Aristotle, Metaphysics

[1087b] [1] Therefore all contraries are predicated of a subject, and none of them exists separately. But there is no contrary to substance; not only is this apparent, but it is borne out by reasoned consideration.¹ Thus none of the contraries is strictly a first principle; the first principle is something different.

But the Platonists treat one of the contraries as matter, some opposing "the unequal" to Unity (on the ground that the former is of the nature of plurality) and others plurality.For according to some,² numbers are generated from the unequal dyad of the Great and Small; and according to another,³ from plurality; but in both cases they are generated by the essence of unity. For he who speaks of "the unequal" and Unity as elements, and describes the unequal as a dyad composed of Great and Small, speaks of the unequal, i.e. the Great and Small, as being one; and does not draw the distinction that they are one in formula but not in number.⁴

Again, they state the first principles, which they call elements, badly; some say that the Great and the Small, together with Unity (making 3⁵ in all), are the elements of numbers; the two former as matter, and Unity as form. Others speak of the Many and Few, because the Great and the Small are in their nature more suited to be the principles of magnitude; and others use the more general term which covers these—"the exceeding" and "the exceeded."But none of these variations makes any appreciable difference with respect to some of the consequences of the theory; [20] they only affect the abstract difficulties, which these thinkers escape because the proofs which they themselves employ are abstract.There is, however, this exception: if "the exceeding" and "the exceeded" are the first principles, and not the Great and the Small, on the same principle number should be derived from the elements before 2 is derived; for as "the exceeding and the exceeded" is more universal than the Great and Small, so number is more universal than 2. But in point of fact they assert the one and not the other.

Others oppose "the different" or "other" to Unity; and others contrast Plurality and Unity.Now if, as they maintain, existing things are derived from contraries, and if there is either no contrary to unity, or if there is to be any contrary it is plurality; and if the unequal is contrary to the equal, and the different to the same, and the other to the thing itself then those who oppose unity to plurality have the best claim to credibility—but even their theory is inadequate, because then unity will be few. For plurality is opposed to paucity, and many to few.

That "unity" denotes a measure⁶ is obvious. And in every case there is something else which underlies it; e.g., in the scale there is the quarter-tone; in spatial magnitude the inch or foot or some similar thing; and in rhythms the foot or syllable. Similarly in the case of gravity there is some definite weight. Unity is predicated of all things in the same way;