrates.

II. Melissos of Samos

Life.

164. In his Life of Perikles, Plutarch tells us, on the authority of Aristotle, that the philosopher Melissos, son of Ithagenes, was the Samian general who defeated the Athenian fleet in 441/0 B.C.:[[896]] and it was no doubt for this reason that Apollodoros fixed his floruit in Ol. LXXXIV. (444-41 B.C.).[[897]] Beyond this, we really know nothing about his life. He is said to have been, like Zeno, a disciple of Parmenides;[[898]] but, as he was a Samian, it is possible that he was originally a member of the Ionic school, and we shall see that certain features of his doctrine tend to bear out this view. On the other hand, he was certainly convinced by the Eleatic dialectic, and renounced the Ionic doctrine in so far as it was inconsistent with that. We note here the effect of the increased facility of intercourse between East and West, which was secured by the supremacy of Athens.

The Fragments.

165. The fragments which we have come from Simplicius, and are given, with the exception of the first, from the text of Diels.[[899]]

(1a) If nothing is, what can be said of it as of something real?[[900]]