1 In 1954 Karl Popper published an article attempting to show that the identification of the quantitative concept degree of confirmation with the quantitative concept degree of probability is a serious error. The error was presumably committed by J. M. Keynes, H. Reichen bach and R. Carnap. 2 It was Popper's intention then, to expose the error and to introduce an explicatum for the prescientific concept of degree of confirmation. A few months later Y. Bar-Hillel published an article attempting to show that no serious error had been committed (particularly by Carnap) and that the problem introduced by Popper was simply a verbal one. 3 Popper replied immediately that Dr. Bar-Hillel forces me [Popper] now to criticize Carnap's theory further, and he [Popper] introduced further objections which, if accepted, destroy Carnap's theory. 4 About eight years after this exchange took place I was in graduate school at the University of Chicago in search of a topic for a doctoral dissertation. An investigation of the issues involved in this exchange seemed to be ideal for me because I had (and still have) a great ad miration for the work of both Carnap and Popper. A thoroughly revised and I hope improved account of that investigation appears in the first five chapters of this book. Put very briefly, what I found were four main points of contention.