Since there can be, and in some cases is, an intermediate between contraries, intermediates must be composed of contraries; for all intermediates are in the same genus as the things between which they are intermediate.
By intermediates we mean those things into which that which changes must first change. E.g., if we change from the highest string to the lowest by the smallest gradations we shall first come to the intermediate notes; and in the case of colors if we change from white to black we shall come to red and grey before we come to black; and similarly in other cases.
But change from one genus into another is impossible except accidentally; e.g., from color to shape. Therefore intermediates must be in the same genus as one another and as the things between which they are intermediate.
But all intermediates are between certain opposites, for it is only from these per se that change is possible.
Hence there can be no intermediate between things which are not opposites; for then there would be change also between things which are not opposites. Of things which are opposites, contradiction has no intermediate term (for contradiction means this: an antithesis one term of which must apply to any given thing, and which contains no intermediate term); of the remaining types of opposites some are relative, others privative, and others contrary.
Those relative opposites which are not contrary have no intermediate. The reason for this is that they are not in the same genus— for what is intermediate between knowledge and the knowable?—but between great and small there is an intermediate. Now since intermediates are in the same genus, as has been shown, and are between contraries, they must be composed of those contraries. For the contraries must either belong to a genus or not. And if there is a genus in such a way
that it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be contraries in a prior sense.
E.g., if white and black are contraries, and the one is a penetrative Footnote 1This is Plato’s definition. Cf. Plat. Tim. 67d, e. and the other a compressive color, these differentiae, penetrative
and compressive,
are prior, and so are opposed to each other in a prior sense.
But it is the species which have contrary differentiae that are more truly contraries; the other, i.e. intermediate, species will consist of genus and differentiae. E.g., all colors which are intermediate between white and black should be described by their genus (i.e. color) and by certain differentiae.
But these differentiae will not be the primary contraries; otherwise every thing will be either white or black. Therefore they will be different from the primary contraries. Therefore they will be intermediate between them, and the primary differentiae will be the penetrative
and the compressive.
Thus we must first investigate the contraries which are not contained in a genus, and discover of what their intermediates are composed.
For things which are in the same genus must either be composed of differentiae which are not compounded with the genus, or be incomposite. Contraries are not compounded with one another, and are therefore first principles; but intermediates are either all incomposite or none of them. Now from the contraries something is generated in such a way that change will reach it before reaching the contraries themselves (for there must be something which is less in degree than one contrary and greater than the other). Therefore this also will be intermediate between the contraries.
Hence all the other intermediates must be composite; for that which is greater in degree than one contrary and less than the other is in some sense a compound of the contraries of which it is said to be greater in degree than one and less than the other. And since there is nothing else homogeneous which is prior to the contraries, all intermediates must be composed of contraries.
Therefore all the lower terms, both contraries and intermediates, must be composed of the primary contraries. Thus it is clear that intermediates are all in the same genus, and are between contraries, and are all composed of contraries.