We may paraphrase Charles Péguy by noting that the philosophical classics are new every morning and nothing is as old as today’s latest philosophical fad. Even fads are not without their value, however, if some new approach or method is introduced and shown to be really contributory to “progress in clarification” in either historical understanding or in the pursuit of new knowledge. In any case, the great enduring philosophical views present a continual challenge to be updated in the light of new knowledge. We know much more now about individuals, classes, relations, predication, identity, and the like, than was known in the days of Peirce and Bradley. It may be helpful to examine the views of these writers on these topics, especially as concerns continuous relations, in the light of what we now know. The result will be not only an updating but to some extent a defense and rational reconstruction of some views which have long been in disrepute among writers who pride themselves upon logical clarity.