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Philosopher Marc Lange gives an overview (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].

My questions are:

Does B's last claim reflect the working Bayesian's position?

Can the skeptic S consistently defend her skeptical position still including the acceptance of Bayesian techniques by her construction of a prior distribution?

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    $\begingroup$ Your sk vs sc vote is a majority for sk, so I've edited to skeptic and skepticism throughout. $\endgroup$
    – Nick Cox
    Commented Oct 27, 2015 at 13:32
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    $\begingroup$ Generally, questions seeking to "collect opinions" are off topic here (see our help center). Given the large number of upvotes, this may be worthy of an exception. But in that case, it should be made CW. You may also prefer to rework this & post it instead on Philosophy (note that primarily opinion-based is an SE-wide policy so you would have to confront that somehow on either site). $\endgroup$
    – gung - Reinstate Monica
    Commented Oct 30, 2015 at 18:27
  • $\begingroup$ I took out the opinion-related parts - though I wonder, if the question will be answered without any debate. Moreover, I prefer to keep it on cross-validated and not on Philosophy, as I am really interested (see wording of the first question) in the working Bayesians' point of view. $\endgroup$
    – Statos
    Commented Nov 2, 2015 at 7:56
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    $\begingroup$ If I'm reading the question right, then the statistical part ("Does B's last claim reflect the working Bayesian's position?") is in no doubt - of course one can't set probabilities to NULL (effectively, "undefined") and then update them, since the updating formula refers to these prior probabilities. But the philosophical part ("Can the skeptic S consistently defend her skeptical position") seems better suited to Philosophy SE. $\endgroup$
    – Silverfish
    Commented Nov 2, 2015 at 9:45
  • $\begingroup$ Replicated this question on philosophy.stackexchange.com/questions/29289/… $\endgroup$
    – Statos
    Commented Nov 3, 2015 at 17:02

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