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Abstract:
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Bayesian probability was called "inverse" probability in the 19th century. That would be the inverse, metaphorically, of-shall we call it-Frequentian probability. In the same metaphorical sense that Bayesian is the inverse of Frequentian, Frequentian is the inverse of Bayesian. Thus, some Bayesian criticisms of Frequentian are invertible. And we can extend the metaphor by pointing out the obvious: the inverse of the inverse is the identity. As I. J. Good has predicted, whereas the 20th century was Frequentian, the 21st century will be Bayesian or, as Good has proposed, an era of Bayes/Non-Bayes compromise. If, in the future, Bayesian were to dominate Frequentian, that would constitute another, rather philosophical, type of inversion, a turning of the tables, and we will have come full circle, the inverse of the inverse. That's not where we ought to go.
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