1. Relation of the Eleatic Principle to the Pythagorean.—While the Pythagoreans had made matter, in so far as it is quantity and the manifold, the basis of their philosophizing, and while in this they only abstracted from the determined elemental condition of matter, the Eleatics carry the process to its ultimate limit, and make, as the principle of their philosophy, a total abstraction from every finite determinateness, from every change and vicissitude which belongs to concrete being. While the Pythagoreans had held fast to the form of being as having existence in space and time, the Eleatics reject this, and make as their fundamental thought the negation of all exterior and posterior. Only being is, and there is no not-being, nor becoming. This being is the purely undetermined, changeless ground of all things. It is not being in becoming, but it is being as exclusive of all becoming; in other words, it is pure being.

Eleaticism is, therefore, Monism, in so far as it strove to carry back the manifoldness of all being to a single ultimate principle; but on the other hand it becomes Dualism, in so far as it could neither carry out its denial of concrete existence, i. e., the phenomenal world, nor yet derive the latter from its presupposed original ground. The phenomenal world, though it might be explained as only an empty appearance, did yet exist; and, since the sensuous perception would not ignore this, there must be allowed it, hypothetically at least, the right of existence. Its origin must be explained, even though with reservations. This contradiction of an unreconciled Dualism between being and existence, is the point where the Eleatic philosophy is at war with itself—though, in the beginning of the school—with Xenophanes, it does not yet appear. The principle itself, with its results, is only fully apparent in the lapse of time. It has three periods of formation, which successively appear in three successive generations. Its foundation belongs to Xenophanes; its systematic formation to Parmenides; its completion and partial dissolution to Zeno and Melissus—the latter of whom we can pass by.

2. Xenophanes.—Xenophanes is considered as the originator of the Eleatic tendency. He was born at Colophon; emigrated to Elea, a Phocian colony in Lucania, and was a younger cotemporary of Pythagoras. He appears to have first uttered the proposition—“every thing is one,” without, however, giving any more explicit determination respecting this unity, whether it be one simply in conception or in actuality. Turning his attention, says Aristotle, upon the world as a whole, he names the unity which he finds, God. God is the One. The Eleatic “One and All” (?? ?a? p??) had, therefore, with Xenophanes, a theological and religious character. The idea of the unity of God, and an opposition to the anthropomorphism of the ordinary views of religion, is his starting point. He declaimed against the delusion that the gods were born, that they had a human voice or form, and railed at the robbery, adultery, and deceit of the gods as sung by Homer and Hesiod. According to him the Godhead is wholly seeing, wholly understanding, wholly hearing, unmoved, undivided, calmly ruling all things by his thought, like men neither in form nor in understanding. In this way, with his thought turned only towards removing from the Godhead all finite determinations and predicates, and holding fast to its unity and unchangeableness, he declared this doctrine of its being to be the highest philosophical principle, without however directing this principle polemically against the doctrine of finite being, or carrying it out in its negative application.

3. Parmenides.—The proper head of the Eleatic school is Parmenides of Elea, a scholar, or at least an adherent of Xenophanes. Though we possess but little reliable information respecting the circumstances of his life, yet we have, in inverse proportion, the harmonious voice of all antiquity in an expression of reverence for the Eleatic sage, and of admiration for the depth of his mind, as well as for the earnestness and elevation of his character. The saying—“a life like Parmenides,” became afterwards a proverb among the Greeks.

Parmenides embodied his philosophy in an epic poem, of which we have still important fragments. It is divided into two parts. In the first he discusses the conception of being. Rising far above the yet unmediated view of Xenophanes, he attains a conception of pure single being, which he sets up as absolutely opposed to every thing manifold and changeable, i. e., to that which has no being, and which consequently cannot be thought. From this conception of being he not only excludes all becoming and departing, but also all relation to space and time, all divisibility and movement. This being he explains as something which has not become and which does not depart, as complete and of its own kind, as unalterable and without limit, as indivisible and present though not in time, and since all these are only negative, he ascribes to it, also, as a positive determination—thought. Being and thought are therefore identical with Parmenides. This pure thought, directed to the pure being, he declares is the only true and undeceptive knowledge, in opposition to the deceptive notions concerning the manifoldness and mutability of the phenomenal. He has no hesitancy in holding that to be only a name which mortals regard as truth, viz., becoming and departing, being and not-being, change of place and vicissitude of circumstance. We must therefore be careful not to hold “the One” of Parmenides, as the collective unity of all concrete being.

So much for the first part of Parmenides’ poem. After the principle that there is only being has been developed according to its negative and positive determinations, we might believe that the system was at an end. But there follows a second part, which is occupied solely with the hypothetical attempt to explain the phenomenal world and give it a physical derivation. Though firmly convinced that, according to reason and conception, there is only “the One,” yet is Parmenides unable to withdraw himself from the recognition of an appearing manifoldness and change. Forced, therefore, by his sensuous perception to enter upon a discussion of the phenomenal world, he prefaces this second part of his poem with the remark, that he had now closed what he had to say respecting the truth, and was hereafter to deal only with the opinion of a mortal. Unfortunately, this second part has been very imperfectly transmitted to us. Enough however remains to show, that he explained the phenomena of nature from the mingling of two unchangeable elements, which Aristotle, though apparently only by way of example, indicates as warm and cold, fire and earth. Concerning these two elements, Aristotle remarks still farther that Parmenides united the warmth with being, and the other element with not-being.

It is scarcely necessary to remark that between the two parts of the Parmenidean philosophy—between the doctrine concerning being and the doctrine concerning appearance—there can exist no inner scientific connection. What Parmenides absolutely denies in the first part, and indeed declares to be unutterable, viz., the not-being, the many and the changeable, he yet in the second part admits to have an existence at least in the representation of men. But it is clear that the not-being cannot once exist in the representation, if it does not exist generally and every where, and that the attempt to explain a not-being of the representation, is in complete contradiction with his exclusive recognition of being. This contradiction, this unmediated juxtaposition of being and not-being, of the one and the many, Zeno, a scholar of Parmenides, sought to remove, by affirming that from the very conception of being, the sensuous representation, and thus the world of the not-being, are dialectically annihilated.

4. Zeno.—The Eleatic Zeno was born about 500 B. C.; was a scholar of Parmenides, and the earliest prose writer among the Grecian philosophers. He is said to have written in the form of dialogues. He perfected, dialectically, the doctrine of his master, and carried out to the completest extent the abstraction of the Eleatic One, in opposition to the manifoldness and determinateness of the finite. He justified the doctrine of a single, simple, and unchangeable being, in a polemical way, by showing up the contradictions into which the ordinary representations of the phenomenal world become involved. While Parmenides affirms that there is only the One, Zeno shows in his well-known proofs (which unfortunately we cannot here more widely unfold), that the many, the changing, that which has relation to space, or that which has relation to time, is not. While Parmenides affirmed the being, Zeno denied the appearance. On account of these proofs, in which Zeno takes up the conceptions of extension, manifoldness and movement, and shows their inner contradictory nature, Aristotle names him the founder of dialectics.

While the philosophizing of Zeno is the completion of the Eleatic principle, so is it at the same time the beginning of its dissolution. Zeno had embraced the opposition of being and existence, of the one and the many, so abstractly, and had carried it so far, that with him the inner contradiction of the Eleatic principle comes forth still more boldly than with Parmenides; for the more logical he is in the denial of the phenomenal world, so much the more striking must be the contradiction, of turning, on the one side, his whole philosophical activity to the refutation of the sensuous representation, while, on the other side, he sets over against it a doctrine which destroys the very possibility of a false representation.