The aims of this chapter are two-fold: first and primarily, to identify and to summarize the development of an important but hitherto unnoticed tradition in 19th-century methodological thought, and secondly, to suggest that certain aspects of the history of this tradition give us a new perspective from which to assess certain strains in contemporary philosophy of science. In Part I below, I attempt to define this tradition, to document its existence, and to note some features of its evolution. In Part II, I briefly indicate the manner in which this history may shed new light on some recent trends in inductive logic.