Before I say anything of the further sequence of these numbers, it must be remarked that they, as we see them represented here, are pure Notions. (_α_) 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. (_β_) The opposition has at the same time subsistence, and in this is found the manifold nature of equivalent things. (_γ_) The return of absolute essence into itself is the negative unity of the individual subject and of the universal or positive. This is, in fact, the pure speculative Idea of absolute existence; it is this movement: with Plato the Idea is nothing else. The speculative makes its appearance here as speculative; whoever does not know the speculative, does not believe that in indicating simple Notions such as these, absolute essence is expressed. One, many, like, unlike, more or less, are trivial, empty, dry moments; that there should be contained in them absolute essence, the riches and the organization of the natural, as of the spiritual world, does not seem possible to him who, accustomed to ordinary ideas, has not gone back from sensuous existence into thought. It does not seem to such a one that God is, in a speculative sense, expressed thereby—that what is most sublime can be put in those common words, what is deepest, in what is so well known, self-evident and open, and what is richest, in the poverty of these abstractions. It is at first in opposition to common reality that this idea of reality as the manifold of simple essence, has in itself its opposition and the subsistence of the same; this essential, simple Notion of reality is elevation into thought, but it is not flight from what is real, but the expression of the real itself in its essence. We here find the Reason which expresses its essence; and absolute reality is unity immediately in itself. Thus it is pre-eminently in relation to this reality that the difficulties of those who do not think speculatively have become so intense. What is its relation to common reality? What has taken place is just what happens with the Platonic Ideas, which approximate very closely to these numbers, or rather to pure Notions. That is to say, the first question is, “Numbers, where are they? Dispersed through space, dwelling in independence in the heaven of ideas? They are not things immediately in themselves, for a thing, a substance, is something quite other than a number: a body bears no similarity to it.” To this we may answer that the Pythagoreans did not signify anything like that which we understand by prototypes—as if ideas, as the laws and relations of things, were present in a creative consciousness as thoughts in the divine understanding, separated from things as are the thoughts of an artist from his work. Still less did they mean only subjective thoughts in our consciousness, for we use the absolute antithesis as the explanation of