Page:The World and the Individual, Second Series (1901).djvu/118

intermediate systems of conceived, or, on occasion, of observed transformations, whereby one passes, in idea or in experience, from A to B. Now because of the general character of the relation between, as defined in the foregoing, all the intermediate transformations in any one system will be capable of being viewed as stages in a single definable process of passing from A to B. This process tends to acquire the unity of a single volitional act. And this process (if we abstract from certain complications that we need not here consider) may always be viewed as having one general direction, that leads from A to B, through the intermediary stages. But A and B will, as systems, resemble one another as well as differ. That depends upon the very nature of discrimination. And by virtue of the nature of the between relationship (just in so far as the intermediate process has one type and direction), all the intermediate stages will resemble each other in the very features in which A and B resemble each other. For all the stages between A and B are, by definition, facts that would not be viewed as different from either A or B, unless A and B were viewed as different each from the other. Hence all the intermediate stages must have in common the features that A and B have in common. These features then remain unvarying throughout the series of transformations in question. Denote these unvarying features (or, in the more technical way of stating the case), the “invariant characters of this system of transformations,” by the letter I. Then the whole process here in question, whether it is merely conceived, or is observed, will be definable as “a series