Note 28 — Chapter I · SPECULATIVE PHILOSOPHY IN GREECE, BEFORE AND IN THE TIME OF SOKRATES.

An analogous application of this principle (Number as the fundamental substance and universal primary agent) may be seen in an eminent physical philosopher of the nineteenth century, Oken’s Elements of Physio-Philosophy, translated by Tulk. Aphorism 57:—“While numbers in a mathematical sense are positions and negations of nothing, in the philosophical sense they are positions and negations of the Eternal. Every thing which is real, posited, finite, has become this, out of numbers; or more strictly speaking, every Real is absolutely nothing else than a number. This must be the sense entertained of numbers in the Pythagorean doctrine — namely, that every thing, or the whole universe, had arisen from numbers. This is not to be taken in a merely quantitative sense, as it has hitherto been erroneously; but in an intrinsic sense, as implying that all things are numbers themselves, or the acts of the Eternal. The essence in numbers is nought else than the Eternal. The Eternal only is or exists, and nothing else is when a number exists. There is therefore nothing real but the Eternal itself; for every Real, or every thing that is, is only a number and only exists by virtue of a number.”

Ibid., Aphorism 105-107:—“Arithmetic is the science of the second idea, or that of time or motion, or life. It is therefore the first science. Mathematics not only begin with it, but creation also, with the becoming of time and of life. Arithmetic is, accordingly, the truly absolute or divine science; and therefore every thing in it is also directly certain, because every thing in it resembles the Divine. Theology is arithmetic personified.” — “A natural thing is nothing but a self-moving number. An organic or living thing is a number moving itself out of itself or spontaneously: an inorganic thing, however, is a number moved by another thing: now as this other thing is also a real number, so then is every inorganic thing a number moved by another number, and so on ad infinitum. The movements in nature are only movements of numbers by numbers: even as arithmetical computation is none other than a movement of numbers by numbers; but with this difference — that in the latter, this operates in an ideal manner, in the former after a real.”