  In rejecting Bayesianism and the method of inverse probabilities, Peirce argued that in fact no probability at all can be assigned to inductive arguments. Instead of probability, a different measure of imperfection of certitude must be assigned to inductive arguments: verisimilitude or likelihood. In explaining this notion Peirce offered an account of hypothesis-testing that is equivalent to standard statistical hypothesis-testing. In effect we get an account of confidence intervals and choices of statistical significance for rejecting null hypotheses. Such ideas became standard only in the twentieth century as a result of the work of R. A. Fisher, Jerzy Neyman, and others. But already by 1878, in his paper “The Probabilitiy of Induction,” Peirce had worked out the whole matter. (This topic has been discussed expertly by Deborah Mayo, who also has shown that the error-correction implicit in statistical hypothesis-testing is intimately affiliated with Peirce’s notion of science as self-correcting and convergent to “the truth.”)