THE PRINCIPLE OF MEDIATE COMPARISON.

When we discriminate an element, we may contrast it with the case of its own absence, of its simply not being there, without reference to what is there; or we may also take the latter into account. Let the first sort of discrimination be called existential, the latter differential discrimination. A peculiarity of differential discriminations is that they result in a perception of differences which are felt as greater or less one than the other. Entire groups of differences may be ranged in series: the musical scale, the color scale, are examples. Every department of our experience may have its data written down in an evenly gradated order, from a lowest to a highest member. And any one datum may be a term in several such orders. A given note may have a high place in the pitch-series, a low place in the loudness-series, and a medium place in the series of agreeablenesses. A given tint must, in order to be fully determined, have its place assigned in the series of qualities, in the series of purities (freedom from white), and in the series of intensities or brightnesses. It may be low in one of these respects, but high in another. In passing from term to term in any such series we are conscious not only of each step of difference being equal to (or greater or less than) the last, but we are conscious of proceeding in a uniform direction, different from other possible directions. This consciousness of serial increase of differences is one of the fundamental facts of our intellectual life. More, more, more, of the same kind of difference, we say, as we advance from term to term, and realize that the farther on we get the larger grows the breach between the term we are at and the one from which we started. Between any two terms of such a series the difference is greater than that between any intermediate terms, or than that between an intermediate term and either of the extremes. The louder than the loud is louder than the less loud; the farther than the far is farther than the less far; the earlier than the early is earlier than the late; the higher than the high is higher than the low; the bigger than the big is bigger than the small; or, to put it briefly and universally, the more than the more is more than the less; such is the great synthetic principle of mediate comparison which is involved in the possession by the human mind of the sense of serial increase. In Chapter XXVIII we shall see the altogether overwhelming importance of this principle in the conduct of all our higher rational operations.