The Humean skeptic seeks not that the future necessarily resembles the past, but only that it is more valid to say that something is always true than it is to say it is true before a certain time. Does Bayesianism provide the argument that Hume missed, thereby justifying inductive reasoning? No. The Bayesian argument sets out to justify the connections between our beliefs based on subjective probability. Although Bayesian conditionalization helps us justify the relative certainty of our beliefs, the Bayesian cannot show that P (h100) is more justified than P(ht), but only that the differential outcome is affected by the arbitrary value of the priors. Bayesian models cannot justify probabilistic inductive hypotheses because Humean counter-examples equally support the opposite each inductive hypothesis. For non-probabilistic hypotheses, the Bayesian model is just an elimination tool. In conclusion, the Humean has not been pacified.
Anderson, David James
"Deep Problems for Bayesianism,"
Episteme: Vol. 12, Article 6.
Available at: https://digitalcommons.denison.edu/episteme/vol12/iss1/6