In the next to last chapter Mayo tries her hand at one of American philosophy's perennial amusements, the game of Peirce Knew It All Along. (If, as Whitehead said, European thought is a series of footnotes to Plato, American thought is a series of footnotes to Peirce --- and Jonathan Edwards, worse luck.) Usually this is a mere demonstration of cleverness, like coining words from the names of opponents, or improving on the proof that if 1+1=3, then Bertrand Russell was the Pope. But in this case it seems that Mayo is really on to something. It is sometimes forgotten that Peirce was by training an experimental scientist, was employed as an experimental physicist for years, and as such lived and breathed error analysis. His opposition to subjective probabilities and paint-by-numbers inductivism is plain. For him "induction" meant the experimental testing of hypotheses; the probabilities employed in induction are the probabilities of inductive procedures leading to correct answers:Well, Shalizi seems a bit jaded at the amount of crediting of Peirce, but his "Peirce Knew It All Along" remark is too delicious to pass up. As to Shalizi, he's an assistant professor in the statistics department at Carnegie Mellon University in Pittsburgh, Pennsylvania, and his original training was in the statistical physics of complex systems.The theory here proposed does not assign any probability to the inductive or hypothetic conclusion, in the sense of undertaking to say how frequently that conclusion would be found true. It does not propose to look through all the possible universes, and say in what proportion of them a certain uniformity occurs; such a proceeding, were it possible, would be quite idle. The theory here presented only says how frequently, in this universe, the special form of induction or hypothesis would lead us right. The probability given by this theory is in every way different --- in meaning, numerical value, and form --- from that of those who would apply to ampliative inference the doctrine of inverse chances [i.e., Bayes's theorem]. [2.748, quoted p. 414]
Note: I redid Shalizi's broken link on coinages to go to the Internet Archive version of that to which he linked. The recentest version is the 2008 edition at an unrelated URL http://www.philosophicallexicon.com/ .
(Now let's see whether for once I've done a post that I don't need to revise afterward! Update: No such luck. I had omitted the year of Shalizi's 1998 review.)