(_α_) They said, according to Aristotle (Metaph. I. 5): “The elements of number are the even and the odd; the latter is the finite” (or principle of limitation) “and the former is the infinite; thus the unity proceeds from both and out of this again comes number.” The elements of immediate number are not yet themselves numbers: the opposition of these elements first appears in arithmetical form rather than as thought. But the one is as yet no number, because as yet it is not quantity; unity and quantity belong to number. Theon of Smyrna[42] says: “Aristotle gives, in his writings on the Pythagoreans, the reason why, in their view, the one partakes of the nature of even and odd; that is, one, posited as even, makes odd; as odd, it makes even. This is what it could not do unless it partook of both natures, for which reason they also called the one, even-odd” (_ἀρτιοπέριττον_). (_β_) If we follow the absolute Idea in this first mode, the opposition will also be called the undetermined duality (_ἀόριστος δυάς_). Sextus speaks more definitely (adv. Math. X. 261, 262) as follows: “Unity, thought of in its identity with itself (_κατ̓ αὐτότητα ἑαυτῆς_), is unity; if this adds itself to itself as something different (_καθ̓ ἑτερότητα_), undetermined duality results, because no one of the determined or otherwise limited numbers is this duality, but all are known through their participation in it, as has been said of unity. There are, according to this, two principles in things; the first unity, through participation in which all number-units are units, and also undetermined duality through participation in which all determined dualities are dualities.” Duality is just as essential a moment in the Notion as is unity. Comparing them with one another, we may either consider the unity to be form and duality matter, or the other way; and both appear in different modes. (_αα_) Unity, as the being-like-self, is the formless; but in duality, as the unlike, there comes division or form. (_ββ_) If, on the other hand, we take form as the simple activity of absolute form, the one is what determines; and duality as the potentiality of multiplicity, or as multiplicity not posited, is matter. Aristotle (Met. I. 6) says that it is characteristic of Plato that “he makes out of matter many, but with him the form originates only once; whereas out of one matter only one table proceeds, whoever brings form to matter, in spite of its unity, makes many tables.” He also ascribes this to Plato, that “instead of showing the undetermined to be simple (_ἀντὶ τοῦ ἀπείρου ὡς ἑνός_), he made of it a duality—the great and small.”