Re: Bayesianism and induction.

Bayesianism is a formalisation of induction. The philosophical problems with the foundations of inductive reasoning are equally problems with the foundations of Bayesianism. These problems are essentially unchanged since Hume's era:

Rather than unproductive radical skepticism about everything, Hume said that he was actually advocating a practical skepticism based on common sense, wherein the inevitability of induction is accepted. Someone who insists on reason for certainty might, for instance, starve to death, as they would not infer the benefits of food based on previous observations of nutrition. - http://en.wikipedia.org/wiki/Problem_of_induction