Elements of Physiophilosophy

by Lorenz Oken

The Real and Ideal are one and the same, only under two kinds of form. The latter is the same under an indefinite, eternal, single form; but the Real is also the same, yet under the form of quantity, and, as will be shown, of multiplicity. An infinity resides in both; in the Real an endlessness of individual forms; in the Ideal but one endless form; in the latter case an eternity, in the former an infinity. The quantity and multiplicity of the whole of mathematics is contained in the same manner in the 0, that the quantity and multiplicity of the triangles are in the ideal or primary triangle. Mathematics is a system of nullities or nothings, and this admits of being easily proved.

37. Zero is indeed the universality of mathematics, this, however, is not real, but only ideal. Every number issues out of zero, like the multiplicity of the real triangles out of the primary triangle. This progression of numbers out of zero takes place through a process of becoming determinate and limited; just as the real triangles are only definitions of the absolute triangle. The process of becoming determined is identical with becoming a Finite; becoming real is called becoming finite. Mathematical singulars or numbers can, therefore, be nothing else than zero disintegrated, or rendered real by determination.

What zero is in infinite intensity, that are numbers in endless extensity. Zero is of two forms: under the ideal it is mere intensity; under the real mere extensity, or a series of numbers. The latter is only expanded intensity; the former, extensity concentrated on the point; both are, consequently, one and the same in toto. Numbers are identical with zero; they are zero in a state of extension, while zero is equivalent to numbers in a state of intensity. The sense in which numbers are said to come out of zero is, therefore, very clear; they have not issued forth from zero as if they had previously resided individually therein, but the zero has emerged out of itself, has itself become apparent, and then was it a finite zero, a number. So, also, does the idea of a circle become a real circle, not from the latter emerging from the former, but from this itself becoming manifest. The individual circle is a manifestation or phenomena of the spiritual circle.

38. All realization, therefore, is not the origin of a something that has not previously been; it is only a manifestation, a process of extension taking place in the idea.

Thus the Real does not arise out of the Ideal, but is the Ideal itself in a condition of definition and limitation, as are, e. g. the actual triangle or the actual circle. If, then, the Ideal and Real be one, everything is necessarily identical, and this identity dominates not merely between the Ideal and Real in a general sense, but between all individual members of the Real.

39. The identity of every Different, or of all things among themselves and with the highest unity, is the essence of things. The limitation or definition of the Ideal is their form. Limitation is the Impartient of form.

40. Limitation is originally only a quantitative relation, e. g. the size of the angle in a triangle; later on it becomes also a relation of direction or of position.

In both cases the limitation is only an ideal relation. Realization also takes place, therefore, only in an ideal manner; and the Real is therefore ideal, not simply as it regards its form, but also its essence. Every Plural resembles itself and the highest principle in essence; or, in other words, all Singulars are united through essence with the highest One. All diversity of the Plural resides merely in the form, limitation or manifestation. The one unchanging essence possesses one ideal form, which is that of pure unity, and the same essence has a limitation, a real form, which is that of subdivision. There is only one essence in all things, the 0, the highest identity; but there are infinitely numerous forms.

Numbers are naught else than different forms of the one unchangeable essence, namely, the 0.

If, then, all numbers are only zero in a state of extension, and are consequently identical with it, the question arises, what are the first finitings of zero, or as what does it appear when it is no longer merely ideal or indefinite; in short, what is the first form of the real zero, or of the essence in general?