inductive inference is also built into Bayes’ theorem itself
As you say, Bayes’ theroem isn’t useful if you start from a “flat” prior; all posterior probabilities come out the same as prior probabilities, at least if A is in the future and B in the past. But nothing in Bayes’ theorem itself says that it has to be useful.
As you say, Bayes’ theroem isn’t useful if you start from a “flat” prior; all posterior probabilities come out the same as prior probabilities, at least if A is in the future and B in the past. But nothing in Bayes’ theorem itself says that it has to be useful.