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This whole, the universal and divine understanding, in unity with which we are logical, is, according to Heraclitus, the essence of truth. Hence that which appears as the universal to all, carries with it conviction, for it has part in the universal and divine Logos, while what is subscribed to by an individual carries with it no conviction from the opposite cause.

From his principle that everything that is, at the same time is not, it immediately follows that he holds that sensuous certainty has no truth; for it is the certainty for which something exists as actual, which is not so in fact. Not this immediate Being, but absolute mediation, Being as thought of, Thought itself, is Thought is the true being

They are not themselves process, but fire is process; and thus he maintains fire to be the elementary principle, and this is the real form of the Heraclitean principle, the soul and substance of the nature­process. Fire is physical time, absolute unrest, absolute disintegration of existence, the passing away of the "other," but also of itself;

To Heraclitus the truth is to have grasped the essential being of nature, i.e. to have represented it as implicitly infinite, as process in itself; and consequently it is evident to us that Heraclitus could not say that the primary principle is air, water, or any such thing.

It is not that time is or is not, for time is non­being immediately in Being and Being immediately in non­being: it is the transition out of Being into non­being, the abstract Notion, but in an objective form, i.e. in so far as it is for us.

''what coincides and what conflicts, what is harmonious and what discordant, and from out of them all comes one, and from one, all."

For Heraclitus says: "Everything is in a state of flux; nothing subsists nor does it ever remain the same." And Plato further says of Heraclitus: "He compares things to the current of a river: no one can go twice into the same stream,"1 for it flows on and other water is disturbed.

"Being and non­being are the same; everything is and yet is not." The truth only is as the unity of distinct opposites and, indeed, of the pure opposition of being and non­being; but with the Eleatics we have the abstract understanding that Being is alone the truth. We say, in place of using the expression of Heraclitus, that the Absolute is the unity of being and non­being.

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.

If Aristotle says that Zeno denied movement because it contains an inner contradiction, it is not to be understood to mean that movement did not exist at all.

The ordinary ideas of science, where propositions result from proof, proof is the movement of intelligence, a connection brought about by mediation. Dialectic is either (a) external dialectic, in which this movement is different from the comprehension of the movement, or (b) not a movement of our intelligence only, but what proceeds from the nature of the thing itself, i.e. from the pure Notion of the content.

We here see a dialectic which may be called metaphysical reasoning, in which the principle of identity is fundamental. "The nothing is like nothing and does not pass into Being or conversely; thus nothing can originate from like." This, the oldest mode of argument, holds its place even to the present day, as, for example, in the so­ called proof of the unity of God.

As to his philosophy, Xenophanes in the first place maintained absolute existence to be the one, and likewise called this God. "The all is One and God is implanted in all things; He is unchangeable, without beginning, middle or end."

On the whole, philosophic utterances and Notions are still poor, and it was in Zeno that Philosophy first attained to a purer expression of itself.

(g) finally, Thought manifests the other in the manifold nature of its determinations. We shall see this in the development and culture of the Eleatics in history. These Eleatic propositions still have interest for Philosophy, and are moments which must necessarily there appear

When we reflect in anticipation on how the course of pure thought must be formed, we find that pure thought manifests itself immediately in its rigid isolation and self-identity, and everything else as null (b) that the hitherto timid thought— which after it is strengthened, ascribes value to the other and constitutes itself—shows that it then grasps the other in its simplicity and even in so doing shows its nullity

The Pythagorean philosophy has not yet got the speculative form of expression for the Notion. Numbers are not pure Notion, but Notion in the form of ordinary idea or sensuous perception, and hence a mixture of both. This expression of absolute essence in what is a pure Notion or something thought, and the movement of the Notion or of Thought and this we discover in the Eleatic school.

secondly, "From number no other corporeal determinations, such as weight and lightness, are conceivable;" or number thus cannot pass into what is concrete. "They say that there is no number outside of those in the heavenly spheres." For instance, a heavenly sphere and a virtue, or a natural manifestation in the earth, are determined as one and the same number

Aristotle says justly, in the first place: "If only the limited and the unlimited, the even and odd are made fundamental ideas, the Pythagoreans do not explain how movement arises, and how, without movement and change there can be coming into being and passing away, or the conditions and activities of heavenly objects."

The triad has now become a most important number, seeing that in it the monad has reached reality and perfection. The monad proceeds through the duad, and again brought into unity with this undetermined manifold, it is the triad.

(a) The absolute, simple essence divides itself into unity and multiplicity, of which the one sublates the other, and at the same time it has its existence in the opposition. (b) The opposition has at the same time subsistence, and in this is found the manifold nature of equivalent things. (g) The return of absolute essence into itself is the negative unity of the individual subject and of the universal or positive.

as the absolute principles of things, not so much immediate numbers in their arithmetic differences, as the principles of number. The first determination is unity generally, the next duality or opposition. It is most important to trace back the infinitely manifold nature of the forms and determinations of finality to their universal thoughts as the most simple principles of all determination.

Pythagoras propounded philosophy in this wise in order to loose thought from its fetters. Without thought nothing true can be discerned or known; thought hears and sees everything in itself, the rest is lame and blind. To obtain his end, Pythagoras makes use of mathematics, since this stands midway between what is sensuous and thought, as a kind of preliminary to what is in and for itself.

The Pythagorean philosophy forms the transition from realistic to intellectual philosophy. 1. Thus the original and simple proposition of the Pythagorean philosophy is, according to Aristotle (Metaph. I. 5), ''that number is the reality of things, and the constitution of the whole universe in its determinations is a harmonious system of numbers and of their relations."

No one recognized better the deficiencies in this philosophy than did Aristotle in the work already quoted. The first great defect here rests in the fact that the universal is expressed in a particular form. 2. the Principle of Motion. 3. object is altogether absent; there is no determination of activity.

The importance of these poor abstract thoughts lies (a) in the comprehension of a universal substance in everything, and (b) in the fact that it is formless, and not encumbered by sensuous ideas.

We see that, as Aristotle said, they placed the first principle in a form of matter—in air and water first, and then, if we may so define Anaximander's matter, in an essence finer than water and coarser than air.