The paper traces the origins and early development of Janina Hosiasson-Lindenbaum’s logic of rational degrees of belief. I discuss the key points of the publications that resulted from Hosiasson-Lindenbaum’s 1926 doctoral dissertation, together with the new material she developed between 1926 and 1934. I argue that while the understanding of inductive reasoning as forming beliefs of various strengths—and hence the concept of degree of belief, or credence—was present in Hosiasson-Lindenbaum’s work from its beginning, the idea that the logic of these degrees of belief is the same as the logic of probability was likely introduced later on.