Section 3

One and Many are opposed in several ways. Unity and Plurality are opposed as being indivisible and divisible; for that which is divided or divisible is called a plurality, and that which is indivisible or undivided is called one. Then since opposition is of four kinds, and one of the present pairs of opposites is used in a privative sense, they must be contraries, and neither contradictories nor relative terms.

Unity is described and explained by its contrary—the indivisible by the divisible—because plurality, i.e. the divisible, is more easily perceptible than the indivisible; and so in formula plurality is prior to the indivisible, on account of our powers of perception.

To Unity belong (as we showed by tabulation in our distinction of the contraries 1 ) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality.

Identity 2 has several meanings. (a) Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one both in formula and in number, e.g., you are one with yourself both in form and in matter; and again (c) if the formula of the primary substance is one, e.g., equal straight lines are the same, and equal quadrilaterals with equal angles, and there are many more examples; but in these equality means unity.

Things are similar 3 (a) if, while not being the same absolutely or indistinguishable in respect of their concrete substance, they are identical in form; e.g the larger square is similar to the smaller, and unequal straight lines are similar. These are similar, but not absolutely the same. (b) If, having the same form, and being capable of difference in degree, they have no difference of degree.

(c) If things have an attribute which is the same and one in form—e.g. white—in different degrees, we say that they are similar because their form is one. (d) If the respects in which they are the same are more than those in which they differ, either in general or as regards their more prominent qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being yellow or flame-colored.

Thus it is obvious that Other 4 and Unlike also have several meanings. (a) In one sense other is used in the sense opposite to the same; thus everything in relation to every other thing is either the same or other. (b) In another sense things are other unless both their matter and their formula are one; thus you are other than your neighbor. (c) The third sense is that which is found in mathematics. 5 Therefore everything in relation to everything else is called either other or the same; that is, in the case of things of which unity and being are predicated;

for other is not the contradictory of the same, and so it is not predicated of non-existent things (they are called not the same), but it is predicated of all things which exist; for whatever is by nature existent and one is either one or not one with something else.

Other and same, then, are opposed in this way; but difference 6 is distinct from otherness.

For that which is other than something need not be other in a particular respect, since everything which is existent is either other or the same. But that which is different from something is different in some particular respect, so that that in which they differ must be the same sort of thing; i.e. the same genus or species.

For everything which is different differs either in genus or in species—in genus, such things as have not common matter and cannot be generated into or out of each other, e.g. things which belong to different categories; and in species, such things as are of the same genus (genus meaning that which is predicated of both the different things alike in respect of their substance).

The contraries 7 are different, and contrariety is a kind of difference. That this is rightly premissed is made clear by induction; for the contraries are obviously all different, since they are not merely other, but some are other in genus, and others are in the same line of predication, and so are in the same genus and the same in genus. We have distinguished elsewhere 8 what sort of things are the same or other in genus.