to reach the position of A is the same. Therefore double the time is equal to the half.[1]
According to Aristotle, the paralogism here depends on 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
164.Life. 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
- ↑ Arist. Phys. Z, 9. 239 b 33 (R. P. 139). I have had to express the argument in my own way, as it is not fully given by any of the authorities. The figure is practically Alexander's (Simpl. Phys. p. 1016, 14), except that he represents the ὄγκοι by letters instead of dots. The conclusion is plainly stated by Aristotle (loc. cit.), συμβαίνειν οἴεται ἴσον εἶναι χρόνον τῷ διπλασίῳ τὸν ἥμισυν, and, however we explain the reasoning, it must be so represented as to lead to the conclusion that, as Mr. Jourdain puts it (loc. cit.), "a body travels twice as fast as it does."
