I would like to collect opinions from the working Bayesians and the theoretical Bayesians on inductive skepticism. Philosopher Marc Lange gives an overview ([pdf](http://stephanhartmann.org/HHL10_Lange.pdf)) of the debate on Hume's Problem of induction. Chapter 9 (starting on p. 80) is called "Bayesian approaches". I understand it as: the justification for induction might be updating believes from a Bayesian point of view. Lange continues with a fictional dialogue between a Bayesian (B) and an inductive skeptic (S). I summarize: > B: if you admit Bayesian approaches are valid, what kind of prior do > you suggest, which fundamentally makes updating believes a > non-justification of induction. > > S: any distribution with "no degree of confidence to which we are > entitled regarding predictions regarding unexamined cases" (Lange), > where "no degree of confidence" does not mean the value zero but no > value at all [e.g. a NULL in the R language]. > > B: this prior violates probability axioms - it is not a distribution > [and not implementable in R either]. What are your opinions on the last claim in the given context? Can the skeptic S consistently defend her skeptical position still including the acceptance of Bayesian techniques by her construction of a prior distribution? Alternatively: any opinions about me misinterpreting Lange's paper?