[roenxi]

That seems a bit long winded since this situation is a direct result of Bayes' theorem. It seems to me equivalent to say:

Bayes' Theorem holds because it can be proven. Therefore, situations can be constructed where considering identical data without considering priors gives nonsense conclusions. For example if we happen to know as a prior that P(outcome of experiment is a certain ratio) = P(experiment is completed) then that must be considered when interpreting the results.