Successfully predicting multiple sunrises doesn’t begin to address the problem.
Bayesian reasoning doesn’t solve the problem. It simply assumes a solution to the problem, and proceeds from there. A perfectly rational agent who denies the validity of induction would be totally unimpressed by Bayesian arguments.
Hume’s problem of induction is ancient. It is a basic issue in the philosophy of science:
“The problem puts in doubt all empirical claims made in everyday life or through the scientific method.”
http://en.wikipedia.org/wiki/Problem_of_induction
Successfully predicting multiple sunrises doesn’t begin to address the problem.
Bayesian reasoning doesn’t solve the problem. It simply assumes a solution to the problem, and proceeds from there. A perfectly rational agent who denies the validity of induction would be totally unimpressed by Bayesian arguments.