The contrast between the two approaches alluded to in the title has gained a certain prominence in our own day. With the knowledge of hindsight it will be of interest therefore to study its incidence in an earlier period, in the writings of Whewell and Mill, Which may thus yield added significance for a later generation. Right at the start there is a difficulty. Not all inductivists agree on their principles, or their interpretation of the logic of scientific reasoning, and (...) the same is true of deductivism, and the differences can therefore be discussed only in connection with individual writers. When this is done, we do find moreover some considerable variations in the treatment of their respective doctrines by the members of each of our two schools. To define these differences, we need a finer structure of elements of classification, indicative of criteria for the acceptance of scientific hypotheses. (shrink)