In his analysis of inference into three types, deduction, induction, and abduction, ...

In his analysis of inference into three types, deduction, induction, and abduction, C. S. Peirce maintains that probability plays an essential role in the first two, but not in the third. For a deductive argument, probability tells us the frequency with which the conclusion will hold given the premises; for an inductive argument, probability tells us the frequency with which the argument will hold true. However, probability has no role to play in abduction because there is, in Peirce's view, no common ground between the conclusion and the premises on which to base a calculation of frequencies. Nevertheless, there is something in the argument that makes the conclusion plausible to our mind. I will argue that this something is a probability which is, in many cases, quantifiable. This probability is the significance level of the statistical logic developed by R. A. Fisher in the 1920's.