Coherently updating degrees of belief: Radical Probabilism, the generalization of Bayes’ Theorem and its consequences on evidence evaluation

The Bayesian perspective is based on conditioning related to reported evidence that is considered to be certain. What is called ‘Radical Probabilism’ replaces such an extreme view by introducing uncertainty on the reported evidence. How can such equivocal evidence be used in further infer- ences about a main hypothesis? The theoretical ground is introduced with the aim of offering to the readership an explanation for the generalization of the Bayes’ Theorem. This extension—that con- siders uncertainty related to the reporting of evidence—also has an impact on the assessment of the value of evidence through the Bayes’ factor. A generalization for such a logical measure of the evi- dence is also presented and justified.