§20.
1. Zeno was born about B.C. 490-485, and was the friend and pupil of Parmenides. It is said that he took part in the efforts of this philosopher for the ethical and political amelioration of his fellow-citizens, but that having failed in an enterprise against the tyrant Nearchus, he was taken prisoner, and died under tortures heroically endured. In his philosophy he aimed at developing in dialectic form the idealistic Monism of Parmenides. He brought forward a number of "proofs" to show that the admission of plurality and change, as of motion of space leads to inexplicable self-contradiction.{1}
2. The principal proofs adduced by Zeno in his attempt to give in dialectic form an indirect demonstration of the Monism of Parmenides are the following. Against the reality of motion he argues (Arist. Phys. 6, 2-9.):--
(a.) Motion cannot begin, for a body cannot reach a new position without passing through innumerable intervening positions. The moving body must first pass through half the intervening space, and then again through half this space, and so on indefinitely.
(b.) Achilles cannot overtake the tortoise, for, no matter what the position he reaches, he will find that the tortoise has advanced still further.
(c.) The arrow, though flying through the air, is, nevertheless, at rest, for at every moment it is in some one place; now here, now there, but always, as long as it is in any one place, it is at rest.
(d.) The half of a given period of time is equal to the whole, for the same point moving with different velocities in passing through the same space will at one time occupy half the period, at another the whole.
As these contradictions cannot be explained away it follows that there can be no motion at all, and that what we call movement is merely an appearance.
Against the reality of space Zeno argued thus (Arist. Phys. 4, 3):--
If Being exists in space this space itself should exist in another space, and so on without end. As this is impossible, it follows that there is no such thing as space.
Against the plurality of things Zeno adduces the following arguments (Simplicius in Phys. Arist. fol. 30, 6):--
(a.) If a plurality of things exist the number of these things is either determinate or infinite. "These things are as many as they are, neither more nor less; but if they are as many as they are, they exist in determinate number." On the other hand "if a plurality of things exist they must be infinite in number; for between things that are different other things must be interposed, and between these again others, and so on till the number becomes infinite." The admission of a plurality of things thus involves a contradiction which it is impossible to solve.
(b.) Again if a plurality of objects existed, the aggregate should be at once infinitely great and infinitesimally small. Each object must have some magnitude. But magnitude is only possible when the component parts of the object are separated by an interval. The interval which must thus be admitted has itself a magnitude, and must therefore be separated by another interval from the things which it separates, and so on without end. It follows from this that every object must be infinitely great since it is composed of an infinitude of parts each of which has some magnitude. On the other hand, from the same premises we must conclude that every object must be infinitesimally small. For if the parts of a thing are infinite in number, eo ipso they must be infinitesimally small. But an aggregate of infinitesimally small magnitudes must be infinitesimally small In this way the admission of a plurality of things again leads us to a contradiction.
Against the truth of sensuous preceptions Zeno argues as follows:--
If a measure of corn in falling produces a sound, then each single grain, and each part of a grain, must also produce a sound. If this be not the case, then the whole measure, the action of which is only the sum of the action of its parts, cannot produce a sound. Here again we have a contradiction from which we cannot escape as on as we admit the truth of sensuous perceptions.
3. In his theory of physical nature Zeno is in accord with the other Eleatics. He admits four elements, the Warm, the Cold, the Dry, and the Moist -- in which we recognise the familiar four elements. He furthermore admits a moving force which controls everything -- Necessity, of which there are two species, Discord and Love. With regard to the soul he holds with Parmenides, that it is a mixture of the four elements. In this compound some elements may predominate, but none can be entirely absent. He seems to have made the purity and godliness of the soul consist in the preponderance of the purer elements over the impure.
{1} In the Parmenides of Plato mention is made of a prose work (suggramma) by Zeno, which was divided into series of arguments, each of which set up some hypothesis (hupothesis) which was then proved absurd, and so the Oneness of Being was indirectly established. On account of this method of demonstration Aristotle has styled Zeno the founder of dialectic.