  Although Carnap's own vision for confirmation theory was ultimately  abandoned,[21]  the quantitative approach that he championed proved influential to the subsequent development of the subject. In particular, the emphasis on attempting to understand confirmation in quantitative terms paved the way for the increased use of mathematics—and specifically, the probability calculus—in the philosophical study of evidence. The idea that the probability calculus provides the key to understanding the relation of confirmation is central to Bayesianism, the dominant view within contemporary confirmation theory. An examination of Bayesianism will not be undertaken  here.[22]  Instead, we will simply take note of the explication of the concept of evidence which the Bayesian offers. At the outset of the present section, we noted that evidence confirms a theory just in case that evidence makes the theory more likely to be true; evidence disconfirms a theory just in case the evidence renders the theory less likely to be true. The Bayesian takes these platitudes at face value and offers the following probabilistic explication of what it is for E to be evidence for H: 