In a definite space such as a table (A B) let us suppose two bodies of equal length with it and with one another, one of which (C D) lies with one end (C) on the middle (g) of the table, and the other (E F), being in the same direction, has the point (E) only touching the end of the table (h); and supposing they move in opposite directions, and the former (C D) reaches in an hour the end (h) of the table; we have the result ensuing that the one (E F) passes in the half of the time through the same space (i k) which the other does in the double (g h); hence the half is equal to the double. That is to say, this second passes (let us say, in the point l) by the whole of the first C D. In the first half-hour l goes from m to i, while k only goes from g to n.
In the second half-hour l goes past o to k, and altogether passes from m to k, or the double of the distance.
This fourth form deals with the contradiction presented in opposite motion; that which is common is given entirely to one body, while it only does part for itself. Here the distance travelled by one body is the sum of the distance travelled by both, just as when I go two feet east, and from the same point another goes two feet west, we are four feet removed from one another; in the distance moved both are positive, and hence have to be added together. Or if I have gone two feet forwards and two feet backwards, although I have walked four feet, I have not moved from the spot; the motion is then nil, for by going forwards and backwards an opposition ensues which annuls itself.
This is the dialectic of Zeno; he had a knowledge of the determinations which our ideas of space and time contain, and showed in them their contradiction; Kant’s antinomies do no more than Zeno did here. The general result of the Eleatic dialectic has thus become, “the truth is the one, all else is untrue,” just as the Kantian philosophy resulted in “we know appearances only.” On the whole the principle is the same; “the content of knowledge is only an appearance and not truth,” but there is also a great difference present. That is to say, Zeno and the Eleatics in their proposition signified “that the sensuous world, with its multitudinous forms, is in itself appearance only, and has no truth.” But Kant does not mean this, for he asserts: “Because we apply the activity of our thought to the outer world, we constitute it appearance; what is without, first becomes an untruth by the fact that we put therein a mass of determinations. Only our knowledge, the spiritual, is thus appearance; the world is in itself absolute truth; it is our action alone that ruins it, our work is good for nothing.” It shows excessive humility of mind to believe that knowledge has no value; but Christ says, “Are ye not better than the sparrows?” and we are so inasmuch as we are thinking; as sensuous we are as good or as bad as sparrows. Zeno’s dialectic has greater objectivity than this modern dialectic.
Zeno’s dialectic is limited to Metaphysics; later, with the Sophists, it became general. We here leave the Eleatic school, which perpetuates itself in Leucippus and, on the other side, in the Sophists, in such a way that these last extended the Eleatic conceptions to all reality, and gave to it the relation of consciousness; the former, however, as one who later on worked out the Notion in its abstraction, makes a physical application of it, and one which is opposed to consciousness. There are several other Eleatics mentioned, to Tennemann’s surprise, who, however, cannot interest us. “It is so unexpected,” he says (Vol. I., p. 190), “that the Eleatic system should find disciples; and yet Sextus mentions a certain Xeniades.”
D. Heraclitus.
If we put aside the Ionics, who did not understand the Absolute as Thought, and the Pythagoreans likewise, we have the pure Being of the Eleatics, and the dialectic which denies all finite relationships. Thought to the latter is the process of such manifestations; the world in itself is the apparent, and pure Being alone the true. The dialectic of Zeno thus lays hold of the determinations which rest in the content itself, but it may, in so far, also be called subjective dialectic, inasmuch as it rests in the contemplative subject, and the one, without this movement of the dialectic, is abstract identity. The next step from the existence of the dialectic as movement in the subject, is that it must necessarily itself become objective. If Aristotle blames Thales for doing away with motion, because change cannot be understood from Being, and likewise misses the actual in the Pythagorean numbers and Platonic Ideas, taken as the substances of the things which participate in them, Heraclitus at least understands the absolute as just this process of the dialectic. The dialectic is thus thre-fold: (α) the external dialectic, a reasoning which goes over and over again without ever reaching the soul of the thing; (β) immanent dialectic of the object, but falling within the contemplation of the subject; (γ) the objectivity of Heraclitus which takes the dialectic itself as principle. The advance requisite and made by Heraclitus is the progression from Being as the first immediate thought, to the category of Becoming as the second. This is the first concrete, the Absolute, as in it the unity of opposites. Thus with Heraclitus the philosophic Idea is to be met with in its speculative form; the reasoning of Parmenides and Zeno is abstract understanding. Heraclitus was thus universally esteemed a deep philosopher and even was decried as such. Here we see land; there is no proposition of Heraclitus which I have not adopted in my Logic.