[21] Aristotel. Physic. vii. 5, p. 250, a. 20, with the Scholia of Simplikius on the passage, p. 423, ed. Brandis.
To appreciate the contradiction brought out by Zeno, we must recollect that he is not here reasoning about facts of sense, phenomenal and relative — but about things in themselves, absolute and ultra-phenomenal realities. He did not deny the fact of sense: to appeal to that fact in reply, would have been to concede his point. The adversaries against whom he reasoned (Protagoras is mentioned, but he can hardly have been among them, if we have regard to his memorable dogma, of which more will be said presently) were those who maintained the plurality of absolute substances, each for itself, with absolute attributes, apart from the fact of sense, and independent of any sentient subject. One grain of millet (Zeno argues) has no absolute sonorousness, neither can ten thousand such grains taken together have any. Upon the hypothesis of absolute reality as a discontinuous multitude, you are here driven to a contradiction which Zeno intends as an argument against the hypothesis. There is no absolute sonorousness in the ten thousand grains: the sound which they make is a phenomenal fact, relative to us as sentients of sound, and having no reality except in correlation with a hearer.[22]
[22] It will be seen that Aristotle in explaining this ἀπορία, takes into consideration the difference of force in the vibrations of air, and the different impressibility of the ear. The explanation is pertinent and just, if applied to the fact of sense: but it is no reply to Zeno, who did not call in question the fact of sense. Zeno is impugning the doctrine of absolute substances and absolute divisibility. To say that ten thousand grains are sonorous, but that no one of them separately taken is so, appears to him a contradiction, similar to what is involved in saying that a real magnitude is made up of mathematical points. Aristotle does not meet this difficulty.
Zenonian arguments in regard to motion.
Other memorable arguments of Zeno against the same hypothesis were those by which he proved that if it were admitted, motion would be impossible. Upon the theory of absolute plurality and discontinuousness, every line or portion of distance was divisible into an infinite number of parts: before a moving body could get from the beginning to the end of this line, it must pass in succession over every one of these parts: but to do this in a finite time was impossible: therefore motion was impossible.[23]
[23] Aristot. Physic. vi. 9, p. 239 b., with the Scholia, p. 412 seq. ed. Brandis; Aristotel. De Lineis Insecabilibus, p. 968, a. 19.
These four arguments against absolute motion caused embarrassment to Aristotle and his contemporaries. τέτταρες δ’ εἰσὶ λόγοι Ζήνωνος οἱ παρέχοντες τὰς δυσκολίας τοῖς λύουσιν, &c.
A second argument of the same tendency was advanced in the form of comparison between Achilles and the tortoise — the swiftest and slowest movers. The two run a race, a certain start being given to the tortoise. Zeno contends that Achilles can never overtake the tortoise. It is plain indeed, according to the preceding argument, that motion both for the one and for the other is an impossibility. Neither one nor the other can advance from the beginning to the end of any line, except by passing successively through all the parts of that line: but those parts are infinite in number, and cannot therefore be passed through in any finite time. But suppose such impossibility to be got over: still Achilles will not overtake the tortoise. For while Achilles advances one hundred yards, the tortoise has advanced ten: while Achilles passes over these additional ten yards, the tortoise will have passed over one more yard: while Achilles is passing over this remaining one yard, the tortoise will have got over one-tenth of another yard: and so on ad infinitum: the tortoise will always be in advance of him by a certain distance, which, though ever diminishing, will never vanish into nothing.
The third Zenonian argument derived its name from the flight of an arrow shot from a bow. The arrow while thus carried forward (says Zeno) is nevertheless at rest.[24] For the time from the beginning to the end of its course consists of a multitude of successive instants. During each of these instants the arrow is in a given place of equal dimension with itself. But that which is during any instant in a given place, is at rest. Accordingly during each successive instant of its flight, the arrow is at rest. Throughout its whole flight it is both in motion and at rest. This argument is a deduction from the doctrine of discontinuous time, as the preceding is a deduction from that of discontinuous space.