d. The Four (_τετράς_) is the triad but more developed, and hence with the Pythagoreans it held a high position. That the tetrad should be considered to be thus complete, reminds one of the four elements, the physical and the chemical, the four continents, &c. In nature four is found to be present everywhere, and hence this number is even now equally esteemed in natural philosophy. As the square of two, the fourfold is the perfection of the two-fold in as far as it—only having itself as determination, i.e. being multiplied with itself—returns into identity with itself. But in the triad the tetrad is in so far contained, as that the former is the unity, the other-being, and the union of both these moments, and thus, since the difference, as posited, is a double, if we count it, four moments result. To make this clearer, the tetrad is comprehended as the _τετρακτύς_, the efficient, active four (from _τέτταρα_ and _ἄγω_); and afterwards this is by the Pythagoreans made the most notable number. In the fragments of a poem of Empedocles, who originally was a Pythagorean, it is shown in what high regard this tetraktus, as represented by Pythagoras, was held: “If thou dost this, It will lead thee in the path of holy piety. I swear it By the one who to our spirit has given the Tetraktus, Which has in it eternal nature’s source and root.”[43] e. From this the Pythagoreans proceed to the ten, another form of this tetrad. As the four is the perfect form of three, this fourfold, thus perfected and developed so that all its moments shall be accepted as real differences, is the number ten (_δεκάς_), the real tetrad. Sextus (adv. Math. IV. 3; VII. 94, 95) says: “Tetraktus means the number which, comprising within itself the four first numbers, forms the most perfect number, that is the number ten; for one and two and three and four make ten. When we come to ten, we again consider it as a unity and begin once more from the beginning. The tetraktus, it is said, has the source and root of eternal nature within itself, because it is the Logos of the universe, of the spiritual and of the corporeal.” It is an important work of thought to show the moments not merely to be four units, but complete numbers; but the reality in which the determinations are laid hold of, is here, however, only the external and superficial one of number; there is no Notion present although the tetraktus does not mean number so much as idea. One of the later philosophers, Proclus, (in Timæum, p. 269) says, in a Pythagorean hymn:— “The divine number goes on,”... “Till from the still unprofaned sanctuary of the Monad It reaches to the holy Tetrad, which creates the mother of all that is; Which received all within itself, or formed the ancient bounds of all, Incapable of turning or of wearying; men call it the holy Dekad.”