Page 62

will have gained more ground. Since Achilles must always reach first the position previously occupied by the tortoise, the tortoise must always keep ahead, at every point.

(ii) Arguments against Plurality and Space:--

(a) If a measure of corn produces a sound, then each grain ought to produce a sound. (This argument is taken from Simplicus: but ascribed to Zeno.)

(b) If Being exists in space, then space itself must exist in space, and the process will have to go on ad infinitum. (This argument is also taken from Simplicus.)

(c) If magnitude exists, it must be infinitely great and infinitely small, at one and the same time, since it has an infinitude of parts which are indivisible. Therefore the idea of the manifold is contradictory.

(William Turner's History of Philosophy p. 49-50).

(Roger's Students' History of Philosophy p. 31-32).

(Zeller's History of Philosophy p. 63-64).

4. The Later Ionian School: (a) Heraclitus, (b) Anaxagoras, (c) Democritus.

(a) HERACLITUS

Believed to have been born B.C. 530, and to have died in 470 B.C. Heraclitus, a native of Ephesus, in Asia Minor, has been credited with the following doctrines:--

(i) THE DOCTRINE OF UNIVERSAL FLUX

There is no static Being, and no Unchanging element. Change is Lord of the Universe. The underlying element of the universe is Fire, and all things are changed for Fire, and Fire for all things.

(a) The change is not at random; but uniform, orderly and cyclic. Thus the heavenly Fires are transmuted successively, into vapour, water and earth;

---