See for illustrations of the impossibility of carrying out a single principle in our actual judgments of particular cases, Mr. Bradley’s already quoted article in _Mind_ for July 1902. Footnote 70: For a fuller exposition of the conception of infinity here adopted I may refer the reader to the famous essay of Dedekind, _Was sind und was sollen die Zahlen_, especially pp. 17-20. The English reader will find an account of Dedekind’s work, with an acute discussion of its metaphysical significance, in Royce, _The World and the Individual_, First Series, Supplementary Essay. It does not seem necessary for the purpose of this chapter to specify the points in which I find myself unable to follow Professor Royce in his use of the theory. See _infra_, chap. 4, § 10. Footnote 71: It would not be hard to show that in the end all systematic structure is teleological. For all such structure in the last resort is a form of order, and depends on the possibility of saying “here this is first, that is second.” And wherever we predicate order we are asserting the embodiment in detail of some dominant purpose. Footnote 72: In fact, it is clear that if we speak of “idea” or “volition” in connection with the absolute individual, we cannot mean _actual_ “ideas” or _actual_ “volitions.” We must be using the psychological terms improperly in something of the same sense in which we speak of a man’s “guiding ideas” or “settled will” to denote what clearly, whatever it may be, is _not_ actual ideational or volitional process. See further, Bk. IV. chap. 6, § 1. ----- CHAPTER IV THE WORLD OF THINGS—(1) SUBSTANCE, QUALITY, AND RELATION