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, is that which we find must come next, and this we discover in the Eleatic school. In it we see thought becoming free for itself; and in that which the Eleatics express as absolute essence, we see Thought grasp itself in purity, and the movement of Thought in Notions. In the physical philosophy we saw movement represented as an objective movement, as an origination and passing away. The Pythagoreans similarly did not reflect upon these Notions, and also treated their essence, Number, as fleeting. But since alteration is now grasped in its highest abstraction as Nothing, this objective movement changes into a subjective one, comes over to the side of consciousness, and existence becomes the unmoved. We here find the beginning of dialectic, _i.e._ simply the pure movement of thought in Notions; likewise we see the opposition of thought to outward appearance or sensuous Being, or of that which is implicit to the being-for-another of this implicitness, and in the objective existence we see the contradiction which it has in itself, or dialectic proper. When we reflect in anticipation on how the course of pure thought must be formed, we find (_α_) that pure thought (pure Being, the One) manifests itself immediately in its rigid isolation and self-identity, and everything else as null; (_β_) that the hitherto timid thought—which after it is strengthened, ascribes value to the “other” and constitutes itself therefrom—shows that it then grasps the other in its simplicity and even in so doing shows its nullity; (_γ_) 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.